Download Anna University (AU) MBA ( Master of Business Administration) Important Question Bank 2nd Sem 1915201 Applied Operations Research (Latest Important Questions Unit Wise)
(An
?
DEPARTMENT OF MANAGEMENT STUDIES
QUESTION BANK
II SEMESTER
1915201? APPLIED OPERATIONS RESEACH
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Dr. Radha Ganesh Kumar ? Asst. Professor (Sel.G) and HOD
Mr.B. Sam Paul ? Asst. Professor (OG)
FirstRanker.com - FirstRanker's Choice
(An
?
DEPARTMENT OF MANAGEMENT STUDIES
QUESTION BANK
II SEMESTER
1915201? APPLIED OPERATIONS RESEACH
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Dr. Radha Ganesh Kumar ? Asst. Professor (Sel.G) and HOD
Mr.B. Sam Paul ? Asst. Professor (OG)
(An
? .
DEPARTMENT OFMANAGEMENT STUDIES
QUESTION BANK
SUBJECT :1915201 ?APPLIED OPERATIONS RESEACH
SEM / YEAR : IISemester / IYear
UNIT ? I ?INTRODUCTION TO LINEAR PROGRAMMING (LP)
SYLLABUS: Introduction to applications of operations research in functional areas of management.
Linear Programming-formulation, solution by graphical and simplex methods, Special cases. Dual
simplex method. Principles of Duality. Sensitivity Analysis.
PART- A
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Define Operations Research (OR). Level 1 Remembering
2. Differentiate between Simplex and Big M Method Level 2 Understanding
3. How do you show your understanding unbounded solution? Level 3 Applying
4. Categorize the forms of LPP. Level 4 Analysing
5.
Discuss why is two phase method is better than Big M
method?
Level 5 Evaluating
6. Interpret the usage of Sensitivity Analysis in LPP. Level 6 Creating
7. What are the assumptions and requirements of LPP? Level 1 Remembering
8. Compare Dual Simplex and Duality. Level 2 Understanding
9. Identify the Advantages of duality. Level 3 Applying
10. What do you think about Infeasible solution? Level 4 Analysing
11. How will you solve LPP graphically? Level 5 Evaluating
12.
Conclude your understanding on the mathematical
formulation of LPP.
Level 6 Creating
13. Define basic variables and artificial variables. Level 1 Remembering
14. Compare Slack variable & Surplus Variable. Level 2 Understanding
15.
Give some example for the role of Surplus variable & Slack
Variable in the simplex method
Level 3 Applying
16. How would you apply Artificial variable? Level 4 Analysing
17. What is Big M Method? Level 1 Remembering
18. Distinguish simplex and Big M method Level 2 Understanding
19.
What do you mean by Duality? List the Rules for primal and
dual.
Level 1 Remembering
20. What is Shadow price? Level 1 Remembering
FirstRanker.com - FirstRanker's Choice
(An
?
DEPARTMENT OF MANAGEMENT STUDIES
QUESTION BANK
II SEMESTER
1915201? APPLIED OPERATIONS RESEACH
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Dr. Radha Ganesh Kumar ? Asst. Professor (Sel.G) and HOD
Mr.B. Sam Paul ? Asst. Professor (OG)
(An
? .
DEPARTMENT OFMANAGEMENT STUDIES
QUESTION BANK
SUBJECT :1915201 ?APPLIED OPERATIONS RESEACH
SEM / YEAR : IISemester / IYear
UNIT ? I ?INTRODUCTION TO LINEAR PROGRAMMING (LP)
SYLLABUS: Introduction to applications of operations research in functional areas of management.
Linear Programming-formulation, solution by graphical and simplex methods, Special cases. Dual
simplex method. Principles of Duality. Sensitivity Analysis.
PART- A
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Define Operations Research (OR). Level 1 Remembering
2. Differentiate between Simplex and Big M Method Level 2 Understanding
3. How do you show your understanding unbounded solution? Level 3 Applying
4. Categorize the forms of LPP. Level 4 Analysing
5.
Discuss why is two phase method is better than Big M
method?
Level 5 Evaluating
6. Interpret the usage of Sensitivity Analysis in LPP. Level 6 Creating
7. What are the assumptions and requirements of LPP? Level 1 Remembering
8. Compare Dual Simplex and Duality. Level 2 Understanding
9. Identify the Advantages of duality. Level 3 Applying
10. What do you think about Infeasible solution? Level 4 Analysing
11. How will you solve LPP graphically? Level 5 Evaluating
12.
Conclude your understanding on the mathematical
formulation of LPP.
Level 6 Creating
13. Define basic variables and artificial variables. Level 1 Remembering
14. Compare Slack variable & Surplus Variable. Level 2 Understanding
15.
Give some example for the role of Surplus variable & Slack
Variable in the simplex method
Level 3 Applying
16. How would you apply Artificial variable? Level 4 Analysing
17. What is Big M Method? Level 1 Remembering
18. Distinguish simplex and Big M method Level 2 Understanding
19.
What do you mean by Duality? List the Rules for primal and
dual.
Level 1 Remembering
20. What is Shadow price? Level 1 Remembering
PART- B
S.NO
QUESTIONS
BT
LEVEL
COMPETENCE
1.
(i)
Maximise Z=3x+4y subject to
2x+5y ?60,
4x+2y ?40.
x, y >0. Solve by Graphical Method
Plot the graph
(8)
Level 1 Remembering
(ii) Which one is the best solution? (5)
2.
(i)
Min Z= 20x
1
+10 x
2
subject to
x
1
+2x
2
? 40,
3x
1
+x
2
? 30,
4x
1
+3x
2
? 60,
x
1
,x
2
? 0.
Solve by Graphical Method,
Plot the graph
(8)
Level 2 Understanding
(ii) Predict the value of x & y. (5)
3 Max Z= 5x1+4x2 subject to
x
1
-2x
2
? 1,
x
1
+2x
2
?3,
x
1
,x
2
? 0. Solve Graphically. Which one is the best
solution?
Level 3 Applying
4.
(i)
A Plant Manufacturer 2 Product A & B. The Profit Contribution
of each product has been estimated as Rs.300 for product A
and Rs.400 for Product B. Each Product passes through 3
departments of the plant. The time required for each product
and total time available in each department is as follows.
Department Hours
Required
Hours
Required
Available
Hours
during
month
Product
A
Product
B
I 2 3 1600
II 3 2 1500
III 1 1 700
The company has a contract to supply atleast 300 units of
Product B per month.
Formulate the LPP
(5)
Level 4
Analysing
(ii) Solve through Graphical Method
(8)
5. Solve the following LPP by graphical method.
Maximize Z= 3x
1
+2x
2
Subject t o
- 2x
1
+x
2
?1,
x
1
? 2,
x
1
+ x
2
? 3
and x
1
,x
2
? 0
Level 5 Evaluating
FirstRanker.com - FirstRanker's Choice
(An
?
DEPARTMENT OF MANAGEMENT STUDIES
QUESTION BANK
II SEMESTER
1915201? APPLIED OPERATIONS RESEACH
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Dr. Radha Ganesh Kumar ? Asst. Professor (Sel.G) and HOD
Mr.B. Sam Paul ? Asst. Professor (OG)
(An
? .
DEPARTMENT OFMANAGEMENT STUDIES
QUESTION BANK
SUBJECT :1915201 ?APPLIED OPERATIONS RESEACH
SEM / YEAR : IISemester / IYear
UNIT ? I ?INTRODUCTION TO LINEAR PROGRAMMING (LP)
SYLLABUS: Introduction to applications of operations research in functional areas of management.
Linear Programming-formulation, solution by graphical and simplex methods, Special cases. Dual
simplex method. Principles of Duality. Sensitivity Analysis.
PART- A
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Define Operations Research (OR). Level 1 Remembering
2. Differentiate between Simplex and Big M Method Level 2 Understanding
3. How do you show your understanding unbounded solution? Level 3 Applying
4. Categorize the forms of LPP. Level 4 Analysing
5.
Discuss why is two phase method is better than Big M
method?
Level 5 Evaluating
6. Interpret the usage of Sensitivity Analysis in LPP. Level 6 Creating
7. What are the assumptions and requirements of LPP? Level 1 Remembering
8. Compare Dual Simplex and Duality. Level 2 Understanding
9. Identify the Advantages of duality. Level 3 Applying
10. What do you think about Infeasible solution? Level 4 Analysing
11. How will you solve LPP graphically? Level 5 Evaluating
12.
Conclude your understanding on the mathematical
formulation of LPP.
Level 6 Creating
13. Define basic variables and artificial variables. Level 1 Remembering
14. Compare Slack variable & Surplus Variable. Level 2 Understanding
15.
Give some example for the role of Surplus variable & Slack
Variable in the simplex method
Level 3 Applying
16. How would you apply Artificial variable? Level 4 Analysing
17. What is Big M Method? Level 1 Remembering
18. Distinguish simplex and Big M method Level 2 Understanding
19.
What do you mean by Duality? List the Rules for primal and
dual.
Level 1 Remembering
20. What is Shadow price? Level 1 Remembering
PART- B
S.NO
QUESTIONS
BT
LEVEL
COMPETENCE
1.
(i)
Maximise Z=3x+4y subject to
2x+5y ?60,
4x+2y ?40.
x, y >0. Solve by Graphical Method
Plot the graph
(8)
Level 1 Remembering
(ii) Which one is the best solution? (5)
2.
(i)
Min Z= 20x
1
+10 x
2
subject to
x
1
+2x
2
? 40,
3x
1
+x
2
? 30,
4x
1
+3x
2
? 60,
x
1
,x
2
? 0.
Solve by Graphical Method,
Plot the graph
(8)
Level 2 Understanding
(ii) Predict the value of x & y. (5)
3 Max Z= 5x1+4x2 subject to
x
1
-2x
2
? 1,
x
1
+2x
2
?3,
x
1
,x
2
? 0. Solve Graphically. Which one is the best
solution?
Level 3 Applying
4.
(i)
A Plant Manufacturer 2 Product A & B. The Profit Contribution
of each product has been estimated as Rs.300 for product A
and Rs.400 for Product B. Each Product passes through 3
departments of the plant. The time required for each product
and total time available in each department is as follows.
Department Hours
Required
Hours
Required
Available
Hours
during
month
Product
A
Product
B
I 2 3 1600
II 3 2 1500
III 1 1 700
The company has a contract to supply atleast 300 units of
Product B per month.
Formulate the LPP
(5)
Level 4
Analysing
(ii) Solve through Graphical Method
(8)
5. Solve the following LPP by graphical method.
Maximize Z= 3x
1
+2x
2
Subject t o
- 2x
1
+x
2
?1,
x
1
? 2,
x
1
+ x
2
? 3
and x
1
,x
2
? 0
Level 5 Evaluating
6. (i) Max Z= 1000x
1
+4000x
2
+5000x
3
Subject to 3x1+3x
3
?22,
x1+2x2+3x
3
? 14,
3x1+2x2 ? 14
& x1,x2 ? 0
Develop a Simplex Table
(5)
Level 6 Creating
(ii) Analyse and find the value of x
1
, x
2
? (8)
7. Analyze the following LPP by Simplex Method:
Min Z = -10y
1
-15y
2
-20y
3
Subject to 2y
1
+4y
2
+6y
3
? 24,
3y
1
+9y
2
+6y
3
? 30,
& y
1
, y
2
, y
3
? 0.
Level 1 Remembering
(i)
Develop a Simplex Table (5)
(ii) Solve and find the value of y1 ,y2 and y3
(8)
8.
Solve By Graphical Method
Minimize Z= 40x
1
+24x
2
Subject to, 20x
1
+50 x
2
> 4,800
80 x
1
+50x
2
> 7,200
x
1
,x
2
>0
Level 2 Understanding
9. Solve the following LPP by simplex method:
Minimize Z= 8x
1
-2x
2
Subject to -4x
1
+2x
2
?1,
5x
1
-4x
2
?3,
and x
1
,x
2
? 0
Level 3 Applying
10. Solve the following LPP by simplex method:
Maximize Z= 3x1+2x
2
Subject to
2x
1
+x
2
?2,
3x
1
+4x
2
?12,
x
1
,x
2
? 0
Level 4 Analyzing
11. Review the LPP and solve by simplex method
Max Z= 25x+10y
Subject to the constraints
x+0.5y? 20
x+y? 50
x,y ? 0
Level 1 Remembering
12. A firm produces three products. These products are
processors on 3 different machines. The time required for
manufacturing one unit of cost of the products and the daily
capacity of the three machines is given in the table below.
Analyse and find the optimum solution.
Mac
hine
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Machine
Capacity
Min /Day
Product1 Product 2 Product 3
M1 2 8 2 940
M2 4 - 8 970
M3 2 5 - 430
It is required to determine the daily no. of units to be
manufactured for each product. The profit for unit for
Level 2 Understanding
FirstRanker.com - FirstRanker's Choice
(An
?
DEPARTMENT OF MANAGEMENT STUDIES
QUESTION BANK
II SEMESTER
1915201? APPLIED OPERATIONS RESEACH
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Dr. Radha Ganesh Kumar ? Asst. Professor (Sel.G) and HOD
Mr.B. Sam Paul ? Asst. Professor (OG)
(An
? .
DEPARTMENT OFMANAGEMENT STUDIES
QUESTION BANK
SUBJECT :1915201 ?APPLIED OPERATIONS RESEACH
SEM / YEAR : IISemester / IYear
UNIT ? I ?INTRODUCTION TO LINEAR PROGRAMMING (LP)
SYLLABUS: Introduction to applications of operations research in functional areas of management.
Linear Programming-formulation, solution by graphical and simplex methods, Special cases. Dual
simplex method. Principles of Duality. Sensitivity Analysis.
PART- A
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Define Operations Research (OR). Level 1 Remembering
2. Differentiate between Simplex and Big M Method Level 2 Understanding
3. How do you show your understanding unbounded solution? Level 3 Applying
4. Categorize the forms of LPP. Level 4 Analysing
5.
Discuss why is two phase method is better than Big M
method?
Level 5 Evaluating
6. Interpret the usage of Sensitivity Analysis in LPP. Level 6 Creating
7. What are the assumptions and requirements of LPP? Level 1 Remembering
8. Compare Dual Simplex and Duality. Level 2 Understanding
9. Identify the Advantages of duality. Level 3 Applying
10. What do you think about Infeasible solution? Level 4 Analysing
11. How will you solve LPP graphically? Level 5 Evaluating
12.
Conclude your understanding on the mathematical
formulation of LPP.
Level 6 Creating
13. Define basic variables and artificial variables. Level 1 Remembering
14. Compare Slack variable & Surplus Variable. Level 2 Understanding
15.
Give some example for the role of Surplus variable & Slack
Variable in the simplex method
Level 3 Applying
16. How would you apply Artificial variable? Level 4 Analysing
17. What is Big M Method? Level 1 Remembering
18. Distinguish simplex and Big M method Level 2 Understanding
19.
What do you mean by Duality? List the Rules for primal and
dual.
Level 1 Remembering
20. What is Shadow price? Level 1 Remembering
PART- B
S.NO
QUESTIONS
BT
LEVEL
COMPETENCE
1.
(i)
Maximise Z=3x+4y subject to
2x+5y ?60,
4x+2y ?40.
x, y >0. Solve by Graphical Method
Plot the graph
(8)
Level 1 Remembering
(ii) Which one is the best solution? (5)
2.
(i)
Min Z= 20x
1
+10 x
2
subject to
x
1
+2x
2
? 40,
3x
1
+x
2
? 30,
4x
1
+3x
2
? 60,
x
1
,x
2
? 0.
Solve by Graphical Method,
Plot the graph
(8)
Level 2 Understanding
(ii) Predict the value of x & y. (5)
3 Max Z= 5x1+4x2 subject to
x
1
-2x
2
? 1,
x
1
+2x
2
?3,
x
1
,x
2
? 0. Solve Graphically. Which one is the best
solution?
Level 3 Applying
4.
(i)
A Plant Manufacturer 2 Product A & B. The Profit Contribution
of each product has been estimated as Rs.300 for product A
and Rs.400 for Product B. Each Product passes through 3
departments of the plant. The time required for each product
and total time available in each department is as follows.
Department Hours
Required
Hours
Required
Available
Hours
during
month
Product
A
Product
B
I 2 3 1600
II 3 2 1500
III 1 1 700
The company has a contract to supply atleast 300 units of
Product B per month.
Formulate the LPP
(5)
Level 4
Analysing
(ii) Solve through Graphical Method
(8)
5. Solve the following LPP by graphical method.
Maximize Z= 3x
1
+2x
2
Subject t o
- 2x
1
+x
2
?1,
x
1
? 2,
x
1
+ x
2
? 3
and x
1
,x
2
? 0
Level 5 Evaluating
6. (i) Max Z= 1000x
1
+4000x
2
+5000x
3
Subject to 3x1+3x
3
?22,
x1+2x2+3x
3
? 14,
3x1+2x2 ? 14
& x1,x2 ? 0
Develop a Simplex Table
(5)
Level 6 Creating
(ii) Analyse and find the value of x
1
, x
2
? (8)
7. Analyze the following LPP by Simplex Method:
Min Z = -10y
1
-15y
2
-20y
3
Subject to 2y
1
+4y
2
+6y
3
? 24,
3y
1
+9y
2
+6y
3
? 30,
& y
1
, y
2
, y
3
? 0.
Level 1 Remembering
(i)
Develop a Simplex Table (5)
(ii) Solve and find the value of y1 ,y2 and y3
(8)
8.
Solve By Graphical Method
Minimize Z= 40x
1
+24x
2
Subject to, 20x
1
+50 x
2
> 4,800
80 x
1
+50x
2
> 7,200
x
1
,x
2
>0
Level 2 Understanding
9. Solve the following LPP by simplex method:
Minimize Z= 8x
1
-2x
2
Subject to -4x
1
+2x
2
?1,
5x
1
-4x
2
?3,
and x
1
,x
2
? 0
Level 3 Applying
10. Solve the following LPP by simplex method:
Maximize Z= 3x1+2x
2
Subject to
2x
1
+x
2
?2,
3x
1
+4x
2
?12,
x
1
,x
2
? 0
Level 4 Analyzing
11. Review the LPP and solve by simplex method
Max Z= 25x+10y
Subject to the constraints
x+0.5y? 20
x+y? 50
x,y ? 0
Level 1 Remembering
12. A firm produces three products. These products are
processors on 3 different machines. The time required for
manufacturing one unit of cost of the products and the daily
capacity of the three machines is given in the table below.
Analyse and find the optimum solution.
Mac
hine
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Machine
Capacity
Min /Day
Product1 Product 2 Product 3
M1 2 8 2 940
M2 4 - 8 970
M3 2 5 - 430
It is required to determine the daily no. of units to be
manufactured for each product. The profit for unit for
Level 2 Understanding
product 1,2,3 is Rs.4,Rs.8,Rs.6 respectively. It is assumed
that all the amount produced are consumed in the market
13. Using dual simplex method , solve and find the optimum
solution for the given LPP.
Maximize Z=6x
1
+4x
2
+4x
3
Subject to 3x
1
,x
2
+2x
3
? 2
2x
1
+x
2
-x
3
? 1
-x
1
+x
2
+2x
3
? 1 &
x
1
,x
2
,x
3
? 0
Level 4 Analysing
14.
(i)
Evaluate by using dual simplex method and solve the LPP.
Minimize Z=2x
1
+x
2
Subject to 3x
1
+2x
2
? 3
4x
1
+3x
2
? 6
x
1
+x
2
? 5 & x
1
,x
2
?
Determine the dual simplex table
(5)
Level 1 Remembering
(ii)
Find the value of x
1
, x
2
(8)
PART - C
S.No Questions BT
LEVEL
COMPETENCE
1.
Max Z=300x+400y subject to
2x+3y ? 1600,
3x+2y ? 1500,
x+y ? 700,
y ? 300, x,y ? 0 Solve by Graphical Method, choose the
value of x & y which maximizes profit.
Level 1 Remembering
2. Solve the following LPP by graphical method.
Minimize Z= 6000x1+4000x
2
Subject t o
3x+x
2
? 40,
x
1
+2.5 x
2
? 22
3x
1
+3 x
2
? 40
and x
1
,x
2
? 0
Level 2 Understanding
3. Develop a Simplex Table and Solve
Max Z = 3 x1+2 x2,
Subject to
x1+ x2 ?4,
x1- x2 ? 2;
x1, x2 ?0.
Level 3 Applying
4. Solve by using Simplex Method.
Maximize Z= 3x+5y
Subject to the constraints
x+y? 60
x? 40
y ? 30
x,y ? 0
Level 1 Remembering
FirstRanker.com - FirstRanker's Choice
(An
?
DEPARTMENT OF MANAGEMENT STUDIES
QUESTION BANK
II SEMESTER
1915201? APPLIED OPERATIONS RESEACH
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Dr. Radha Ganesh Kumar ? Asst. Professor (Sel.G) and HOD
Mr.B. Sam Paul ? Asst. Professor (OG)
(An
? .
DEPARTMENT OFMANAGEMENT STUDIES
QUESTION BANK
SUBJECT :1915201 ?APPLIED OPERATIONS RESEACH
SEM / YEAR : IISemester / IYear
UNIT ? I ?INTRODUCTION TO LINEAR PROGRAMMING (LP)
SYLLABUS: Introduction to applications of operations research in functional areas of management.
Linear Programming-formulation, solution by graphical and simplex methods, Special cases. Dual
simplex method. Principles of Duality. Sensitivity Analysis.
PART- A
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Define Operations Research (OR). Level 1 Remembering
2. Differentiate between Simplex and Big M Method Level 2 Understanding
3. How do you show your understanding unbounded solution? Level 3 Applying
4. Categorize the forms of LPP. Level 4 Analysing
5.
Discuss why is two phase method is better than Big M
method?
Level 5 Evaluating
6. Interpret the usage of Sensitivity Analysis in LPP. Level 6 Creating
7. What are the assumptions and requirements of LPP? Level 1 Remembering
8. Compare Dual Simplex and Duality. Level 2 Understanding
9. Identify the Advantages of duality. Level 3 Applying
10. What do you think about Infeasible solution? Level 4 Analysing
11. How will you solve LPP graphically? Level 5 Evaluating
12.
Conclude your understanding on the mathematical
formulation of LPP.
Level 6 Creating
13. Define basic variables and artificial variables. Level 1 Remembering
14. Compare Slack variable & Surplus Variable. Level 2 Understanding
15.
Give some example for the role of Surplus variable & Slack
Variable in the simplex method
Level 3 Applying
16. How would you apply Artificial variable? Level 4 Analysing
17. What is Big M Method? Level 1 Remembering
18. Distinguish simplex and Big M method Level 2 Understanding
19.
What do you mean by Duality? List the Rules for primal and
dual.
Level 1 Remembering
20. What is Shadow price? Level 1 Remembering
PART- B
S.NO
QUESTIONS
BT
LEVEL
COMPETENCE
1.
(i)
Maximise Z=3x+4y subject to
2x+5y ?60,
4x+2y ?40.
x, y >0. Solve by Graphical Method
Plot the graph
(8)
Level 1 Remembering
(ii) Which one is the best solution? (5)
2.
(i)
Min Z= 20x
1
+10 x
2
subject to
x
1
+2x
2
? 40,
3x
1
+x
2
? 30,
4x
1
+3x
2
? 60,
x
1
,x
2
? 0.
Solve by Graphical Method,
Plot the graph
(8)
Level 2 Understanding
(ii) Predict the value of x & y. (5)
3 Max Z= 5x1+4x2 subject to
x
1
-2x
2
? 1,
x
1
+2x
2
?3,
x
1
,x
2
? 0. Solve Graphically. Which one is the best
solution?
Level 3 Applying
4.
(i)
A Plant Manufacturer 2 Product A & B. The Profit Contribution
of each product has been estimated as Rs.300 for product A
and Rs.400 for Product B. Each Product passes through 3
departments of the plant. The time required for each product
and total time available in each department is as follows.
Department Hours
Required
Hours
Required
Available
Hours
during
month
Product
A
Product
B
I 2 3 1600
II 3 2 1500
III 1 1 700
The company has a contract to supply atleast 300 units of
Product B per month.
Formulate the LPP
(5)
Level 4
Analysing
(ii) Solve through Graphical Method
(8)
5. Solve the following LPP by graphical method.
Maximize Z= 3x
1
+2x
2
Subject t o
- 2x
1
+x
2
?1,
x
1
? 2,
x
1
+ x
2
? 3
and x
1
,x
2
? 0
Level 5 Evaluating
6. (i) Max Z= 1000x
1
+4000x
2
+5000x
3
Subject to 3x1+3x
3
?22,
x1+2x2+3x
3
? 14,
3x1+2x2 ? 14
& x1,x2 ? 0
Develop a Simplex Table
(5)
Level 6 Creating
(ii) Analyse and find the value of x
1
, x
2
? (8)
7. Analyze the following LPP by Simplex Method:
Min Z = -10y
1
-15y
2
-20y
3
Subject to 2y
1
+4y
2
+6y
3
? 24,
3y
1
+9y
2
+6y
3
? 30,
& y
1
, y
2
, y
3
? 0.
Level 1 Remembering
(i)
Develop a Simplex Table (5)
(ii) Solve and find the value of y1 ,y2 and y3
(8)
8.
Solve By Graphical Method
Minimize Z= 40x
1
+24x
2
Subject to, 20x
1
+50 x
2
> 4,800
80 x
1
+50x
2
> 7,200
x
1
,x
2
>0
Level 2 Understanding
9. Solve the following LPP by simplex method:
Minimize Z= 8x
1
-2x
2
Subject to -4x
1
+2x
2
?1,
5x
1
-4x
2
?3,
and x
1
,x
2
? 0
Level 3 Applying
10. Solve the following LPP by simplex method:
Maximize Z= 3x1+2x
2
Subject to
2x
1
+x
2
?2,
3x
1
+4x
2
?12,
x
1
,x
2
? 0
Level 4 Analyzing
11. Review the LPP and solve by simplex method
Max Z= 25x+10y
Subject to the constraints
x+0.5y? 20
x+y? 50
x,y ? 0
Level 1 Remembering
12. A firm produces three products. These products are
processors on 3 different machines. The time required for
manufacturing one unit of cost of the products and the daily
capacity of the three machines is given in the table below.
Analyse and find the optimum solution.
Mac
hine
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Machine
Capacity
Min /Day
Product1 Product 2 Product 3
M1 2 8 2 940
M2 4 - 8 970
M3 2 5 - 430
It is required to determine the daily no. of units to be
manufactured for each product. The profit for unit for
Level 2 Understanding
product 1,2,3 is Rs.4,Rs.8,Rs.6 respectively. It is assumed
that all the amount produced are consumed in the market
13. Using dual simplex method , solve and find the optimum
solution for the given LPP.
Maximize Z=6x
1
+4x
2
+4x
3
Subject to 3x
1
,x
2
+2x
3
? 2
2x
1
+x
2
-x
3
? 1
-x
1
+x
2
+2x
3
? 1 &
x
1
,x
2
,x
3
? 0
Level 4 Analysing
14.
(i)
Evaluate by using dual simplex method and solve the LPP.
Minimize Z=2x
1
+x
2
Subject to 3x
1
+2x
2
? 3
4x
1
+3x
2
? 6
x
1
+x
2
? 5 & x
1
,x
2
?
Determine the dual simplex table
(5)
Level 1 Remembering
(ii)
Find the value of x
1
, x
2
(8)
PART - C
S.No Questions BT
LEVEL
COMPETENCE
1.
Max Z=300x+400y subject to
2x+3y ? 1600,
3x+2y ? 1500,
x+y ? 700,
y ? 300, x,y ? 0 Solve by Graphical Method, choose the
value of x & y which maximizes profit.
Level 1 Remembering
2. Solve the following LPP by graphical method.
Minimize Z= 6000x1+4000x
2
Subject t o
3x+x
2
? 40,
x
1
+2.5 x
2
? 22
3x
1
+3 x
2
? 40
and x
1
,x
2
? 0
Level 2 Understanding
3. Develop a Simplex Table and Solve
Max Z = 3 x1+2 x2,
Subject to
x1+ x2 ?4,
x1- x2 ? 2;
x1, x2 ?0.
Level 3 Applying
4. Solve by using Simplex Method.
Maximize Z= 3x+5y
Subject to the constraints
x+y? 60
x? 40
y ? 30
x,y ? 0
Level 1 Remembering
UNIT - II LINEAR PROGRAMMING EXTENSIONS
SYLLABUS: Transportation Models (Minimizing and Maximizing Problems) ? Balanced and unbalanced
Problems ? Initial Basic feasible solution by N-W Corner Rule, Least cost and Vogel?s approximation methods.
Check for optimality. Solution by MODI /. Case of Degeneracy. Trans-shipment Models. Assignment Models
(Minimising and Maximising Problems) ? Balanced and Unbalanced Problems. Solution by Hungarian and
Branch and Bound Algorithms. Travelling Salesman problem.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define Transportation & Transhipment. Level 1 Remembering
2. Differentiate balanced transportation problem & Unbalanced
Transportation Problem.
Level 2 Understanding
3. How would you show your understanding on unbalanced
transportation problem?
Level 3 Applying
4. Categorize the Phases of transportation model. Level 4 Analysing
5. Construct the basic feasible solution for the following
transportation problem.
1 2 3 4 SUPPLY
1 2 3 11 7 6
2 1 0 6 1 1
3 5 8 15 9 10
DEMAN D 7 5 3 2
Level 5 Evaluating
6 Interpret the need for Optimum solution in transportation. Level 6 Creating
7. What do you mean by Least cost method (LCM)? Level 1 Remembering
8. Compare Vogel approximation method (VAM) & Least Cost
Method.
Level 2 Understanding
9. How do you represent a travelling salesman problem
through mathematical formulation?
Level 3 Applying
10. Analyse the rules of travelling salesman Problem. Level 4 Analysing
11. Discuss the meaning of Assignment Level 5 Evaluating
12. Compare Balanced assignment problem & Unbalanced
Assignment Problem.
Level 6 Creating
13. What example can you give for Unbalanced assignment
problem?
Level 1 Remembering
14. How will you resolve degeneracy in Transportation Problem? Level 2 Understanding
15. Classify transportation problem. Level 3 Applying
FirstRanker.com - FirstRanker's Choice
(An
?
DEPARTMENT OF MANAGEMENT STUDIES
QUESTION BANK
II SEMESTER
1915201? APPLIED OPERATIONS RESEACH
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Dr. Radha Ganesh Kumar ? Asst. Professor (Sel.G) and HOD
Mr.B. Sam Paul ? Asst. Professor (OG)
(An
? .
DEPARTMENT OFMANAGEMENT STUDIES
QUESTION BANK
SUBJECT :1915201 ?APPLIED OPERATIONS RESEACH
SEM / YEAR : IISemester / IYear
UNIT ? I ?INTRODUCTION TO LINEAR PROGRAMMING (LP)
SYLLABUS: Introduction to applications of operations research in functional areas of management.
Linear Programming-formulation, solution by graphical and simplex methods, Special cases. Dual
simplex method. Principles of Duality. Sensitivity Analysis.
PART- A
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Define Operations Research (OR). Level 1 Remembering
2. Differentiate between Simplex and Big M Method Level 2 Understanding
3. How do you show your understanding unbounded solution? Level 3 Applying
4. Categorize the forms of LPP. Level 4 Analysing
5.
Discuss why is two phase method is better than Big M
method?
Level 5 Evaluating
6. Interpret the usage of Sensitivity Analysis in LPP. Level 6 Creating
7. What are the assumptions and requirements of LPP? Level 1 Remembering
8. Compare Dual Simplex and Duality. Level 2 Understanding
9. Identify the Advantages of duality. Level 3 Applying
10. What do you think about Infeasible solution? Level 4 Analysing
11. How will you solve LPP graphically? Level 5 Evaluating
12.
Conclude your understanding on the mathematical
formulation of LPP.
Level 6 Creating
13. Define basic variables and artificial variables. Level 1 Remembering
14. Compare Slack variable & Surplus Variable. Level 2 Understanding
15.
Give some example for the role of Surplus variable & Slack
Variable in the simplex method
Level 3 Applying
16. How would you apply Artificial variable? Level 4 Analysing
17. What is Big M Method? Level 1 Remembering
18. Distinguish simplex and Big M method Level 2 Understanding
19.
What do you mean by Duality? List the Rules for primal and
dual.
Level 1 Remembering
20. What is Shadow price? Level 1 Remembering
PART- B
S.NO
QUESTIONS
BT
LEVEL
COMPETENCE
1.
(i)
Maximise Z=3x+4y subject to
2x+5y ?60,
4x+2y ?40.
x, y >0. Solve by Graphical Method
Plot the graph
(8)
Level 1 Remembering
(ii) Which one is the best solution? (5)
2.
(i)
Min Z= 20x
1
+10 x
2
subject to
x
1
+2x
2
? 40,
3x
1
+x
2
? 30,
4x
1
+3x
2
? 60,
x
1
,x
2
? 0.
Solve by Graphical Method,
Plot the graph
(8)
Level 2 Understanding
(ii) Predict the value of x & y. (5)
3 Max Z= 5x1+4x2 subject to
x
1
-2x
2
? 1,
x
1
+2x
2
?3,
x
1
,x
2
? 0. Solve Graphically. Which one is the best
solution?
Level 3 Applying
4.
(i)
A Plant Manufacturer 2 Product A & B. The Profit Contribution
of each product has been estimated as Rs.300 for product A
and Rs.400 for Product B. Each Product passes through 3
departments of the plant. The time required for each product
and total time available in each department is as follows.
Department Hours
Required
Hours
Required
Available
Hours
during
month
Product
A
Product
B
I 2 3 1600
II 3 2 1500
III 1 1 700
The company has a contract to supply atleast 300 units of
Product B per month.
Formulate the LPP
(5)
Level 4
Analysing
(ii) Solve through Graphical Method
(8)
5. Solve the following LPP by graphical method.
Maximize Z= 3x
1
+2x
2
Subject t o
- 2x
1
+x
2
?1,
x
1
? 2,
x
1
+ x
2
? 3
and x
1
,x
2
? 0
Level 5 Evaluating
6. (i) Max Z= 1000x
1
+4000x
2
+5000x
3
Subject to 3x1+3x
3
?22,
x1+2x2+3x
3
? 14,
3x1+2x2 ? 14
& x1,x2 ? 0
Develop a Simplex Table
(5)
Level 6 Creating
(ii) Analyse and find the value of x
1
, x
2
? (8)
7. Analyze the following LPP by Simplex Method:
Min Z = -10y
1
-15y
2
-20y
3
Subject to 2y
1
+4y
2
+6y
3
? 24,
3y
1
+9y
2
+6y
3
? 30,
& y
1
, y
2
, y
3
? 0.
Level 1 Remembering
(i)
Develop a Simplex Table (5)
(ii) Solve and find the value of y1 ,y2 and y3
(8)
8.
Solve By Graphical Method
Minimize Z= 40x
1
+24x
2
Subject to, 20x
1
+50 x
2
> 4,800
80 x
1
+50x
2
> 7,200
x
1
,x
2
>0
Level 2 Understanding
9. Solve the following LPP by simplex method:
Minimize Z= 8x
1
-2x
2
Subject to -4x
1
+2x
2
?1,
5x
1
-4x
2
?3,
and x
1
,x
2
? 0
Level 3 Applying
10. Solve the following LPP by simplex method:
Maximize Z= 3x1+2x
2
Subject to
2x
1
+x
2
?2,
3x
1
+4x
2
?12,
x
1
,x
2
? 0
Level 4 Analyzing
11. Review the LPP and solve by simplex method
Max Z= 25x+10y
Subject to the constraints
x+0.5y? 20
x+y? 50
x,y ? 0
Level 1 Remembering
12. A firm produces three products. These products are
processors on 3 different machines. The time required for
manufacturing one unit of cost of the products and the daily
capacity of the three machines is given in the table below.
Analyse and find the optimum solution.
Mac
hine
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Machine
Capacity
Min /Day
Product1 Product 2 Product 3
M1 2 8 2 940
M2 4 - 8 970
M3 2 5 - 430
It is required to determine the daily no. of units to be
manufactured for each product. The profit for unit for
Level 2 Understanding
product 1,2,3 is Rs.4,Rs.8,Rs.6 respectively. It is assumed
that all the amount produced are consumed in the market
13. Using dual simplex method , solve and find the optimum
solution for the given LPP.
Maximize Z=6x
1
+4x
2
+4x
3
Subject to 3x
1
,x
2
+2x
3
? 2
2x
1
+x
2
-x
3
? 1
-x
1
+x
2
+2x
3
? 1 &
x
1
,x
2
,x
3
? 0
Level 4 Analysing
14.
(i)
Evaluate by using dual simplex method and solve the LPP.
Minimize Z=2x
1
+x
2
Subject to 3x
1
+2x
2
? 3
4x
1
+3x
2
? 6
x
1
+x
2
? 5 & x
1
,x
2
?
Determine the dual simplex table
(5)
Level 1 Remembering
(ii)
Find the value of x
1
, x
2
(8)
PART - C
S.No Questions BT
LEVEL
COMPETENCE
1.
Max Z=300x+400y subject to
2x+3y ? 1600,
3x+2y ? 1500,
x+y ? 700,
y ? 300, x,y ? 0 Solve by Graphical Method, choose the
value of x & y which maximizes profit.
Level 1 Remembering
2. Solve the following LPP by graphical method.
Minimize Z= 6000x1+4000x
2
Subject t o
3x+x
2
? 40,
x
1
+2.5 x
2
? 22
3x
1
+3 x
2
? 40
and x
1
,x
2
? 0
Level 2 Understanding
3. Develop a Simplex Table and Solve
Max Z = 3 x1+2 x2,
Subject to
x1+ x2 ?4,
x1- x2 ? 2;
x1, x2 ?0.
Level 3 Applying
4. Solve by using Simplex Method.
Maximize Z= 3x+5y
Subject to the constraints
x+y? 60
x? 40
y ? 30
x,y ? 0
Level 1 Remembering
UNIT - II LINEAR PROGRAMMING EXTENSIONS
SYLLABUS: Transportation Models (Minimizing and Maximizing Problems) ? Balanced and unbalanced
Problems ? Initial Basic feasible solution by N-W Corner Rule, Least cost and Vogel?s approximation methods.
Check for optimality. Solution by MODI /. Case of Degeneracy. Trans-shipment Models. Assignment Models
(Minimising and Maximising Problems) ? Balanced and Unbalanced Problems. Solution by Hungarian and
Branch and Bound Algorithms. Travelling Salesman problem.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define Transportation & Transhipment. Level 1 Remembering
2. Differentiate balanced transportation problem & Unbalanced
Transportation Problem.
Level 2 Understanding
3. How would you show your understanding on unbalanced
transportation problem?
Level 3 Applying
4. Categorize the Phases of transportation model. Level 4 Analysing
5. Construct the basic feasible solution for the following
transportation problem.
1 2 3 4 SUPPLY
1 2 3 11 7 6
2 1 0 6 1 1
3 5 8 15 9 10
DEMAN D 7 5 3 2
Level 5 Evaluating
6 Interpret the need for Optimum solution in transportation. Level 6 Creating
7. What do you mean by Least cost method (LCM)? Level 1 Remembering
8. Compare Vogel approximation method (VAM) & Least Cost
Method.
Level 2 Understanding
9. How do you represent a travelling salesman problem
through mathematical formulation?
Level 3 Applying
10. Analyse the rules of travelling salesman Problem. Level 4 Analysing
11. Discuss the meaning of Assignment Level 5 Evaluating
12. Compare Balanced assignment problem & Unbalanced
Assignment Problem.
Level 6 Creating
13. What example can you give for Unbalanced assignment
problem?
Level 1 Remembering
14. How will you resolve degeneracy in Transportation Problem? Level 2 Understanding
15. Classify transportation problem. Level 3 Applying
16. Examine the Steps in Hungarian algorithm. Level 4 Analysing
17. What is Branch and bound algorithm in Assignment? Level 1 Remembering
18. Compare Assignment and transportation Problem. Level 2 Understanding
19. What do you mean by Travelling Salesman Problem? Level 1 Remembering
20. What is Restricted Assignment? Level 1 Remembering
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Solve and find the Transportation Problem and Which method will
you select if you want toMinimize Cost?
Destination Supply
1 2 3 4
I 21 16 25 13 11
II 17 18 14 23 13
III 32 27 18 41 19
Demand 6 10 12 15
Level 1 Remembering
2. Find the Initial Basic Feasible solution for following TP. Using NW
Rule, LCM, and VAM. Which method will you select if you want to
Minimize Cost?
D1 D2 D3 Supply
S1 7 3 2 2
S2 2 1 3 3
S3 3 4 6 5
Demand 4 1 5 10
Level 2 Understanding
FirstRanker.com - FirstRanker's Choice
(An
?
DEPARTMENT OF MANAGEMENT STUDIES
QUESTION BANK
II SEMESTER
1915201? APPLIED OPERATIONS RESEACH
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Dr. Radha Ganesh Kumar ? Asst. Professor (Sel.G) and HOD
Mr.B. Sam Paul ? Asst. Professor (OG)
(An
? .
DEPARTMENT OFMANAGEMENT STUDIES
QUESTION BANK
SUBJECT :1915201 ?APPLIED OPERATIONS RESEACH
SEM / YEAR : IISemester / IYear
UNIT ? I ?INTRODUCTION TO LINEAR PROGRAMMING (LP)
SYLLABUS: Introduction to applications of operations research in functional areas of management.
Linear Programming-formulation, solution by graphical and simplex methods, Special cases. Dual
simplex method. Principles of Duality. Sensitivity Analysis.
PART- A
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Define Operations Research (OR). Level 1 Remembering
2. Differentiate between Simplex and Big M Method Level 2 Understanding
3. How do you show your understanding unbounded solution? Level 3 Applying
4. Categorize the forms of LPP. Level 4 Analysing
5.
Discuss why is two phase method is better than Big M
method?
Level 5 Evaluating
6. Interpret the usage of Sensitivity Analysis in LPP. Level 6 Creating
7. What are the assumptions and requirements of LPP? Level 1 Remembering
8. Compare Dual Simplex and Duality. Level 2 Understanding
9. Identify the Advantages of duality. Level 3 Applying
10. What do you think about Infeasible solution? Level 4 Analysing
11. How will you solve LPP graphically? Level 5 Evaluating
12.
Conclude your understanding on the mathematical
formulation of LPP.
Level 6 Creating
13. Define basic variables and artificial variables. Level 1 Remembering
14. Compare Slack variable & Surplus Variable. Level 2 Understanding
15.
Give some example for the role of Surplus variable & Slack
Variable in the simplex method
Level 3 Applying
16. How would you apply Artificial variable? Level 4 Analysing
17. What is Big M Method? Level 1 Remembering
18. Distinguish simplex and Big M method Level 2 Understanding
19.
What do you mean by Duality? List the Rules for primal and
dual.
Level 1 Remembering
20. What is Shadow price? Level 1 Remembering
PART- B
S.NO
QUESTIONS
BT
LEVEL
COMPETENCE
1.
(i)
Maximise Z=3x+4y subject to
2x+5y ?60,
4x+2y ?40.
x, y >0. Solve by Graphical Method
Plot the graph
(8)
Level 1 Remembering
(ii) Which one is the best solution? (5)
2.
(i)
Min Z= 20x
1
+10 x
2
subject to
x
1
+2x
2
? 40,
3x
1
+x
2
? 30,
4x
1
+3x
2
? 60,
x
1
,x
2
? 0.
Solve by Graphical Method,
Plot the graph
(8)
Level 2 Understanding
(ii) Predict the value of x & y. (5)
3 Max Z= 5x1+4x2 subject to
x
1
-2x
2
? 1,
x
1
+2x
2
?3,
x
1
,x
2
? 0. Solve Graphically. Which one is the best
solution?
Level 3 Applying
4.
(i)
A Plant Manufacturer 2 Product A & B. The Profit Contribution
of each product has been estimated as Rs.300 for product A
and Rs.400 for Product B. Each Product passes through 3
departments of the plant. The time required for each product
and total time available in each department is as follows.
Department Hours
Required
Hours
Required
Available
Hours
during
month
Product
A
Product
B
I 2 3 1600
II 3 2 1500
III 1 1 700
The company has a contract to supply atleast 300 units of
Product B per month.
Formulate the LPP
(5)
Level 4
Analysing
(ii) Solve through Graphical Method
(8)
5. Solve the following LPP by graphical method.
Maximize Z= 3x
1
+2x
2
Subject t o
- 2x
1
+x
2
?1,
x
1
? 2,
x
1
+ x
2
? 3
and x
1
,x
2
? 0
Level 5 Evaluating
6. (i) Max Z= 1000x
1
+4000x
2
+5000x
3
Subject to 3x1+3x
3
?22,
x1+2x2+3x
3
? 14,
3x1+2x2 ? 14
& x1,x2 ? 0
Develop a Simplex Table
(5)
Level 6 Creating
(ii) Analyse and find the value of x
1
, x
2
? (8)
7. Analyze the following LPP by Simplex Method:
Min Z = -10y
1
-15y
2
-20y
3
Subject to 2y
1
+4y
2
+6y
3
? 24,
3y
1
+9y
2
+6y
3
? 30,
& y
1
, y
2
, y
3
? 0.
Level 1 Remembering
(i)
Develop a Simplex Table (5)
(ii) Solve and find the value of y1 ,y2 and y3
(8)
8.
Solve By Graphical Method
Minimize Z= 40x
1
+24x
2
Subject to, 20x
1
+50 x
2
> 4,800
80 x
1
+50x
2
> 7,200
x
1
,x
2
>0
Level 2 Understanding
9. Solve the following LPP by simplex method:
Minimize Z= 8x
1
-2x
2
Subject to -4x
1
+2x
2
?1,
5x
1
-4x
2
?3,
and x
1
,x
2
? 0
Level 3 Applying
10. Solve the following LPP by simplex method:
Maximize Z= 3x1+2x
2
Subject to
2x
1
+x
2
?2,
3x
1
+4x
2
?12,
x
1
,x
2
? 0
Level 4 Analyzing
11. Review the LPP and solve by simplex method
Max Z= 25x+10y
Subject to the constraints
x+0.5y? 20
x+y? 50
x,y ? 0
Level 1 Remembering
12. A firm produces three products. These products are
processors on 3 different machines. The time required for
manufacturing one unit of cost of the products and the daily
capacity of the three machines is given in the table below.
Analyse and find the optimum solution.
Mac
hine
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Machine
Capacity
Min /Day
Product1 Product 2 Product 3
M1 2 8 2 940
M2 4 - 8 970
M3 2 5 - 430
It is required to determine the daily no. of units to be
manufactured for each product. The profit for unit for
Level 2 Understanding
product 1,2,3 is Rs.4,Rs.8,Rs.6 respectively. It is assumed
that all the amount produced are consumed in the market
13. Using dual simplex method , solve and find the optimum
solution for the given LPP.
Maximize Z=6x
1
+4x
2
+4x
3
Subject to 3x
1
,x
2
+2x
3
? 2
2x
1
+x
2
-x
3
? 1
-x
1
+x
2
+2x
3
? 1 &
x
1
,x
2
,x
3
? 0
Level 4 Analysing
14.
(i)
Evaluate by using dual simplex method and solve the LPP.
Minimize Z=2x
1
+x
2
Subject to 3x
1
+2x
2
? 3
4x
1
+3x
2
? 6
x
1
+x
2
? 5 & x
1
,x
2
?
Determine the dual simplex table
(5)
Level 1 Remembering
(ii)
Find the value of x
1
, x
2
(8)
PART - C
S.No Questions BT
LEVEL
COMPETENCE
1.
Max Z=300x+400y subject to
2x+3y ? 1600,
3x+2y ? 1500,
x+y ? 700,
y ? 300, x,y ? 0 Solve by Graphical Method, choose the
value of x & y which maximizes profit.
Level 1 Remembering
2. Solve the following LPP by graphical method.
Minimize Z= 6000x1+4000x
2
Subject t o
3x+x
2
? 40,
x
1
+2.5 x
2
? 22
3x
1
+3 x
2
? 40
and x
1
,x
2
? 0
Level 2 Understanding
3. Develop a Simplex Table and Solve
Max Z = 3 x1+2 x2,
Subject to
x1+ x2 ?4,
x1- x2 ? 2;
x1, x2 ?0.
Level 3 Applying
4. Solve by using Simplex Method.
Maximize Z= 3x+5y
Subject to the constraints
x+y? 60
x? 40
y ? 30
x,y ? 0
Level 1 Remembering
UNIT - II LINEAR PROGRAMMING EXTENSIONS
SYLLABUS: Transportation Models (Minimizing and Maximizing Problems) ? Balanced and unbalanced
Problems ? Initial Basic feasible solution by N-W Corner Rule, Least cost and Vogel?s approximation methods.
Check for optimality. Solution by MODI /. Case of Degeneracy. Trans-shipment Models. Assignment Models
(Minimising and Maximising Problems) ? Balanced and Unbalanced Problems. Solution by Hungarian and
Branch and Bound Algorithms. Travelling Salesman problem.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define Transportation & Transhipment. Level 1 Remembering
2. Differentiate balanced transportation problem & Unbalanced
Transportation Problem.
Level 2 Understanding
3. How would you show your understanding on unbalanced
transportation problem?
Level 3 Applying
4. Categorize the Phases of transportation model. Level 4 Analysing
5. Construct the basic feasible solution for the following
transportation problem.
1 2 3 4 SUPPLY
1 2 3 11 7 6
2 1 0 6 1 1
3 5 8 15 9 10
DEMAN D 7 5 3 2
Level 5 Evaluating
6 Interpret the need for Optimum solution in transportation. Level 6 Creating
7. What do you mean by Least cost method (LCM)? Level 1 Remembering
8. Compare Vogel approximation method (VAM) & Least Cost
Method.
Level 2 Understanding
9. How do you represent a travelling salesman problem
through mathematical formulation?
Level 3 Applying
10. Analyse the rules of travelling salesman Problem. Level 4 Analysing
11. Discuss the meaning of Assignment Level 5 Evaluating
12. Compare Balanced assignment problem & Unbalanced
Assignment Problem.
Level 6 Creating
13. What example can you give for Unbalanced assignment
problem?
Level 1 Remembering
14. How will you resolve degeneracy in Transportation Problem? Level 2 Understanding
15. Classify transportation problem. Level 3 Applying
16. Examine the Steps in Hungarian algorithm. Level 4 Analysing
17. What is Branch and bound algorithm in Assignment? Level 1 Remembering
18. Compare Assignment and transportation Problem. Level 2 Understanding
19. What do you mean by Travelling Salesman Problem? Level 1 Remembering
20. What is Restricted Assignment? Level 1 Remembering
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Solve and find the Transportation Problem and Which method will
you select if you want toMinimize Cost?
Destination Supply
1 2 3 4
I 21 16 25 13 11
II 17 18 14 23 13
III 32 27 18 41 19
Demand 6 10 12 15
Level 1 Remembering
2. Find the Initial Basic Feasible solution for following TP. Using NW
Rule, LCM, and VAM. Which method will you select if you want to
Minimize Cost?
D1 D2 D3 Supply
S1 7 3 2 2
S2 2 1 3 3
S3 3 4 6 5
Demand 4 1 5 10
Level 2 Understanding
3.
(i)
Analyze the transportation problem with unit transportation
costs,demand, and supply as given below:
Destination
Supply
Source
D1 D2 D3 D4
S1
6 1 9 3
70
11 5 2 8
S2 55
10 12 4 7
S3
70
Demand 85 35 50 45
Apply VAM for Initial solution.
(5)
Level 3 Applying
(ii)
Construct the final Solution by using MODIMethod.
(8)
4.
(i)
Analyze & solve the following transportation problem to maximize
profit.
A B C D Supply
1
Source 2
3
Demand
15 51 42 33 23
80 42 26 81 44
90 40 66 60 33
23
31
16
30
100
Examine Initial solution using VAM.
(5)
Level 4 Analysing
(ii)
Analyze and find out the final Solution by using MODI Method.
(8)
5. Solve the following transportation problem using Vogel?s
method
Factory? Warehouse ?Available
A B C D E F
1 9 12 9 6 9 10 5
2 7 3 7 7 5 5 6
3 6 5 9 11 3 11 2
4 6 8 11 2 2 10 9
4 4 6 2 4 2
Requirement?
(5)
Level 5 Evaluating
6. (i) Solve the transportation problem and decide using VAM for initial
solution.
(5) Level 6 Creating
FirstRanker.com - FirstRanker's Choice
(An
?
DEPARTMENT OF MANAGEMENT STUDIES
QUESTION BANK
II SEMESTER
1915201? APPLIED OPERATIONS RESEACH
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Dr. Radha Ganesh Kumar ? Asst. Professor (Sel.G) and HOD
Mr.B. Sam Paul ? Asst. Professor (OG)
(An
? .
DEPARTMENT OFMANAGEMENT STUDIES
QUESTION BANK
SUBJECT :1915201 ?APPLIED OPERATIONS RESEACH
SEM / YEAR : IISemester / IYear
UNIT ? I ?INTRODUCTION TO LINEAR PROGRAMMING (LP)
SYLLABUS: Introduction to applications of operations research in functional areas of management.
Linear Programming-formulation, solution by graphical and simplex methods, Special cases. Dual
simplex method. Principles of Duality. Sensitivity Analysis.
PART- A
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Define Operations Research (OR). Level 1 Remembering
2. Differentiate between Simplex and Big M Method Level 2 Understanding
3. How do you show your understanding unbounded solution? Level 3 Applying
4. Categorize the forms of LPP. Level 4 Analysing
5.
Discuss why is two phase method is better than Big M
method?
Level 5 Evaluating
6. Interpret the usage of Sensitivity Analysis in LPP. Level 6 Creating
7. What are the assumptions and requirements of LPP? Level 1 Remembering
8. Compare Dual Simplex and Duality. Level 2 Understanding
9. Identify the Advantages of duality. Level 3 Applying
10. What do you think about Infeasible solution? Level 4 Analysing
11. How will you solve LPP graphically? Level 5 Evaluating
12.
Conclude your understanding on the mathematical
formulation of LPP.
Level 6 Creating
13. Define basic variables and artificial variables. Level 1 Remembering
14. Compare Slack variable & Surplus Variable. Level 2 Understanding
15.
Give some example for the role of Surplus variable & Slack
Variable in the simplex method
Level 3 Applying
16. How would you apply Artificial variable? Level 4 Analysing
17. What is Big M Method? Level 1 Remembering
18. Distinguish simplex and Big M method Level 2 Understanding
19.
What do you mean by Duality? List the Rules for primal and
dual.
Level 1 Remembering
20. What is Shadow price? Level 1 Remembering
PART- B
S.NO
QUESTIONS
BT
LEVEL
COMPETENCE
1.
(i)
Maximise Z=3x+4y subject to
2x+5y ?60,
4x+2y ?40.
x, y >0. Solve by Graphical Method
Plot the graph
(8)
Level 1 Remembering
(ii) Which one is the best solution? (5)
2.
(i)
Min Z= 20x
1
+10 x
2
subject to
x
1
+2x
2
? 40,
3x
1
+x
2
? 30,
4x
1
+3x
2
? 60,
x
1
,x
2
? 0.
Solve by Graphical Method,
Plot the graph
(8)
Level 2 Understanding
(ii) Predict the value of x & y. (5)
3 Max Z= 5x1+4x2 subject to
x
1
-2x
2
? 1,
x
1
+2x
2
?3,
x
1
,x
2
? 0. Solve Graphically. Which one is the best
solution?
Level 3 Applying
4.
(i)
A Plant Manufacturer 2 Product A & B. The Profit Contribution
of each product has been estimated as Rs.300 for product A
and Rs.400 for Product B. Each Product passes through 3
departments of the plant. The time required for each product
and total time available in each department is as follows.
Department Hours
Required
Hours
Required
Available
Hours
during
month
Product
A
Product
B
I 2 3 1600
II 3 2 1500
III 1 1 700
The company has a contract to supply atleast 300 units of
Product B per month.
Formulate the LPP
(5)
Level 4
Analysing
(ii) Solve through Graphical Method
(8)
5. Solve the following LPP by graphical method.
Maximize Z= 3x
1
+2x
2
Subject t o
- 2x
1
+x
2
?1,
x
1
? 2,
x
1
+ x
2
? 3
and x
1
,x
2
? 0
Level 5 Evaluating
6. (i) Max Z= 1000x
1
+4000x
2
+5000x
3
Subject to 3x1+3x
3
?22,
x1+2x2+3x
3
? 14,
3x1+2x2 ? 14
& x1,x2 ? 0
Develop a Simplex Table
(5)
Level 6 Creating
(ii) Analyse and find the value of x
1
, x
2
? (8)
7. Analyze the following LPP by Simplex Method:
Min Z = -10y
1
-15y
2
-20y
3
Subject to 2y
1
+4y
2
+6y
3
? 24,
3y
1
+9y
2
+6y
3
? 30,
& y
1
, y
2
, y
3
? 0.
Level 1 Remembering
(i)
Develop a Simplex Table (5)
(ii) Solve and find the value of y1 ,y2 and y3
(8)
8.
Solve By Graphical Method
Minimize Z= 40x
1
+24x
2
Subject to, 20x
1
+50 x
2
> 4,800
80 x
1
+50x
2
> 7,200
x
1
,x
2
>0
Level 2 Understanding
9. Solve the following LPP by simplex method:
Minimize Z= 8x
1
-2x
2
Subject to -4x
1
+2x
2
?1,
5x
1
-4x
2
?3,
and x
1
,x
2
? 0
Level 3 Applying
10. Solve the following LPP by simplex method:
Maximize Z= 3x1+2x
2
Subject to
2x
1
+x
2
?2,
3x
1
+4x
2
?12,
x
1
,x
2
? 0
Level 4 Analyzing
11. Review the LPP and solve by simplex method
Max Z= 25x+10y
Subject to the constraints
x+0.5y? 20
x+y? 50
x,y ? 0
Level 1 Remembering
12. A firm produces three products. These products are
processors on 3 different machines. The time required for
manufacturing one unit of cost of the products and the daily
capacity of the three machines is given in the table below.
Analyse and find the optimum solution.
Mac
hine
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Machine
Capacity
Min /Day
Product1 Product 2 Product 3
M1 2 8 2 940
M2 4 - 8 970
M3 2 5 - 430
It is required to determine the daily no. of units to be
manufactured for each product. The profit for unit for
Level 2 Understanding
product 1,2,3 is Rs.4,Rs.8,Rs.6 respectively. It is assumed
that all the amount produced are consumed in the market
13. Using dual simplex method , solve and find the optimum
solution for the given LPP.
Maximize Z=6x
1
+4x
2
+4x
3
Subject to 3x
1
,x
2
+2x
3
? 2
2x
1
+x
2
-x
3
? 1
-x
1
+x
2
+2x
3
? 1 &
x
1
,x
2
,x
3
? 0
Level 4 Analysing
14.
(i)
Evaluate by using dual simplex method and solve the LPP.
Minimize Z=2x
1
+x
2
Subject to 3x
1
+2x
2
? 3
4x
1
+3x
2
? 6
x
1
+x
2
? 5 & x
1
,x
2
?
Determine the dual simplex table
(5)
Level 1 Remembering
(ii)
Find the value of x
1
, x
2
(8)
PART - C
S.No Questions BT
LEVEL
COMPETENCE
1.
Max Z=300x+400y subject to
2x+3y ? 1600,
3x+2y ? 1500,
x+y ? 700,
y ? 300, x,y ? 0 Solve by Graphical Method, choose the
value of x & y which maximizes profit.
Level 1 Remembering
2. Solve the following LPP by graphical method.
Minimize Z= 6000x1+4000x
2
Subject t o
3x+x
2
? 40,
x
1
+2.5 x
2
? 22
3x
1
+3 x
2
? 40
and x
1
,x
2
? 0
Level 2 Understanding
3. Develop a Simplex Table and Solve
Max Z = 3 x1+2 x2,
Subject to
x1+ x2 ?4,
x1- x2 ? 2;
x1, x2 ?0.
Level 3 Applying
4. Solve by using Simplex Method.
Maximize Z= 3x+5y
Subject to the constraints
x+y? 60
x? 40
y ? 30
x,y ? 0
Level 1 Remembering
UNIT - II LINEAR PROGRAMMING EXTENSIONS
SYLLABUS: Transportation Models (Minimizing and Maximizing Problems) ? Balanced and unbalanced
Problems ? Initial Basic feasible solution by N-W Corner Rule, Least cost and Vogel?s approximation methods.
Check for optimality. Solution by MODI /. Case of Degeneracy. Trans-shipment Models. Assignment Models
(Minimising and Maximising Problems) ? Balanced and Unbalanced Problems. Solution by Hungarian and
Branch and Bound Algorithms. Travelling Salesman problem.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define Transportation & Transhipment. Level 1 Remembering
2. Differentiate balanced transportation problem & Unbalanced
Transportation Problem.
Level 2 Understanding
3. How would you show your understanding on unbalanced
transportation problem?
Level 3 Applying
4. Categorize the Phases of transportation model. Level 4 Analysing
5. Construct the basic feasible solution for the following
transportation problem.
1 2 3 4 SUPPLY
1 2 3 11 7 6
2 1 0 6 1 1
3 5 8 15 9 10
DEMAN D 7 5 3 2
Level 5 Evaluating
6 Interpret the need for Optimum solution in transportation. Level 6 Creating
7. What do you mean by Least cost method (LCM)? Level 1 Remembering
8. Compare Vogel approximation method (VAM) & Least Cost
Method.
Level 2 Understanding
9. How do you represent a travelling salesman problem
through mathematical formulation?
Level 3 Applying
10. Analyse the rules of travelling salesman Problem. Level 4 Analysing
11. Discuss the meaning of Assignment Level 5 Evaluating
12. Compare Balanced assignment problem & Unbalanced
Assignment Problem.
Level 6 Creating
13. What example can you give for Unbalanced assignment
problem?
Level 1 Remembering
14. How will you resolve degeneracy in Transportation Problem? Level 2 Understanding
15. Classify transportation problem. Level 3 Applying
16. Examine the Steps in Hungarian algorithm. Level 4 Analysing
17. What is Branch and bound algorithm in Assignment? Level 1 Remembering
18. Compare Assignment and transportation Problem. Level 2 Understanding
19. What do you mean by Travelling Salesman Problem? Level 1 Remembering
20. What is Restricted Assignment? Level 1 Remembering
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Solve and find the Transportation Problem and Which method will
you select if you want toMinimize Cost?
Destination Supply
1 2 3 4
I 21 16 25 13 11
II 17 18 14 23 13
III 32 27 18 41 19
Demand 6 10 12 15
Level 1 Remembering
2. Find the Initial Basic Feasible solution for following TP. Using NW
Rule, LCM, and VAM. Which method will you select if you want to
Minimize Cost?
D1 D2 D3 Supply
S1 7 3 2 2
S2 2 1 3 3
S3 3 4 6 5
Demand 4 1 5 10
Level 2 Understanding
3.
(i)
Analyze the transportation problem with unit transportation
costs,demand, and supply as given below:
Destination
Supply
Source
D1 D2 D3 D4
S1
6 1 9 3
70
11 5 2 8
S2 55
10 12 4 7
S3
70
Demand 85 35 50 45
Apply VAM for Initial solution.
(5)
Level 3 Applying
(ii)
Construct the final Solution by using MODIMethod.
(8)
4.
(i)
Analyze & solve the following transportation problem to maximize
profit.
A B C D Supply
1
Source 2
3
Demand
15 51 42 33 23
80 42 26 81 44
90 40 66 60 33
23
31
16
30
100
Examine Initial solution using VAM.
(5)
Level 4 Analysing
(ii)
Analyze and find out the final Solution by using MODI Method.
(8)
5. Solve the following transportation problem using Vogel?s
method
Factory? Warehouse ?Available
A B C D E F
1 9 12 9 6 9 10 5
2 7 3 7 7 5 5 6
3 6 5 9 11 3 11 2
4 6 8 11 2 2 10 9
4 4 6 2 4 2
Requirement?
(5)
Level 5 Evaluating
6. (i) Solve the transportation problem and decide using VAM for initial
solution.
(5) Level 6 Creating
(ii) Evaluate using NWC and Least Cost method for initial solution?
Destination Supply
I 2 1 25 13 11
II 1 1 14 23 13
III 3 2 18 41 19
Demand 6 1 22 15
(8)
7.
Maximize profit from the following transportationproblem.
A B C D Supply
I 40 25 22 33 100
SourceII 44 35 30 30 30
III 38 38 28 30 70
Demand 40 20 60 30
Level 1 Remembering
(i) How will you convert maximization problem to minimization.
Find the maximum profit
(8)
(ii) Explain stepping stone method for checking the
solution for optimality transportation problems.
(5)
8. A company has one surplus truck in each of the cities A, B, C, D, &
E and one deficit trucks in each of the cities 1,2,3,4,5,6. The
distance between the cities in kms is shown in the matrix below.
Can you select the assignment of trucks from cities in surplus to
cities in deficiency .so that total distance covered by the vehicles is
minimum?
1 2 3 4 5 6
A 12 10 15 22 18 8
B 10 18 25 15 16 12
C 11 10 3 8 5 9
D 6 4 10 13 13 12
E 8 12 11 7 13 10
Level 2 Understanding
9.
Consider the problem of assigning five jobs to five persons. The
assignment costs are given as follows:
PERSONS?JOBS ?
1 2 3 4 5
A 8 4 2 6 1
B 0 9 5 5 4
C 3 8 9 2 6
D 4 3 1 0 3
Level 3 Applying
FirstRanker.com - FirstRanker's Choice
(An
?
DEPARTMENT OF MANAGEMENT STUDIES
QUESTION BANK
II SEMESTER
1915201? APPLIED OPERATIONS RESEACH
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Dr. Radha Ganesh Kumar ? Asst. Professor (Sel.G) and HOD
Mr.B. Sam Paul ? Asst. Professor (OG)
(An
? .
DEPARTMENT OFMANAGEMENT STUDIES
QUESTION BANK
SUBJECT :1915201 ?APPLIED OPERATIONS RESEACH
SEM / YEAR : IISemester / IYear
UNIT ? I ?INTRODUCTION TO LINEAR PROGRAMMING (LP)
SYLLABUS: Introduction to applications of operations research in functional areas of management.
Linear Programming-formulation, solution by graphical and simplex methods, Special cases. Dual
simplex method. Principles of Duality. Sensitivity Analysis.
PART- A
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Define Operations Research (OR). Level 1 Remembering
2. Differentiate between Simplex and Big M Method Level 2 Understanding
3. How do you show your understanding unbounded solution? Level 3 Applying
4. Categorize the forms of LPP. Level 4 Analysing
5.
Discuss why is two phase method is better than Big M
method?
Level 5 Evaluating
6. Interpret the usage of Sensitivity Analysis in LPP. Level 6 Creating
7. What are the assumptions and requirements of LPP? Level 1 Remembering
8. Compare Dual Simplex and Duality. Level 2 Understanding
9. Identify the Advantages of duality. Level 3 Applying
10. What do you think about Infeasible solution? Level 4 Analysing
11. How will you solve LPP graphically? Level 5 Evaluating
12.
Conclude your understanding on the mathematical
formulation of LPP.
Level 6 Creating
13. Define basic variables and artificial variables. Level 1 Remembering
14. Compare Slack variable & Surplus Variable. Level 2 Understanding
15.
Give some example for the role of Surplus variable & Slack
Variable in the simplex method
Level 3 Applying
16. How would you apply Artificial variable? Level 4 Analysing
17. What is Big M Method? Level 1 Remembering
18. Distinguish simplex and Big M method Level 2 Understanding
19.
What do you mean by Duality? List the Rules for primal and
dual.
Level 1 Remembering
20. What is Shadow price? Level 1 Remembering
PART- B
S.NO
QUESTIONS
BT
LEVEL
COMPETENCE
1.
(i)
Maximise Z=3x+4y subject to
2x+5y ?60,
4x+2y ?40.
x, y >0. Solve by Graphical Method
Plot the graph
(8)
Level 1 Remembering
(ii) Which one is the best solution? (5)
2.
(i)
Min Z= 20x
1
+10 x
2
subject to
x
1
+2x
2
? 40,
3x
1
+x
2
? 30,
4x
1
+3x
2
? 60,
x
1
,x
2
? 0.
Solve by Graphical Method,
Plot the graph
(8)
Level 2 Understanding
(ii) Predict the value of x & y. (5)
3 Max Z= 5x1+4x2 subject to
x
1
-2x
2
? 1,
x
1
+2x
2
?3,
x
1
,x
2
? 0. Solve Graphically. Which one is the best
solution?
Level 3 Applying
4.
(i)
A Plant Manufacturer 2 Product A & B. The Profit Contribution
of each product has been estimated as Rs.300 for product A
and Rs.400 for Product B. Each Product passes through 3
departments of the plant. The time required for each product
and total time available in each department is as follows.
Department Hours
Required
Hours
Required
Available
Hours
during
month
Product
A
Product
B
I 2 3 1600
II 3 2 1500
III 1 1 700
The company has a contract to supply atleast 300 units of
Product B per month.
Formulate the LPP
(5)
Level 4
Analysing
(ii) Solve through Graphical Method
(8)
5. Solve the following LPP by graphical method.
Maximize Z= 3x
1
+2x
2
Subject t o
- 2x
1
+x
2
?1,
x
1
? 2,
x
1
+ x
2
? 3
and x
1
,x
2
? 0
Level 5 Evaluating
6. (i) Max Z= 1000x
1
+4000x
2
+5000x
3
Subject to 3x1+3x
3
?22,
x1+2x2+3x
3
? 14,
3x1+2x2 ? 14
& x1,x2 ? 0
Develop a Simplex Table
(5)
Level 6 Creating
(ii) Analyse and find the value of x
1
, x
2
? (8)
7. Analyze the following LPP by Simplex Method:
Min Z = -10y
1
-15y
2
-20y
3
Subject to 2y
1
+4y
2
+6y
3
? 24,
3y
1
+9y
2
+6y
3
? 30,
& y
1
, y
2
, y
3
? 0.
Level 1 Remembering
(i)
Develop a Simplex Table (5)
(ii) Solve and find the value of y1 ,y2 and y3
(8)
8.
Solve By Graphical Method
Minimize Z= 40x
1
+24x
2
Subject to, 20x
1
+50 x
2
> 4,800
80 x
1
+50x
2
> 7,200
x
1
,x
2
>0
Level 2 Understanding
9. Solve the following LPP by simplex method:
Minimize Z= 8x
1
-2x
2
Subject to -4x
1
+2x
2
?1,
5x
1
-4x
2
?3,
and x
1
,x
2
? 0
Level 3 Applying
10. Solve the following LPP by simplex method:
Maximize Z= 3x1+2x
2
Subject to
2x
1
+x
2
?2,
3x
1
+4x
2
?12,
x
1
,x
2
? 0
Level 4 Analyzing
11. Review the LPP and solve by simplex method
Max Z= 25x+10y
Subject to the constraints
x+0.5y? 20
x+y? 50
x,y ? 0
Level 1 Remembering
12. A firm produces three products. These products are
processors on 3 different machines. The time required for
manufacturing one unit of cost of the products and the daily
capacity of the three machines is given in the table below.
Analyse and find the optimum solution.
Mac
hine
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Machine
Capacity
Min /Day
Product1 Product 2 Product 3
M1 2 8 2 940
M2 4 - 8 970
M3 2 5 - 430
It is required to determine the daily no. of units to be
manufactured for each product. The profit for unit for
Level 2 Understanding
product 1,2,3 is Rs.4,Rs.8,Rs.6 respectively. It is assumed
that all the amount produced are consumed in the market
13. Using dual simplex method , solve and find the optimum
solution for the given LPP.
Maximize Z=6x
1
+4x
2
+4x
3
Subject to 3x
1
,x
2
+2x
3
? 2
2x
1
+x
2
-x
3
? 1
-x
1
+x
2
+2x
3
? 1 &
x
1
,x
2
,x
3
? 0
Level 4 Analysing
14.
(i)
Evaluate by using dual simplex method and solve the LPP.
Minimize Z=2x
1
+x
2
Subject to 3x
1
+2x
2
? 3
4x
1
+3x
2
? 6
x
1
+x
2
? 5 & x
1
,x
2
?
Determine the dual simplex table
(5)
Level 1 Remembering
(ii)
Find the value of x
1
, x
2
(8)
PART - C
S.No Questions BT
LEVEL
COMPETENCE
1.
Max Z=300x+400y subject to
2x+3y ? 1600,
3x+2y ? 1500,
x+y ? 700,
y ? 300, x,y ? 0 Solve by Graphical Method, choose the
value of x & y which maximizes profit.
Level 1 Remembering
2. Solve the following LPP by graphical method.
Minimize Z= 6000x1+4000x
2
Subject t o
3x+x
2
? 40,
x
1
+2.5 x
2
? 22
3x
1
+3 x
2
? 40
and x
1
,x
2
? 0
Level 2 Understanding
3. Develop a Simplex Table and Solve
Max Z = 3 x1+2 x2,
Subject to
x1+ x2 ?4,
x1- x2 ? 2;
x1, x2 ?0.
Level 3 Applying
4. Solve by using Simplex Method.
Maximize Z= 3x+5y
Subject to the constraints
x+y? 60
x? 40
y ? 30
x,y ? 0
Level 1 Remembering
UNIT - II LINEAR PROGRAMMING EXTENSIONS
SYLLABUS: Transportation Models (Minimizing and Maximizing Problems) ? Balanced and unbalanced
Problems ? Initial Basic feasible solution by N-W Corner Rule, Least cost and Vogel?s approximation methods.
Check for optimality. Solution by MODI /. Case of Degeneracy. Trans-shipment Models. Assignment Models
(Minimising and Maximising Problems) ? Balanced and Unbalanced Problems. Solution by Hungarian and
Branch and Bound Algorithms. Travelling Salesman problem.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define Transportation & Transhipment. Level 1 Remembering
2. Differentiate balanced transportation problem & Unbalanced
Transportation Problem.
Level 2 Understanding
3. How would you show your understanding on unbalanced
transportation problem?
Level 3 Applying
4. Categorize the Phases of transportation model. Level 4 Analysing
5. Construct the basic feasible solution for the following
transportation problem.
1 2 3 4 SUPPLY
1 2 3 11 7 6
2 1 0 6 1 1
3 5 8 15 9 10
DEMAN D 7 5 3 2
Level 5 Evaluating
6 Interpret the need for Optimum solution in transportation. Level 6 Creating
7. What do you mean by Least cost method (LCM)? Level 1 Remembering
8. Compare Vogel approximation method (VAM) & Least Cost
Method.
Level 2 Understanding
9. How do you represent a travelling salesman problem
through mathematical formulation?
Level 3 Applying
10. Analyse the rules of travelling salesman Problem. Level 4 Analysing
11. Discuss the meaning of Assignment Level 5 Evaluating
12. Compare Balanced assignment problem & Unbalanced
Assignment Problem.
Level 6 Creating
13. What example can you give for Unbalanced assignment
problem?
Level 1 Remembering
14. How will you resolve degeneracy in Transportation Problem? Level 2 Understanding
15. Classify transportation problem. Level 3 Applying
16. Examine the Steps in Hungarian algorithm. Level 4 Analysing
17. What is Branch and bound algorithm in Assignment? Level 1 Remembering
18. Compare Assignment and transportation Problem. Level 2 Understanding
19. What do you mean by Travelling Salesman Problem? Level 1 Remembering
20. What is Restricted Assignment? Level 1 Remembering
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Solve and find the Transportation Problem and Which method will
you select if you want toMinimize Cost?
Destination Supply
1 2 3 4
I 21 16 25 13 11
II 17 18 14 23 13
III 32 27 18 41 19
Demand 6 10 12 15
Level 1 Remembering
2. Find the Initial Basic Feasible solution for following TP. Using NW
Rule, LCM, and VAM. Which method will you select if you want to
Minimize Cost?
D1 D2 D3 Supply
S1 7 3 2 2
S2 2 1 3 3
S3 3 4 6 5
Demand 4 1 5 10
Level 2 Understanding
3.
(i)
Analyze the transportation problem with unit transportation
costs,demand, and supply as given below:
Destination
Supply
Source
D1 D2 D3 D4
S1
6 1 9 3
70
11 5 2 8
S2 55
10 12 4 7
S3
70
Demand 85 35 50 45
Apply VAM for Initial solution.
(5)
Level 3 Applying
(ii)
Construct the final Solution by using MODIMethod.
(8)
4.
(i)
Analyze & solve the following transportation problem to maximize
profit.
A B C D Supply
1
Source 2
3
Demand
15 51 42 33 23
80 42 26 81 44
90 40 66 60 33
23
31
16
30
100
Examine Initial solution using VAM.
(5)
Level 4 Analysing
(ii)
Analyze and find out the final Solution by using MODI Method.
(8)
5. Solve the following transportation problem using Vogel?s
method
Factory? Warehouse ?Available
A B C D E F
1 9 12 9 6 9 10 5
2 7 3 7 7 5 5 6
3 6 5 9 11 3 11 2
4 6 8 11 2 2 10 9
4 4 6 2 4 2
Requirement?
(5)
Level 5 Evaluating
6. (i) Solve the transportation problem and decide using VAM for initial
solution.
(5) Level 6 Creating
(ii) Evaluate using NWC and Least Cost method for initial solution?
Destination Supply
I 2 1 25 13 11
II 1 1 14 23 13
III 3 2 18 41 19
Demand 6 1 22 15
(8)
7.
Maximize profit from the following transportationproblem.
A B C D Supply
I 40 25 22 33 100
SourceII 44 35 30 30 30
III 38 38 28 30 70
Demand 40 20 60 30
Level 1 Remembering
(i) How will you convert maximization problem to minimization.
Find the maximum profit
(8)
(ii) Explain stepping stone method for checking the
solution for optimality transportation problems.
(5)
8. A company has one surplus truck in each of the cities A, B, C, D, &
E and one deficit trucks in each of the cities 1,2,3,4,5,6. The
distance between the cities in kms is shown in the matrix below.
Can you select the assignment of trucks from cities in surplus to
cities in deficiency .so that total distance covered by the vehicles is
minimum?
1 2 3 4 5 6
A 12 10 15 22 18 8
B 10 18 25 15 16 12
C 11 10 3 8 5 9
D 6 4 10 13 13 12
E 8 12 11 7 13 10
Level 2 Understanding
9.
Consider the problem of assigning five jobs to five persons. The
assignment costs are given as follows:
PERSONS?JOBS ?
1 2 3 4 5
A 8 4 2 6 1
B 0 9 5 5 4
C 3 8 9 2 6
D 4 3 1 0 3
Level 3 Applying
E 9 5 8 9 5
Determine the optimum assignment schedule.
10. The assignment cost of assigning any one operator to any one
machine is given in the following table.
MACHINE?OPERATORS ?
I II III IV
A 10 5 13 15
B 3 9 18 3
C 10 7 3 2
D 5 11 9 7
Find the optimal assignment by Hungarian method.
Level 4 Analysing
11. A machine shop purchased a drilling machine and two lathes of
different capacities. The Positioning of the machines among 4
possible locations on the shop floor is important forms the
standard of materials handling. Given the cost estimate per unit
time of materials below, find the optimum location of the
machines.
LOCATIONS
1 2 3 4
Lathe 1 12 9 12 9
Drill 15 Not
suitable
13 20
Lathe 2 4 8 10 6
Level 1 Remembering
12.
Solve the assignment problem for maximization given profit
matrix(profit in rupees).
Machines
P Q R S
JOB
51 53 54 50
47 50 48 50
49 50 60 61
63 64 60 60
Level 2 Understanding
FirstRanker.com - FirstRanker's Choice
(An
?
DEPARTMENT OF MANAGEMENT STUDIES
QUESTION BANK
II SEMESTER
1915201? APPLIED OPERATIONS RESEACH
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Dr. Radha Ganesh Kumar ? Asst. Professor (Sel.G) and HOD
Mr.B. Sam Paul ? Asst. Professor (OG)
(An
? .
DEPARTMENT OFMANAGEMENT STUDIES
QUESTION BANK
SUBJECT :1915201 ?APPLIED OPERATIONS RESEACH
SEM / YEAR : IISemester / IYear
UNIT ? I ?INTRODUCTION TO LINEAR PROGRAMMING (LP)
SYLLABUS: Introduction to applications of operations research in functional areas of management.
Linear Programming-formulation, solution by graphical and simplex methods, Special cases. Dual
simplex method. Principles of Duality. Sensitivity Analysis.
PART- A
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Define Operations Research (OR). Level 1 Remembering
2. Differentiate between Simplex and Big M Method Level 2 Understanding
3. How do you show your understanding unbounded solution? Level 3 Applying
4. Categorize the forms of LPP. Level 4 Analysing
5.
Discuss why is two phase method is better than Big M
method?
Level 5 Evaluating
6. Interpret the usage of Sensitivity Analysis in LPP. Level 6 Creating
7. What are the assumptions and requirements of LPP? Level 1 Remembering
8. Compare Dual Simplex and Duality. Level 2 Understanding
9. Identify the Advantages of duality. Level 3 Applying
10. What do you think about Infeasible solution? Level 4 Analysing
11. How will you solve LPP graphically? Level 5 Evaluating
12.
Conclude your understanding on the mathematical
formulation of LPP.
Level 6 Creating
13. Define basic variables and artificial variables. Level 1 Remembering
14. Compare Slack variable & Surplus Variable. Level 2 Understanding
15.
Give some example for the role of Surplus variable & Slack
Variable in the simplex method
Level 3 Applying
16. How would you apply Artificial variable? Level 4 Analysing
17. What is Big M Method? Level 1 Remembering
18. Distinguish simplex and Big M method Level 2 Understanding
19.
What do you mean by Duality? List the Rules for primal and
dual.
Level 1 Remembering
20. What is Shadow price? Level 1 Remembering
PART- B
S.NO
QUESTIONS
BT
LEVEL
COMPETENCE
1.
(i)
Maximise Z=3x+4y subject to
2x+5y ?60,
4x+2y ?40.
x, y >0. Solve by Graphical Method
Plot the graph
(8)
Level 1 Remembering
(ii) Which one is the best solution? (5)
2.
(i)
Min Z= 20x
1
+10 x
2
subject to
x
1
+2x
2
? 40,
3x
1
+x
2
? 30,
4x
1
+3x
2
? 60,
x
1
,x
2
? 0.
Solve by Graphical Method,
Plot the graph
(8)
Level 2 Understanding
(ii) Predict the value of x & y. (5)
3 Max Z= 5x1+4x2 subject to
x
1
-2x
2
? 1,
x
1
+2x
2
?3,
x
1
,x
2
? 0. Solve Graphically. Which one is the best
solution?
Level 3 Applying
4.
(i)
A Plant Manufacturer 2 Product A & B. The Profit Contribution
of each product has been estimated as Rs.300 for product A
and Rs.400 for Product B. Each Product passes through 3
departments of the plant. The time required for each product
and total time available in each department is as follows.
Department Hours
Required
Hours
Required
Available
Hours
during
month
Product
A
Product
B
I 2 3 1600
II 3 2 1500
III 1 1 700
The company has a contract to supply atleast 300 units of
Product B per month.
Formulate the LPP
(5)
Level 4
Analysing
(ii) Solve through Graphical Method
(8)
5. Solve the following LPP by graphical method.
Maximize Z= 3x
1
+2x
2
Subject t o
- 2x
1
+x
2
?1,
x
1
? 2,
x
1
+ x
2
? 3
and x
1
,x
2
? 0
Level 5 Evaluating
6. (i) Max Z= 1000x
1
+4000x
2
+5000x
3
Subject to 3x1+3x
3
?22,
x1+2x2+3x
3
? 14,
3x1+2x2 ? 14
& x1,x2 ? 0
Develop a Simplex Table
(5)
Level 6 Creating
(ii) Analyse and find the value of x
1
, x
2
? (8)
7. Analyze the following LPP by Simplex Method:
Min Z = -10y
1
-15y
2
-20y
3
Subject to 2y
1
+4y
2
+6y
3
? 24,
3y
1
+9y
2
+6y
3
? 30,
& y
1
, y
2
, y
3
? 0.
Level 1 Remembering
(i)
Develop a Simplex Table (5)
(ii) Solve and find the value of y1 ,y2 and y3
(8)
8.
Solve By Graphical Method
Minimize Z= 40x
1
+24x
2
Subject to, 20x
1
+50 x
2
> 4,800
80 x
1
+50x
2
> 7,200
x
1
,x
2
>0
Level 2 Understanding
9. Solve the following LPP by simplex method:
Minimize Z= 8x
1
-2x
2
Subject to -4x
1
+2x
2
?1,
5x
1
-4x
2
?3,
and x
1
,x
2
? 0
Level 3 Applying
10. Solve the following LPP by simplex method:
Maximize Z= 3x1+2x
2
Subject to
2x
1
+x
2
?2,
3x
1
+4x
2
?12,
x
1
,x
2
? 0
Level 4 Analyzing
11. Review the LPP and solve by simplex method
Max Z= 25x+10y
Subject to the constraints
x+0.5y? 20
x+y? 50
x,y ? 0
Level 1 Remembering
12. A firm produces three products. These products are
processors on 3 different machines. The time required for
manufacturing one unit of cost of the products and the daily
capacity of the three machines is given in the table below.
Analyse and find the optimum solution.
Mac
hine
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Machine
Capacity
Min /Day
Product1 Product 2 Product 3
M1 2 8 2 940
M2 4 - 8 970
M3 2 5 - 430
It is required to determine the daily no. of units to be
manufactured for each product. The profit for unit for
Level 2 Understanding
product 1,2,3 is Rs.4,Rs.8,Rs.6 respectively. It is assumed
that all the amount produced are consumed in the market
13. Using dual simplex method , solve and find the optimum
solution for the given LPP.
Maximize Z=6x
1
+4x
2
+4x
3
Subject to 3x
1
,x
2
+2x
3
? 2
2x
1
+x
2
-x
3
? 1
-x
1
+x
2
+2x
3
? 1 &
x
1
,x
2
,x
3
? 0
Level 4 Analysing
14.
(i)
Evaluate by using dual simplex method and solve the LPP.
Minimize Z=2x
1
+x
2
Subject to 3x
1
+2x
2
? 3
4x
1
+3x
2
? 6
x
1
+x
2
? 5 & x
1
,x
2
?
Determine the dual simplex table
(5)
Level 1 Remembering
(ii)
Find the value of x
1
, x
2
(8)
PART - C
S.No Questions BT
LEVEL
COMPETENCE
1.
Max Z=300x+400y subject to
2x+3y ? 1600,
3x+2y ? 1500,
x+y ? 700,
y ? 300, x,y ? 0 Solve by Graphical Method, choose the
value of x & y which maximizes profit.
Level 1 Remembering
2. Solve the following LPP by graphical method.
Minimize Z= 6000x1+4000x
2
Subject t o
3x+x
2
? 40,
x
1
+2.5 x
2
? 22
3x
1
+3 x
2
? 40
and x
1
,x
2
? 0
Level 2 Understanding
3. Develop a Simplex Table and Solve
Max Z = 3 x1+2 x2,
Subject to
x1+ x2 ?4,
x1- x2 ? 2;
x1, x2 ?0.
Level 3 Applying
4. Solve by using Simplex Method.
Maximize Z= 3x+5y
Subject to the constraints
x+y? 60
x? 40
y ? 30
x,y ? 0
Level 1 Remembering
UNIT - II LINEAR PROGRAMMING EXTENSIONS
SYLLABUS: Transportation Models (Minimizing and Maximizing Problems) ? Balanced and unbalanced
Problems ? Initial Basic feasible solution by N-W Corner Rule, Least cost and Vogel?s approximation methods.
Check for optimality. Solution by MODI /. Case of Degeneracy. Trans-shipment Models. Assignment Models
(Minimising and Maximising Problems) ? Balanced and Unbalanced Problems. Solution by Hungarian and
Branch and Bound Algorithms. Travelling Salesman problem.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define Transportation & Transhipment. Level 1 Remembering
2. Differentiate balanced transportation problem & Unbalanced
Transportation Problem.
Level 2 Understanding
3. How would you show your understanding on unbalanced
transportation problem?
Level 3 Applying
4. Categorize the Phases of transportation model. Level 4 Analysing
5. Construct the basic feasible solution for the following
transportation problem.
1 2 3 4 SUPPLY
1 2 3 11 7 6
2 1 0 6 1 1
3 5 8 15 9 10
DEMAN D 7 5 3 2
Level 5 Evaluating
6 Interpret the need for Optimum solution in transportation. Level 6 Creating
7. What do you mean by Least cost method (LCM)? Level 1 Remembering
8. Compare Vogel approximation method (VAM) & Least Cost
Method.
Level 2 Understanding
9. How do you represent a travelling salesman problem
through mathematical formulation?
Level 3 Applying
10. Analyse the rules of travelling salesman Problem. Level 4 Analysing
11. Discuss the meaning of Assignment Level 5 Evaluating
12. Compare Balanced assignment problem & Unbalanced
Assignment Problem.
Level 6 Creating
13. What example can you give for Unbalanced assignment
problem?
Level 1 Remembering
14. How will you resolve degeneracy in Transportation Problem? Level 2 Understanding
15. Classify transportation problem. Level 3 Applying
16. Examine the Steps in Hungarian algorithm. Level 4 Analysing
17. What is Branch and bound algorithm in Assignment? Level 1 Remembering
18. Compare Assignment and transportation Problem. Level 2 Understanding
19. What do you mean by Travelling Salesman Problem? Level 1 Remembering
20. What is Restricted Assignment? Level 1 Remembering
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Solve and find the Transportation Problem and Which method will
you select if you want toMinimize Cost?
Destination Supply
1 2 3 4
I 21 16 25 13 11
II 17 18 14 23 13
III 32 27 18 41 19
Demand 6 10 12 15
Level 1 Remembering
2. Find the Initial Basic Feasible solution for following TP. Using NW
Rule, LCM, and VAM. Which method will you select if you want to
Minimize Cost?
D1 D2 D3 Supply
S1 7 3 2 2
S2 2 1 3 3
S3 3 4 6 5
Demand 4 1 5 10
Level 2 Understanding
3.
(i)
Analyze the transportation problem with unit transportation
costs,demand, and supply as given below:
Destination
Supply
Source
D1 D2 D3 D4
S1
6 1 9 3
70
11 5 2 8
S2 55
10 12 4 7
S3
70
Demand 85 35 50 45
Apply VAM for Initial solution.
(5)
Level 3 Applying
(ii)
Construct the final Solution by using MODIMethod.
(8)
4.
(i)
Analyze & solve the following transportation problem to maximize
profit.
A B C D Supply
1
Source 2
3
Demand
15 51 42 33 23
80 42 26 81 44
90 40 66 60 33
23
31
16
30
100
Examine Initial solution using VAM.
(5)
Level 4 Analysing
(ii)
Analyze and find out the final Solution by using MODI Method.
(8)
5. Solve the following transportation problem using Vogel?s
method
Factory? Warehouse ?Available
A B C D E F
1 9 12 9 6 9 10 5
2 7 3 7 7 5 5 6
3 6 5 9 11 3 11 2
4 6 8 11 2 2 10 9
4 4 6 2 4 2
Requirement?
(5)
Level 5 Evaluating
6. (i) Solve the transportation problem and decide using VAM for initial
solution.
(5) Level 6 Creating
(ii) Evaluate using NWC and Least Cost method for initial solution?
Destination Supply
I 2 1 25 13 11
II 1 1 14 23 13
III 3 2 18 41 19
Demand 6 1 22 15
(8)
7.
Maximize profit from the following transportationproblem.
A B C D Supply
I 40 25 22 33 100
SourceII 44 35 30 30 30
III 38 38 28 30 70
Demand 40 20 60 30
Level 1 Remembering
(i) How will you convert maximization problem to minimization.
Find the maximum profit
(8)
(ii) Explain stepping stone method for checking the
solution for optimality transportation problems.
(5)
8. A company has one surplus truck in each of the cities A, B, C, D, &
E and one deficit trucks in each of the cities 1,2,3,4,5,6. The
distance between the cities in kms is shown in the matrix below.
Can you select the assignment of trucks from cities in surplus to
cities in deficiency .so that total distance covered by the vehicles is
minimum?
1 2 3 4 5 6
A 12 10 15 22 18 8
B 10 18 25 15 16 12
C 11 10 3 8 5 9
D 6 4 10 13 13 12
E 8 12 11 7 13 10
Level 2 Understanding
9.
Consider the problem of assigning five jobs to five persons. The
assignment costs are given as follows:
PERSONS?JOBS ?
1 2 3 4 5
A 8 4 2 6 1
B 0 9 5 5 4
C 3 8 9 2 6
D 4 3 1 0 3
Level 3 Applying
E 9 5 8 9 5
Determine the optimum assignment schedule.
10. The assignment cost of assigning any one operator to any one
machine is given in the following table.
MACHINE?OPERATORS ?
I II III IV
A 10 5 13 15
B 3 9 18 3
C 10 7 3 2
D 5 11 9 7
Find the optimal assignment by Hungarian method.
Level 4 Analysing
11. A machine shop purchased a drilling machine and two lathes of
different capacities. The Positioning of the machines among 4
possible locations on the shop floor is important forms the
standard of materials handling. Given the cost estimate per unit
time of materials below, find the optimum location of the
machines.
LOCATIONS
1 2 3 4
Lathe 1 12 9 12 9
Drill 15 Not
suitable
13 20
Lathe 2 4 8 10 6
Level 1 Remembering
12.
Solve the assignment problem for maximization given profit
matrix(profit in rupees).
Machines
P Q R S
JOB
51 53 54 50
47 50 48 50
49 50 60 61
63 64 60 60
Level 2 Understanding
PART - C
S.No Questions Marks BT
Level
Competence
1.
a
Assume that you are an OR specialist. Identify the procedure
for each of the following Method to the employees in order to
help them achieve solution to Transportation Problems.
Northwest Corner Cell Method
(3)
Level 1 Remembering
b Least Cost cell Method (4)
c Vogel?s Approximation Method (4)
d U V Method. (4)
13. The processing time in hours for the jobs when allocated to the
different machines is indicated below. Select the best assignment
of the machines for the jobs so that the total processing time is
Minimum.
Machines
M1 M2 M3 M4 M5
J1 9 22 58 11 19
JOB J2 43 78 72 50 63
J3 41 28 91 37 45
J4 74 42 27 49 39
J5 36 11 57 22 25
Level 4 Analysing
14. For the given travelling salesman problem, Minimize the total cost.
To
1 2 3 4
From A - 46 16 40
B 41 - 50 40
C 82 32 - 60
D 40 40 36 -
Level 1 Remembering
(i) Observe the above travelling salesman
problem and find out minimize the cost per
cycle.
(8)
(ii) Find whether path is satisfied. (5)
FirstRanker.com - FirstRanker's Choice
(An
?
DEPARTMENT OF MANAGEMENT STUDIES
QUESTION BANK
II SEMESTER
1915201? APPLIED OPERATIONS RESEACH
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Dr. Radha Ganesh Kumar ? Asst. Professor (Sel.G) and HOD
Mr.B. Sam Paul ? Asst. Professor (OG)
(An
? .
DEPARTMENT OFMANAGEMENT STUDIES
QUESTION BANK
SUBJECT :1915201 ?APPLIED OPERATIONS RESEACH
SEM / YEAR : IISemester / IYear
UNIT ? I ?INTRODUCTION TO LINEAR PROGRAMMING (LP)
SYLLABUS: Introduction to applications of operations research in functional areas of management.
Linear Programming-formulation, solution by graphical and simplex methods, Special cases. Dual
simplex method. Principles of Duality. Sensitivity Analysis.
PART- A
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Define Operations Research (OR). Level 1 Remembering
2. Differentiate between Simplex and Big M Method Level 2 Understanding
3. How do you show your understanding unbounded solution? Level 3 Applying
4. Categorize the forms of LPP. Level 4 Analysing
5.
Discuss why is two phase method is better than Big M
method?
Level 5 Evaluating
6. Interpret the usage of Sensitivity Analysis in LPP. Level 6 Creating
7. What are the assumptions and requirements of LPP? Level 1 Remembering
8. Compare Dual Simplex and Duality. Level 2 Understanding
9. Identify the Advantages of duality. Level 3 Applying
10. What do you think about Infeasible solution? Level 4 Analysing
11. How will you solve LPP graphically? Level 5 Evaluating
12.
Conclude your understanding on the mathematical
formulation of LPP.
Level 6 Creating
13. Define basic variables and artificial variables. Level 1 Remembering
14. Compare Slack variable & Surplus Variable. Level 2 Understanding
15.
Give some example for the role of Surplus variable & Slack
Variable in the simplex method
Level 3 Applying
16. How would you apply Artificial variable? Level 4 Analysing
17. What is Big M Method? Level 1 Remembering
18. Distinguish simplex and Big M method Level 2 Understanding
19.
What do you mean by Duality? List the Rules for primal and
dual.
Level 1 Remembering
20. What is Shadow price? Level 1 Remembering
PART- B
S.NO
QUESTIONS
BT
LEVEL
COMPETENCE
1.
(i)
Maximise Z=3x+4y subject to
2x+5y ?60,
4x+2y ?40.
x, y >0. Solve by Graphical Method
Plot the graph
(8)
Level 1 Remembering
(ii) Which one is the best solution? (5)
2.
(i)
Min Z= 20x
1
+10 x
2
subject to
x
1
+2x
2
? 40,
3x
1
+x
2
? 30,
4x
1
+3x
2
? 60,
x
1
,x
2
? 0.
Solve by Graphical Method,
Plot the graph
(8)
Level 2 Understanding
(ii) Predict the value of x & y. (5)
3 Max Z= 5x1+4x2 subject to
x
1
-2x
2
? 1,
x
1
+2x
2
?3,
x
1
,x
2
? 0. Solve Graphically. Which one is the best
solution?
Level 3 Applying
4.
(i)
A Plant Manufacturer 2 Product A & B. The Profit Contribution
of each product has been estimated as Rs.300 for product A
and Rs.400 for Product B. Each Product passes through 3
departments of the plant. The time required for each product
and total time available in each department is as follows.
Department Hours
Required
Hours
Required
Available
Hours
during
month
Product
A
Product
B
I 2 3 1600
II 3 2 1500
III 1 1 700
The company has a contract to supply atleast 300 units of
Product B per month.
Formulate the LPP
(5)
Level 4
Analysing
(ii) Solve through Graphical Method
(8)
5. Solve the following LPP by graphical method.
Maximize Z= 3x
1
+2x
2
Subject t o
- 2x
1
+x
2
?1,
x
1
? 2,
x
1
+ x
2
? 3
and x
1
,x
2
? 0
Level 5 Evaluating
6. (i) Max Z= 1000x
1
+4000x
2
+5000x
3
Subject to 3x1+3x
3
?22,
x1+2x2+3x
3
? 14,
3x1+2x2 ? 14
& x1,x2 ? 0
Develop a Simplex Table
(5)
Level 6 Creating
(ii) Analyse and find the value of x
1
, x
2
? (8)
7. Analyze the following LPP by Simplex Method:
Min Z = -10y
1
-15y
2
-20y
3
Subject to 2y
1
+4y
2
+6y
3
? 24,
3y
1
+9y
2
+6y
3
? 30,
& y
1
, y
2
, y
3
? 0.
Level 1 Remembering
(i)
Develop a Simplex Table (5)
(ii) Solve and find the value of y1 ,y2 and y3
(8)
8.
Solve By Graphical Method
Minimize Z= 40x
1
+24x
2
Subject to, 20x
1
+50 x
2
> 4,800
80 x
1
+50x
2
> 7,200
x
1
,x
2
>0
Level 2 Understanding
9. Solve the following LPP by simplex method:
Minimize Z= 8x
1
-2x
2
Subject to -4x
1
+2x
2
?1,
5x
1
-4x
2
?3,
and x
1
,x
2
? 0
Level 3 Applying
10. Solve the following LPP by simplex method:
Maximize Z= 3x1+2x
2
Subject to
2x
1
+x
2
?2,
3x
1
+4x
2
?12,
x
1
,x
2
? 0
Level 4 Analyzing
11. Review the LPP and solve by simplex method
Max Z= 25x+10y
Subject to the constraints
x+0.5y? 20
x+y? 50
x,y ? 0
Level 1 Remembering
12. A firm produces three products. These products are
processors on 3 different machines. The time required for
manufacturing one unit of cost of the products and the daily
capacity of the three machines is given in the table below.
Analyse and find the optimum solution.
Mac
hine
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Machine
Capacity
Min /Day
Product1 Product 2 Product 3
M1 2 8 2 940
M2 4 - 8 970
M3 2 5 - 430
It is required to determine the daily no. of units to be
manufactured for each product. The profit for unit for
Level 2 Understanding
product 1,2,3 is Rs.4,Rs.8,Rs.6 respectively. It is assumed
that all the amount produced are consumed in the market
13. Using dual simplex method , solve and find the optimum
solution for the given LPP.
Maximize Z=6x
1
+4x
2
+4x
3
Subject to 3x
1
,x
2
+2x
3
? 2
2x
1
+x
2
-x
3
? 1
-x
1
+x
2
+2x
3
? 1 &
x
1
,x
2
,x
3
? 0
Level 4 Analysing
14.
(i)
Evaluate by using dual simplex method and solve the LPP.
Minimize Z=2x
1
+x
2
Subject to 3x
1
+2x
2
? 3
4x
1
+3x
2
? 6
x
1
+x
2
? 5 & x
1
,x
2
?
Determine the dual simplex table
(5)
Level 1 Remembering
(ii)
Find the value of x
1
, x
2
(8)
PART - C
S.No Questions BT
LEVEL
COMPETENCE
1.
Max Z=300x+400y subject to
2x+3y ? 1600,
3x+2y ? 1500,
x+y ? 700,
y ? 300, x,y ? 0 Solve by Graphical Method, choose the
value of x & y which maximizes profit.
Level 1 Remembering
2. Solve the following LPP by graphical method.
Minimize Z= 6000x1+4000x
2
Subject t o
3x+x
2
? 40,
x
1
+2.5 x
2
? 22
3x
1
+3 x
2
? 40
and x
1
,x
2
? 0
Level 2 Understanding
3. Develop a Simplex Table and Solve
Max Z = 3 x1+2 x2,
Subject to
x1+ x2 ?4,
x1- x2 ? 2;
x1, x2 ?0.
Level 3 Applying
4. Solve by using Simplex Method.
Maximize Z= 3x+5y
Subject to the constraints
x+y? 60
x? 40
y ? 30
x,y ? 0
Level 1 Remembering
UNIT - II LINEAR PROGRAMMING EXTENSIONS
SYLLABUS: Transportation Models (Minimizing and Maximizing Problems) ? Balanced and unbalanced
Problems ? Initial Basic feasible solution by N-W Corner Rule, Least cost and Vogel?s approximation methods.
Check for optimality. Solution by MODI /. Case of Degeneracy. Trans-shipment Models. Assignment Models
(Minimising and Maximising Problems) ? Balanced and Unbalanced Problems. Solution by Hungarian and
Branch and Bound Algorithms. Travelling Salesman problem.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define Transportation & Transhipment. Level 1 Remembering
2. Differentiate balanced transportation problem & Unbalanced
Transportation Problem.
Level 2 Understanding
3. How would you show your understanding on unbalanced
transportation problem?
Level 3 Applying
4. Categorize the Phases of transportation model. Level 4 Analysing
5. Construct the basic feasible solution for the following
transportation problem.
1 2 3 4 SUPPLY
1 2 3 11 7 6
2 1 0 6 1 1
3 5 8 15 9 10
DEMAN D 7 5 3 2
Level 5 Evaluating
6 Interpret the need for Optimum solution in transportation. Level 6 Creating
7. What do you mean by Least cost method (LCM)? Level 1 Remembering
8. Compare Vogel approximation method (VAM) & Least Cost
Method.
Level 2 Understanding
9. How do you represent a travelling salesman problem
through mathematical formulation?
Level 3 Applying
10. Analyse the rules of travelling salesman Problem. Level 4 Analysing
11. Discuss the meaning of Assignment Level 5 Evaluating
12. Compare Balanced assignment problem & Unbalanced
Assignment Problem.
Level 6 Creating
13. What example can you give for Unbalanced assignment
problem?
Level 1 Remembering
14. How will you resolve degeneracy in Transportation Problem? Level 2 Understanding
15. Classify transportation problem. Level 3 Applying
16. Examine the Steps in Hungarian algorithm. Level 4 Analysing
17. What is Branch and bound algorithm in Assignment? Level 1 Remembering
18. Compare Assignment and transportation Problem. Level 2 Understanding
19. What do you mean by Travelling Salesman Problem? Level 1 Remembering
20. What is Restricted Assignment? Level 1 Remembering
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Solve and find the Transportation Problem and Which method will
you select if you want toMinimize Cost?
Destination Supply
1 2 3 4
I 21 16 25 13 11
II 17 18 14 23 13
III 32 27 18 41 19
Demand 6 10 12 15
Level 1 Remembering
2. Find the Initial Basic Feasible solution for following TP. Using NW
Rule, LCM, and VAM. Which method will you select if you want to
Minimize Cost?
D1 D2 D3 Supply
S1 7 3 2 2
S2 2 1 3 3
S3 3 4 6 5
Demand 4 1 5 10
Level 2 Understanding
3.
(i)
Analyze the transportation problem with unit transportation
costs,demand, and supply as given below:
Destination
Supply
Source
D1 D2 D3 D4
S1
6 1 9 3
70
11 5 2 8
S2 55
10 12 4 7
S3
70
Demand 85 35 50 45
Apply VAM for Initial solution.
(5)
Level 3 Applying
(ii)
Construct the final Solution by using MODIMethod.
(8)
4.
(i)
Analyze & solve the following transportation problem to maximize
profit.
A B C D Supply
1
Source 2
3
Demand
15 51 42 33 23
80 42 26 81 44
90 40 66 60 33
23
31
16
30
100
Examine Initial solution using VAM.
(5)
Level 4 Analysing
(ii)
Analyze and find out the final Solution by using MODI Method.
(8)
5. Solve the following transportation problem using Vogel?s
method
Factory? Warehouse ?Available
A B C D E F
1 9 12 9 6 9 10 5
2 7 3 7 7 5 5 6
3 6 5 9 11 3 11 2
4 6 8 11 2 2 10 9
4 4 6 2 4 2
Requirement?
(5)
Level 5 Evaluating
6. (i) Solve the transportation problem and decide using VAM for initial
solution.
(5) Level 6 Creating
(ii) Evaluate using NWC and Least Cost method for initial solution?
Destination Supply
I 2 1 25 13 11
II 1 1 14 23 13
III 3 2 18 41 19
Demand 6 1 22 15
(8)
7.
Maximize profit from the following transportationproblem.
A B C D Supply
I 40 25 22 33 100
SourceII 44 35 30 30 30
III 38 38 28 30 70
Demand 40 20 60 30
Level 1 Remembering
(i) How will you convert maximization problem to minimization.
Find the maximum profit
(8)
(ii) Explain stepping stone method for checking the
solution for optimality transportation problems.
(5)
8. A company has one surplus truck in each of the cities A, B, C, D, &
E and one deficit trucks in each of the cities 1,2,3,4,5,6. The
distance between the cities in kms is shown in the matrix below.
Can you select the assignment of trucks from cities in surplus to
cities in deficiency .so that total distance covered by the vehicles is
minimum?
1 2 3 4 5 6
A 12 10 15 22 18 8
B 10 18 25 15 16 12
C 11 10 3 8 5 9
D 6 4 10 13 13 12
E 8 12 11 7 13 10
Level 2 Understanding
9.
Consider the problem of assigning five jobs to five persons. The
assignment costs are given as follows:
PERSONS?JOBS ?
1 2 3 4 5
A 8 4 2 6 1
B 0 9 5 5 4
C 3 8 9 2 6
D 4 3 1 0 3
Level 3 Applying
E 9 5 8 9 5
Determine the optimum assignment schedule.
10. The assignment cost of assigning any one operator to any one
machine is given in the following table.
MACHINE?OPERATORS ?
I II III IV
A 10 5 13 15
B 3 9 18 3
C 10 7 3 2
D 5 11 9 7
Find the optimal assignment by Hungarian method.
Level 4 Analysing
11. A machine shop purchased a drilling machine and two lathes of
different capacities. The Positioning of the machines among 4
possible locations on the shop floor is important forms the
standard of materials handling. Given the cost estimate per unit
time of materials below, find the optimum location of the
machines.
LOCATIONS
1 2 3 4
Lathe 1 12 9 12 9
Drill 15 Not
suitable
13 20
Lathe 2 4 8 10 6
Level 1 Remembering
12.
Solve the assignment problem for maximization given profit
matrix(profit in rupees).
Machines
P Q R S
JOB
51 53 54 50
47 50 48 50
49 50 60 61
63 64 60 60
Level 2 Understanding
PART - C
S.No Questions Marks BT
Level
Competence
1.
a
Assume that you are an OR specialist. Identify the procedure
for each of the following Method to the employees in order to
help them achieve solution to Transportation Problems.
Northwest Corner Cell Method
(3)
Level 1 Remembering
b Least Cost cell Method (4)
c Vogel?s Approximation Method (4)
d U V Method. (4)
13. The processing time in hours for the jobs when allocated to the
different machines is indicated below. Select the best assignment
of the machines for the jobs so that the total processing time is
Minimum.
Machines
M1 M2 M3 M4 M5
J1 9 22 58 11 19
JOB J2 43 78 72 50 63
J3 41 28 91 37 45
J4 74 42 27 49 39
J5 36 11 57 22 25
Level 4 Analysing
14. For the given travelling salesman problem, Minimize the total cost.
To
1 2 3 4
From A - 46 16 40
B 41 - 50 40
C 82 32 - 60
D 40 40 36 -
Level 1 Remembering
(i) Observe the above travelling salesman
problem and find out minimize the cost per
cycle.
(8)
(ii) Find whether path is satisfied. (5)
2.
Solve the following transportation problem, in which a
i
is the
availability at Origin
O
i
and b
j
is the requirement at the destination D
j
and cell entries
are unit costs of transportation from any origin to any
destination:
D1 D2 D3 D4 D5 a
j
O1 4 7 3 8 2 4
O2 1 4 7 3 8 7
O3 7 2 4 7 7 9
O4 4 8 2 4 7 2
b
j
8 3 7 2 2
Predict the allocation to minimize the cost.
Level 2 Understanding
3. A company has a team of 4 Salesman and the company wants to
do in 4 districts. Considering the capabilities of salesmen
and nature of the district, the company has estimated the profit per
day in Rs. For each salesmen in each district as follows.
District
s
Salesmen 1 2 3 4
A 16 10 14 11
B 14 11 15 15
C 15 15 13 12
D 13 12 14 15
Develop the best assignment schedule and analyze the total cost.
Level 3 Applying
4. Five operators have to be assigned to Five Machines. The
assignment costs are given in thetablebelow.
Analyse using Hungarian algorithm & find out the assignment to
minimize the cost.
Machine
I II III IV V
Operator
A 5 5 - 2 6
B 7 4 2 3 4
C 9 3 5 - 3
D 7 2 6 7 2
E 6 5 7 9 1
Level 4 Analyzing
FirstRanker.com - FirstRanker's Choice
(An
?
DEPARTMENT OF MANAGEMENT STUDIES
QUESTION BANK
II SEMESTER
1915201? APPLIED OPERATIONS RESEACH
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Dr. Radha Ganesh Kumar ? Asst. Professor (Sel.G) and HOD
Mr.B. Sam Paul ? Asst. Professor (OG)
(An
? .
DEPARTMENT OFMANAGEMENT STUDIES
QUESTION BANK
SUBJECT :1915201 ?APPLIED OPERATIONS RESEACH
SEM / YEAR : IISemester / IYear
UNIT ? I ?INTRODUCTION TO LINEAR PROGRAMMING (LP)
SYLLABUS: Introduction to applications of operations research in functional areas of management.
Linear Programming-formulation, solution by graphical and simplex methods, Special cases. Dual
simplex method. Principles of Duality. Sensitivity Analysis.
PART- A
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Define Operations Research (OR). Level 1 Remembering
2. Differentiate between Simplex and Big M Method Level 2 Understanding
3. How do you show your understanding unbounded solution? Level 3 Applying
4. Categorize the forms of LPP. Level 4 Analysing
5.
Discuss why is two phase method is better than Big M
method?
Level 5 Evaluating
6. Interpret the usage of Sensitivity Analysis in LPP. Level 6 Creating
7. What are the assumptions and requirements of LPP? Level 1 Remembering
8. Compare Dual Simplex and Duality. Level 2 Understanding
9. Identify the Advantages of duality. Level 3 Applying
10. What do you think about Infeasible solution? Level 4 Analysing
11. How will you solve LPP graphically? Level 5 Evaluating
12.
Conclude your understanding on the mathematical
formulation of LPP.
Level 6 Creating
13. Define basic variables and artificial variables. Level 1 Remembering
14. Compare Slack variable & Surplus Variable. Level 2 Understanding
15.
Give some example for the role of Surplus variable & Slack
Variable in the simplex method
Level 3 Applying
16. How would you apply Artificial variable? Level 4 Analysing
17. What is Big M Method? Level 1 Remembering
18. Distinguish simplex and Big M method Level 2 Understanding
19.
What do you mean by Duality? List the Rules for primal and
dual.
Level 1 Remembering
20. What is Shadow price? Level 1 Remembering
PART- B
S.NO
QUESTIONS
BT
LEVEL
COMPETENCE
1.
(i)
Maximise Z=3x+4y subject to
2x+5y ?60,
4x+2y ?40.
x, y >0. Solve by Graphical Method
Plot the graph
(8)
Level 1 Remembering
(ii) Which one is the best solution? (5)
2.
(i)
Min Z= 20x
1
+10 x
2
subject to
x
1
+2x
2
? 40,
3x
1
+x
2
? 30,
4x
1
+3x
2
? 60,
x
1
,x
2
? 0.
Solve by Graphical Method,
Plot the graph
(8)
Level 2 Understanding
(ii) Predict the value of x & y. (5)
3 Max Z= 5x1+4x2 subject to
x
1
-2x
2
? 1,
x
1
+2x
2
?3,
x
1
,x
2
? 0. Solve Graphically. Which one is the best
solution?
Level 3 Applying
4.
(i)
A Plant Manufacturer 2 Product A & B. The Profit Contribution
of each product has been estimated as Rs.300 for product A
and Rs.400 for Product B. Each Product passes through 3
departments of the plant. The time required for each product
and total time available in each department is as follows.
Department Hours
Required
Hours
Required
Available
Hours
during
month
Product
A
Product
B
I 2 3 1600
II 3 2 1500
III 1 1 700
The company has a contract to supply atleast 300 units of
Product B per month.
Formulate the LPP
(5)
Level 4
Analysing
(ii) Solve through Graphical Method
(8)
5. Solve the following LPP by graphical method.
Maximize Z= 3x
1
+2x
2
Subject t o
- 2x
1
+x
2
?1,
x
1
? 2,
x
1
+ x
2
? 3
and x
1
,x
2
? 0
Level 5 Evaluating
6. (i) Max Z= 1000x
1
+4000x
2
+5000x
3
Subject to 3x1+3x
3
?22,
x1+2x2+3x
3
? 14,
3x1+2x2 ? 14
& x1,x2 ? 0
Develop a Simplex Table
(5)
Level 6 Creating
(ii) Analyse and find the value of x
1
, x
2
? (8)
7. Analyze the following LPP by Simplex Method:
Min Z = -10y
1
-15y
2
-20y
3
Subject to 2y
1
+4y
2
+6y
3
? 24,
3y
1
+9y
2
+6y
3
? 30,
& y
1
, y
2
, y
3
? 0.
Level 1 Remembering
(i)
Develop a Simplex Table (5)
(ii) Solve and find the value of y1 ,y2 and y3
(8)
8.
Solve By Graphical Method
Minimize Z= 40x
1
+24x
2
Subject to, 20x
1
+50 x
2
> 4,800
80 x
1
+50x
2
> 7,200
x
1
,x
2
>0
Level 2 Understanding
9. Solve the following LPP by simplex method:
Minimize Z= 8x
1
-2x
2
Subject to -4x
1
+2x
2
?1,
5x
1
-4x
2
?3,
and x
1
,x
2
? 0
Level 3 Applying
10. Solve the following LPP by simplex method:
Maximize Z= 3x1+2x
2
Subject to
2x
1
+x
2
?2,
3x
1
+4x
2
?12,
x
1
,x
2
? 0
Level 4 Analyzing
11. Review the LPP and solve by simplex method
Max Z= 25x+10y
Subject to the constraints
x+0.5y? 20
x+y? 50
x,y ? 0
Level 1 Remembering
12. A firm produces three products. These products are
processors on 3 different machines. The time required for
manufacturing one unit of cost of the products and the daily
capacity of the three machines is given in the table below.
Analyse and find the optimum solution.
Mac
hine
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Machine
Capacity
Min /Day
Product1 Product 2 Product 3
M1 2 8 2 940
M2 4 - 8 970
M3 2 5 - 430
It is required to determine the daily no. of units to be
manufactured for each product. The profit for unit for
Level 2 Understanding
product 1,2,3 is Rs.4,Rs.8,Rs.6 respectively. It is assumed
that all the amount produced are consumed in the market
13. Using dual simplex method , solve and find the optimum
solution for the given LPP.
Maximize Z=6x
1
+4x
2
+4x
3
Subject to 3x
1
,x
2
+2x
3
? 2
2x
1
+x
2
-x
3
? 1
-x
1
+x
2
+2x
3
? 1 &
x
1
,x
2
,x
3
? 0
Level 4 Analysing
14.
(i)
Evaluate by using dual simplex method and solve the LPP.
Minimize Z=2x
1
+x
2
Subject to 3x
1
+2x
2
? 3
4x
1
+3x
2
? 6
x
1
+x
2
? 5 & x
1
,x
2
?
Determine the dual simplex table
(5)
Level 1 Remembering
(ii)
Find the value of x
1
, x
2
(8)
PART - C
S.No Questions BT
LEVEL
COMPETENCE
1.
Max Z=300x+400y subject to
2x+3y ? 1600,
3x+2y ? 1500,
x+y ? 700,
y ? 300, x,y ? 0 Solve by Graphical Method, choose the
value of x & y which maximizes profit.
Level 1 Remembering
2. Solve the following LPP by graphical method.
Minimize Z= 6000x1+4000x
2
Subject t o
3x+x
2
? 40,
x
1
+2.5 x
2
? 22
3x
1
+3 x
2
? 40
and x
1
,x
2
? 0
Level 2 Understanding
3. Develop a Simplex Table and Solve
Max Z = 3 x1+2 x2,
Subject to
x1+ x2 ?4,
x1- x2 ? 2;
x1, x2 ?0.
Level 3 Applying
4. Solve by using Simplex Method.
Maximize Z= 3x+5y
Subject to the constraints
x+y? 60
x? 40
y ? 30
x,y ? 0
Level 1 Remembering
UNIT - II LINEAR PROGRAMMING EXTENSIONS
SYLLABUS: Transportation Models (Minimizing and Maximizing Problems) ? Balanced and unbalanced
Problems ? Initial Basic feasible solution by N-W Corner Rule, Least cost and Vogel?s approximation methods.
Check for optimality. Solution by MODI /. Case of Degeneracy. Trans-shipment Models. Assignment Models
(Minimising and Maximising Problems) ? Balanced and Unbalanced Problems. Solution by Hungarian and
Branch and Bound Algorithms. Travelling Salesman problem.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define Transportation & Transhipment. Level 1 Remembering
2. Differentiate balanced transportation problem & Unbalanced
Transportation Problem.
Level 2 Understanding
3. How would you show your understanding on unbalanced
transportation problem?
Level 3 Applying
4. Categorize the Phases of transportation model. Level 4 Analysing
5. Construct the basic feasible solution for the following
transportation problem.
1 2 3 4 SUPPLY
1 2 3 11 7 6
2 1 0 6 1 1
3 5 8 15 9 10
DEMAN D 7 5 3 2
Level 5 Evaluating
6 Interpret the need for Optimum solution in transportation. Level 6 Creating
7. What do you mean by Least cost method (LCM)? Level 1 Remembering
8. Compare Vogel approximation method (VAM) & Least Cost
Method.
Level 2 Understanding
9. How do you represent a travelling salesman problem
through mathematical formulation?
Level 3 Applying
10. Analyse the rules of travelling salesman Problem. Level 4 Analysing
11. Discuss the meaning of Assignment Level 5 Evaluating
12. Compare Balanced assignment problem & Unbalanced
Assignment Problem.
Level 6 Creating
13. What example can you give for Unbalanced assignment
problem?
Level 1 Remembering
14. How will you resolve degeneracy in Transportation Problem? Level 2 Understanding
15. Classify transportation problem. Level 3 Applying
16. Examine the Steps in Hungarian algorithm. Level 4 Analysing
17. What is Branch and bound algorithm in Assignment? Level 1 Remembering
18. Compare Assignment and transportation Problem. Level 2 Understanding
19. What do you mean by Travelling Salesman Problem? Level 1 Remembering
20. What is Restricted Assignment? Level 1 Remembering
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Solve and find the Transportation Problem and Which method will
you select if you want toMinimize Cost?
Destination Supply
1 2 3 4
I 21 16 25 13 11
II 17 18 14 23 13
III 32 27 18 41 19
Demand 6 10 12 15
Level 1 Remembering
2. Find the Initial Basic Feasible solution for following TP. Using NW
Rule, LCM, and VAM. Which method will you select if you want to
Minimize Cost?
D1 D2 D3 Supply
S1 7 3 2 2
S2 2 1 3 3
S3 3 4 6 5
Demand 4 1 5 10
Level 2 Understanding
3.
(i)
Analyze the transportation problem with unit transportation
costs,demand, and supply as given below:
Destination
Supply
Source
D1 D2 D3 D4
S1
6 1 9 3
70
11 5 2 8
S2 55
10 12 4 7
S3
70
Demand 85 35 50 45
Apply VAM for Initial solution.
(5)
Level 3 Applying
(ii)
Construct the final Solution by using MODIMethod.
(8)
4.
(i)
Analyze & solve the following transportation problem to maximize
profit.
A B C D Supply
1
Source 2
3
Demand
15 51 42 33 23
80 42 26 81 44
90 40 66 60 33
23
31
16
30
100
Examine Initial solution using VAM.
(5)
Level 4 Analysing
(ii)
Analyze and find out the final Solution by using MODI Method.
(8)
5. Solve the following transportation problem using Vogel?s
method
Factory? Warehouse ?Available
A B C D E F
1 9 12 9 6 9 10 5
2 7 3 7 7 5 5 6
3 6 5 9 11 3 11 2
4 6 8 11 2 2 10 9
4 4 6 2 4 2
Requirement?
(5)
Level 5 Evaluating
6. (i) Solve the transportation problem and decide using VAM for initial
solution.
(5) Level 6 Creating
(ii) Evaluate using NWC and Least Cost method for initial solution?
Destination Supply
I 2 1 25 13 11
II 1 1 14 23 13
III 3 2 18 41 19
Demand 6 1 22 15
(8)
7.
Maximize profit from the following transportationproblem.
A B C D Supply
I 40 25 22 33 100
SourceII 44 35 30 30 30
III 38 38 28 30 70
Demand 40 20 60 30
Level 1 Remembering
(i) How will you convert maximization problem to minimization.
Find the maximum profit
(8)
(ii) Explain stepping stone method for checking the
solution for optimality transportation problems.
(5)
8. A company has one surplus truck in each of the cities A, B, C, D, &
E and one deficit trucks in each of the cities 1,2,3,4,5,6. The
distance between the cities in kms is shown in the matrix below.
Can you select the assignment of trucks from cities in surplus to
cities in deficiency .so that total distance covered by the vehicles is
minimum?
1 2 3 4 5 6
A 12 10 15 22 18 8
B 10 18 25 15 16 12
C 11 10 3 8 5 9
D 6 4 10 13 13 12
E 8 12 11 7 13 10
Level 2 Understanding
9.
Consider the problem of assigning five jobs to five persons. The
assignment costs are given as follows:
PERSONS?JOBS ?
1 2 3 4 5
A 8 4 2 6 1
B 0 9 5 5 4
C 3 8 9 2 6
D 4 3 1 0 3
Level 3 Applying
E 9 5 8 9 5
Determine the optimum assignment schedule.
10. The assignment cost of assigning any one operator to any one
machine is given in the following table.
MACHINE?OPERATORS ?
I II III IV
A 10 5 13 15
B 3 9 18 3
C 10 7 3 2
D 5 11 9 7
Find the optimal assignment by Hungarian method.
Level 4 Analysing
11. A machine shop purchased a drilling machine and two lathes of
different capacities. The Positioning of the machines among 4
possible locations on the shop floor is important forms the
standard of materials handling. Given the cost estimate per unit
time of materials below, find the optimum location of the
machines.
LOCATIONS
1 2 3 4
Lathe 1 12 9 12 9
Drill 15 Not
suitable
13 20
Lathe 2 4 8 10 6
Level 1 Remembering
12.
Solve the assignment problem for maximization given profit
matrix(profit in rupees).
Machines
P Q R S
JOB
51 53 54 50
47 50 48 50
49 50 60 61
63 64 60 60
Level 2 Understanding
PART - C
S.No Questions Marks BT
Level
Competence
1.
a
Assume that you are an OR specialist. Identify the procedure
for each of the following Method to the employees in order to
help them achieve solution to Transportation Problems.
Northwest Corner Cell Method
(3)
Level 1 Remembering
b Least Cost cell Method (4)
c Vogel?s Approximation Method (4)
d U V Method. (4)
13. The processing time in hours for the jobs when allocated to the
different machines is indicated below. Select the best assignment
of the machines for the jobs so that the total processing time is
Minimum.
Machines
M1 M2 M3 M4 M5
J1 9 22 58 11 19
JOB J2 43 78 72 50 63
J3 41 28 91 37 45
J4 74 42 27 49 39
J5 36 11 57 22 25
Level 4 Analysing
14. For the given travelling salesman problem, Minimize the total cost.
To
1 2 3 4
From A - 46 16 40
B 41 - 50 40
C 82 32 - 60
D 40 40 36 -
Level 1 Remembering
(i) Observe the above travelling salesman
problem and find out minimize the cost per
cycle.
(8)
(ii) Find whether path is satisfied. (5)
2.
Solve the following transportation problem, in which a
i
is the
availability at Origin
O
i
and b
j
is the requirement at the destination D
j
and cell entries
are unit costs of transportation from any origin to any
destination:
D1 D2 D3 D4 D5 a
j
O1 4 7 3 8 2 4
O2 1 4 7 3 8 7
O3 7 2 4 7 7 9
O4 4 8 2 4 7 2
b
j
8 3 7 2 2
Predict the allocation to minimize the cost.
Level 2 Understanding
3. A company has a team of 4 Salesman and the company wants to
do in 4 districts. Considering the capabilities of salesmen
and nature of the district, the company has estimated the profit per
day in Rs. For each salesmen in each district as follows.
District
s
Salesmen 1 2 3 4
A 16 10 14 11
B 14 11 15 15
C 15 15 13 12
D 13 12 14 15
Develop the best assignment schedule and analyze the total cost.
Level 3 Applying
4. Five operators have to be assigned to Five Machines. The
assignment costs are given in thetablebelow.
Analyse using Hungarian algorithm & find out the assignment to
minimize the cost.
Machine
I II III IV V
Operator
A 5 5 - 2 6
B 7 4 2 3 4
C 9 3 5 - 3
D 7 2 6 7 2
E 6 5 7 9 1
Level 4 Analyzing
UNIT ? III ? INTEGER PROGRAMMING AND GAME THEORY
SYLLABUS: Integer Programming ? Introduction and types - Game Theory-Two-person Zero sum
games-Saddle point, Dominance Rule, graphical and LP solutions, Nash Equilibrium
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. What do you mean by integer programming problem?
Level 1 Remembering
2. In what respect a mixed IPP differs from pure IPP?
Level 2 Understanding
3. What is Nash Equilibrium?
Level 3 Applying
4. Classify the different types of strategy.
Level 4 Analysing
5. Compile the Characteristics of game.
Level 5 Evaluating
6. Can you assess the applications of integer
programming?
Level 6 Creating
7. Define Game.
Level 1 Remembering
8. Compare Mixed Strategy and Pure Strategy.
Level 2 Understanding
9. How would you make use of the concept of Game theory
in Managerial Decision Making?
Level 3 Applying
10. Conclude your understanding about Payoff Matrix.
Level 4 Analysing
11. How will you find the optimal strategies and value of the
following game?
Player B
Player
A
H T
H 2 -1
T -1 0
Level 5 Evaluating
12. Interpret the concept of two person zero sum game.
Level 6 Creating
13. What is Saddle point?
Level 1 Remembering
14. Compare Dominance Principle of Rows and Columns.
Level 2 Understanding
15. Identify the basic assumptions of the Game.
Level 3 Applying
16. Conclude the advantages of Game theory.
Level 4 Analysing
17. What are the Methods of Matrices?
Level 1 Remembering
FirstRanker.com - FirstRanker's Choice
(An
?
DEPARTMENT OF MANAGEMENT STUDIES
QUESTION BANK
II SEMESTER
1915201? APPLIED OPERATIONS RESEACH
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Dr. Radha Ganesh Kumar ? Asst. Professor (Sel.G) and HOD
Mr.B. Sam Paul ? Asst. Professor (OG)
(An
? .
DEPARTMENT OFMANAGEMENT STUDIES
QUESTION BANK
SUBJECT :1915201 ?APPLIED OPERATIONS RESEACH
SEM / YEAR : IISemester / IYear
UNIT ? I ?INTRODUCTION TO LINEAR PROGRAMMING (LP)
SYLLABUS: Introduction to applications of operations research in functional areas of management.
Linear Programming-formulation, solution by graphical and simplex methods, Special cases. Dual
simplex method. Principles of Duality. Sensitivity Analysis.
PART- A
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Define Operations Research (OR). Level 1 Remembering
2. Differentiate between Simplex and Big M Method Level 2 Understanding
3. How do you show your understanding unbounded solution? Level 3 Applying
4. Categorize the forms of LPP. Level 4 Analysing
5.
Discuss why is two phase method is better than Big M
method?
Level 5 Evaluating
6. Interpret the usage of Sensitivity Analysis in LPP. Level 6 Creating
7. What are the assumptions and requirements of LPP? Level 1 Remembering
8. Compare Dual Simplex and Duality. Level 2 Understanding
9. Identify the Advantages of duality. Level 3 Applying
10. What do you think about Infeasible solution? Level 4 Analysing
11. How will you solve LPP graphically? Level 5 Evaluating
12.
Conclude your understanding on the mathematical
formulation of LPP.
Level 6 Creating
13. Define basic variables and artificial variables. Level 1 Remembering
14. Compare Slack variable & Surplus Variable. Level 2 Understanding
15.
Give some example for the role of Surplus variable & Slack
Variable in the simplex method
Level 3 Applying
16. How would you apply Artificial variable? Level 4 Analysing
17. What is Big M Method? Level 1 Remembering
18. Distinguish simplex and Big M method Level 2 Understanding
19.
What do you mean by Duality? List the Rules for primal and
dual.
Level 1 Remembering
20. What is Shadow price? Level 1 Remembering
PART- B
S.NO
QUESTIONS
BT
LEVEL
COMPETENCE
1.
(i)
Maximise Z=3x+4y subject to
2x+5y ?60,
4x+2y ?40.
x, y >0. Solve by Graphical Method
Plot the graph
(8)
Level 1 Remembering
(ii) Which one is the best solution? (5)
2.
(i)
Min Z= 20x
1
+10 x
2
subject to
x
1
+2x
2
? 40,
3x
1
+x
2
? 30,
4x
1
+3x
2
? 60,
x
1
,x
2
? 0.
Solve by Graphical Method,
Plot the graph
(8)
Level 2 Understanding
(ii) Predict the value of x & y. (5)
3 Max Z= 5x1+4x2 subject to
x
1
-2x
2
? 1,
x
1
+2x
2
?3,
x
1
,x
2
? 0. Solve Graphically. Which one is the best
solution?
Level 3 Applying
4.
(i)
A Plant Manufacturer 2 Product A & B. The Profit Contribution
of each product has been estimated as Rs.300 for product A
and Rs.400 for Product B. Each Product passes through 3
departments of the plant. The time required for each product
and total time available in each department is as follows.
Department Hours
Required
Hours
Required
Available
Hours
during
month
Product
A
Product
B
I 2 3 1600
II 3 2 1500
III 1 1 700
The company has a contract to supply atleast 300 units of
Product B per month.
Formulate the LPP
(5)
Level 4
Analysing
(ii) Solve through Graphical Method
(8)
5. Solve the following LPP by graphical method.
Maximize Z= 3x
1
+2x
2
Subject t o
- 2x
1
+x
2
?1,
x
1
? 2,
x
1
+ x
2
? 3
and x
1
,x
2
? 0
Level 5 Evaluating
6. (i) Max Z= 1000x
1
+4000x
2
+5000x
3
Subject to 3x1+3x
3
?22,
x1+2x2+3x
3
? 14,
3x1+2x2 ? 14
& x1,x2 ? 0
Develop a Simplex Table
(5)
Level 6 Creating
(ii) Analyse and find the value of x
1
, x
2
? (8)
7. Analyze the following LPP by Simplex Method:
Min Z = -10y
1
-15y
2
-20y
3
Subject to 2y
1
+4y
2
+6y
3
? 24,
3y
1
+9y
2
+6y
3
? 30,
& y
1
, y
2
, y
3
? 0.
Level 1 Remembering
(i)
Develop a Simplex Table (5)
(ii) Solve and find the value of y1 ,y2 and y3
(8)
8.
Solve By Graphical Method
Minimize Z= 40x
1
+24x
2
Subject to, 20x
1
+50 x
2
> 4,800
80 x
1
+50x
2
> 7,200
x
1
,x
2
>0
Level 2 Understanding
9. Solve the following LPP by simplex method:
Minimize Z= 8x
1
-2x
2
Subject to -4x
1
+2x
2
?1,
5x
1
-4x
2
?3,
and x
1
,x
2
? 0
Level 3 Applying
10. Solve the following LPP by simplex method:
Maximize Z= 3x1+2x
2
Subject to
2x
1
+x
2
?2,
3x
1
+4x
2
?12,
x
1
,x
2
? 0
Level 4 Analyzing
11. Review the LPP and solve by simplex method
Max Z= 25x+10y
Subject to the constraints
x+0.5y? 20
x+y? 50
x,y ? 0
Level 1 Remembering
12. A firm produces three products. These products are
processors on 3 different machines. The time required for
manufacturing one unit of cost of the products and the daily
capacity of the three machines is given in the table below.
Analyse and find the optimum solution.
Mac
hine
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Machine
Capacity
Min /Day
Product1 Product 2 Product 3
M1 2 8 2 940
M2 4 - 8 970
M3 2 5 - 430
It is required to determine the daily no. of units to be
manufactured for each product. The profit for unit for
Level 2 Understanding
product 1,2,3 is Rs.4,Rs.8,Rs.6 respectively. It is assumed
that all the amount produced are consumed in the market
13. Using dual simplex method , solve and find the optimum
solution for the given LPP.
Maximize Z=6x
1
+4x
2
+4x
3
Subject to 3x
1
,x
2
+2x
3
? 2
2x
1
+x
2
-x
3
? 1
-x
1
+x
2
+2x
3
? 1 &
x
1
,x
2
,x
3
? 0
Level 4 Analysing
14.
(i)
Evaluate by using dual simplex method and solve the LPP.
Minimize Z=2x
1
+x
2
Subject to 3x
1
+2x
2
? 3
4x
1
+3x
2
? 6
x
1
+x
2
? 5 & x
1
,x
2
?
Determine the dual simplex table
(5)
Level 1 Remembering
(ii)
Find the value of x
1
, x
2
(8)
PART - C
S.No Questions BT
LEVEL
COMPETENCE
1.
Max Z=300x+400y subject to
2x+3y ? 1600,
3x+2y ? 1500,
x+y ? 700,
y ? 300, x,y ? 0 Solve by Graphical Method, choose the
value of x & y which maximizes profit.
Level 1 Remembering
2. Solve the following LPP by graphical method.
Minimize Z= 6000x1+4000x
2
Subject t o
3x+x
2
? 40,
x
1
+2.5 x
2
? 22
3x
1
+3 x
2
? 40
and x
1
,x
2
? 0
Level 2 Understanding
3. Develop a Simplex Table and Solve
Max Z = 3 x1+2 x2,
Subject to
x1+ x2 ?4,
x1- x2 ? 2;
x1, x2 ?0.
Level 3 Applying
4. Solve by using Simplex Method.
Maximize Z= 3x+5y
Subject to the constraints
x+y? 60
x? 40
y ? 30
x,y ? 0
Level 1 Remembering
UNIT - II LINEAR PROGRAMMING EXTENSIONS
SYLLABUS: Transportation Models (Minimizing and Maximizing Problems) ? Balanced and unbalanced
Problems ? Initial Basic feasible solution by N-W Corner Rule, Least cost and Vogel?s approximation methods.
Check for optimality. Solution by MODI /. Case of Degeneracy. Trans-shipment Models. Assignment Models
(Minimising and Maximising Problems) ? Balanced and Unbalanced Problems. Solution by Hungarian and
Branch and Bound Algorithms. Travelling Salesman problem.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define Transportation & Transhipment. Level 1 Remembering
2. Differentiate balanced transportation problem & Unbalanced
Transportation Problem.
Level 2 Understanding
3. How would you show your understanding on unbalanced
transportation problem?
Level 3 Applying
4. Categorize the Phases of transportation model. Level 4 Analysing
5. Construct the basic feasible solution for the following
transportation problem.
1 2 3 4 SUPPLY
1 2 3 11 7 6
2 1 0 6 1 1
3 5 8 15 9 10
DEMAN D 7 5 3 2
Level 5 Evaluating
6 Interpret the need for Optimum solution in transportation. Level 6 Creating
7. What do you mean by Least cost method (LCM)? Level 1 Remembering
8. Compare Vogel approximation method (VAM) & Least Cost
Method.
Level 2 Understanding
9. How do you represent a travelling salesman problem
through mathematical formulation?
Level 3 Applying
10. Analyse the rules of travelling salesman Problem. Level 4 Analysing
11. Discuss the meaning of Assignment Level 5 Evaluating
12. Compare Balanced assignment problem & Unbalanced
Assignment Problem.
Level 6 Creating
13. What example can you give for Unbalanced assignment
problem?
Level 1 Remembering
14. How will you resolve degeneracy in Transportation Problem? Level 2 Understanding
15. Classify transportation problem. Level 3 Applying
16. Examine the Steps in Hungarian algorithm. Level 4 Analysing
17. What is Branch and bound algorithm in Assignment? Level 1 Remembering
18. Compare Assignment and transportation Problem. Level 2 Understanding
19. What do you mean by Travelling Salesman Problem? Level 1 Remembering
20. What is Restricted Assignment? Level 1 Remembering
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Solve and find the Transportation Problem and Which method will
you select if you want toMinimize Cost?
Destination Supply
1 2 3 4
I 21 16 25 13 11
II 17 18 14 23 13
III 32 27 18 41 19
Demand 6 10 12 15
Level 1 Remembering
2. Find the Initial Basic Feasible solution for following TP. Using NW
Rule, LCM, and VAM. Which method will you select if you want to
Minimize Cost?
D1 D2 D3 Supply
S1 7 3 2 2
S2 2 1 3 3
S3 3 4 6 5
Demand 4 1 5 10
Level 2 Understanding
3.
(i)
Analyze the transportation problem with unit transportation
costs,demand, and supply as given below:
Destination
Supply
Source
D1 D2 D3 D4
S1
6 1 9 3
70
11 5 2 8
S2 55
10 12 4 7
S3
70
Demand 85 35 50 45
Apply VAM for Initial solution.
(5)
Level 3 Applying
(ii)
Construct the final Solution by using MODIMethod.
(8)
4.
(i)
Analyze & solve the following transportation problem to maximize
profit.
A B C D Supply
1
Source 2
3
Demand
15 51 42 33 23
80 42 26 81 44
90 40 66 60 33
23
31
16
30
100
Examine Initial solution using VAM.
(5)
Level 4 Analysing
(ii)
Analyze and find out the final Solution by using MODI Method.
(8)
5. Solve the following transportation problem using Vogel?s
method
Factory? Warehouse ?Available
A B C D E F
1 9 12 9 6 9 10 5
2 7 3 7 7 5 5 6
3 6 5 9 11 3 11 2
4 6 8 11 2 2 10 9
4 4 6 2 4 2
Requirement?
(5)
Level 5 Evaluating
6. (i) Solve the transportation problem and decide using VAM for initial
solution.
(5) Level 6 Creating
(ii) Evaluate using NWC and Least Cost method for initial solution?
Destination Supply
I 2 1 25 13 11
II 1 1 14 23 13
III 3 2 18 41 19
Demand 6 1 22 15
(8)
7.
Maximize profit from the following transportationproblem.
A B C D Supply
I 40 25 22 33 100
SourceII 44 35 30 30 30
III 38 38 28 30 70
Demand 40 20 60 30
Level 1 Remembering
(i) How will you convert maximization problem to minimization.
Find the maximum profit
(8)
(ii) Explain stepping stone method for checking the
solution for optimality transportation problems.
(5)
8. A company has one surplus truck in each of the cities A, B, C, D, &
E and one deficit trucks in each of the cities 1,2,3,4,5,6. The
distance between the cities in kms is shown in the matrix below.
Can you select the assignment of trucks from cities in surplus to
cities in deficiency .so that total distance covered by the vehicles is
minimum?
1 2 3 4 5 6
A 12 10 15 22 18 8
B 10 18 25 15 16 12
C 11 10 3 8 5 9
D 6 4 10 13 13 12
E 8 12 11 7 13 10
Level 2 Understanding
9.
Consider the problem of assigning five jobs to five persons. The
assignment costs are given as follows:
PERSONS?JOBS ?
1 2 3 4 5
A 8 4 2 6 1
B 0 9 5 5 4
C 3 8 9 2 6
D 4 3 1 0 3
Level 3 Applying
E 9 5 8 9 5
Determine the optimum assignment schedule.
10. The assignment cost of assigning any one operator to any one
machine is given in the following table.
MACHINE?OPERATORS ?
I II III IV
A 10 5 13 15
B 3 9 18 3
C 10 7 3 2
D 5 11 9 7
Find the optimal assignment by Hungarian method.
Level 4 Analysing
11. A machine shop purchased a drilling machine and two lathes of
different capacities. The Positioning of the machines among 4
possible locations on the shop floor is important forms the
standard of materials handling. Given the cost estimate per unit
time of materials below, find the optimum location of the
machines.
LOCATIONS
1 2 3 4
Lathe 1 12 9 12 9
Drill 15 Not
suitable
13 20
Lathe 2 4 8 10 6
Level 1 Remembering
12.
Solve the assignment problem for maximization given profit
matrix(profit in rupees).
Machines
P Q R S
JOB
51 53 54 50
47 50 48 50
49 50 60 61
63 64 60 60
Level 2 Understanding
PART - C
S.No Questions Marks BT
Level
Competence
1.
a
Assume that you are an OR specialist. Identify the procedure
for each of the following Method to the employees in order to
help them achieve solution to Transportation Problems.
Northwest Corner Cell Method
(3)
Level 1 Remembering
b Least Cost cell Method (4)
c Vogel?s Approximation Method (4)
d U V Method. (4)
13. The processing time in hours for the jobs when allocated to the
different machines is indicated below. Select the best assignment
of the machines for the jobs so that the total processing time is
Minimum.
Machines
M1 M2 M3 M4 M5
J1 9 22 58 11 19
JOB J2 43 78 72 50 63
J3 41 28 91 37 45
J4 74 42 27 49 39
J5 36 11 57 22 25
Level 4 Analysing
14. For the given travelling salesman problem, Minimize the total cost.
To
1 2 3 4
From A - 46 16 40
B 41 - 50 40
C 82 32 - 60
D 40 40 36 -
Level 1 Remembering
(i) Observe the above travelling salesman
problem and find out minimize the cost per
cycle.
(8)
(ii) Find whether path is satisfied. (5)
2.
Solve the following transportation problem, in which a
i
is the
availability at Origin
O
i
and b
j
is the requirement at the destination D
j
and cell entries
are unit costs of transportation from any origin to any
destination:
D1 D2 D3 D4 D5 a
j
O1 4 7 3 8 2 4
O2 1 4 7 3 8 7
O3 7 2 4 7 7 9
O4 4 8 2 4 7 2
b
j
8 3 7 2 2
Predict the allocation to minimize the cost.
Level 2 Understanding
3. A company has a team of 4 Salesman and the company wants to
do in 4 districts. Considering the capabilities of salesmen
and nature of the district, the company has estimated the profit per
day in Rs. For each salesmen in each district as follows.
District
s
Salesmen 1 2 3 4
A 16 10 14 11
B 14 11 15 15
C 15 15 13 12
D 13 12 14 15
Develop the best assignment schedule and analyze the total cost.
Level 3 Applying
4. Five operators have to be assigned to Five Machines. The
assignment costs are given in thetablebelow.
Analyse using Hungarian algorithm & find out the assignment to
minimize the cost.
Machine
I II III IV V
Operator
A 5 5 - 2 6
B 7 4 2 3 4
C 9 3 5 - 3
D 7 2 6 7 2
E 6 5 7 9 1
Level 4 Analyzing
UNIT ? III ? INTEGER PROGRAMMING AND GAME THEORY
SYLLABUS: Integer Programming ? Introduction and types - Game Theory-Two-person Zero sum
games-Saddle point, Dominance Rule, graphical and LP solutions, Nash Equilibrium
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. What do you mean by integer programming problem?
Level 1 Remembering
2. In what respect a mixed IPP differs from pure IPP?
Level 2 Understanding
3. What is Nash Equilibrium?
Level 3 Applying
4. Classify the different types of strategy.
Level 4 Analysing
5. Compile the Characteristics of game.
Level 5 Evaluating
6. Can you assess the applications of integer
programming?
Level 6 Creating
7. Define Game.
Level 1 Remembering
8. Compare Mixed Strategy and Pure Strategy.
Level 2 Understanding
9. How would you make use of the concept of Game theory
in Managerial Decision Making?
Level 3 Applying
10. Conclude your understanding about Payoff Matrix.
Level 4 Analysing
11. How will you find the optimal strategies and value of the
following game?
Player B
Player
A
H T
H 2 -1
T -1 0
Level 5 Evaluating
12. Interpret the concept of two person zero sum game.
Level 6 Creating
13. What is Saddle point?
Level 1 Remembering
14. Compare Dominance Principle of Rows and Columns.
Level 2 Understanding
15. Identify the basic assumptions of the Game.
Level 3 Applying
16. Conclude the advantages of Game theory.
Level 4 Analysing
17. What are the Methods of Matrices?
Level 1 Remembering
18. Summarize how graphs and LP solution are used in
Game theory.
Level 2 Understanding
19. What is a Decision Tree?
Level 1 Remembering
20. Define Dominance principle.
Level 1 Remembering
S.N
O
PART - B QUESTIONS MA
RK
S
BT
LEVEL
COMPETENCE
1. (i) What do you mean by Pure IPP? (3) Level 1 Remembering
(ii) What do you mean by Mixed IPP? (5)
(iii)
List out the difference between Pure and Mixed IPP.
(5)
2. (i) For what value of ?,the game with the following
matrix is strictly determined
B
1
B
2
B
3
A
1
? 6 2
A
2
-1 ? -7
A
3
-2 4 ?
(8) Level 2 Understanding
(ii) Write down the assumptions of game theory. (5)
3. (i) Solve the game whose pay-off matrix is given by
B
1
B
2
B
3
A
1
1 3 1
A
2
0 -4 -3
A
3
1 5 -1
(8)
Level 3 Applying
(ii) Explain the concept of Nash Equilibrium. (5)
4.
Analyze the Value of the game graphically
B1 B2
A1 4 4
A2 2 7
A3 5 3
A4 6 2
Level 4 Analysing
5.
What inference can be made using Dominance
Principle to reduce the following game and estimate
the game value?
B1 B2 B3 B4
A1 3 2 4 0
A2 3 4 2 4
A3 4 2 2 0
A4 2 1 6 3
Level 5 Evaluating
FirstRanker.com - FirstRanker's Choice
(An
?
DEPARTMENT OF MANAGEMENT STUDIES
QUESTION BANK
II SEMESTER
1915201? APPLIED OPERATIONS RESEACH
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Dr. Radha Ganesh Kumar ? Asst. Professor (Sel.G) and HOD
Mr.B. Sam Paul ? Asst. Professor (OG)
(An
? .
DEPARTMENT OFMANAGEMENT STUDIES
QUESTION BANK
SUBJECT :1915201 ?APPLIED OPERATIONS RESEACH
SEM / YEAR : IISemester / IYear
UNIT ? I ?INTRODUCTION TO LINEAR PROGRAMMING (LP)
SYLLABUS: Introduction to applications of operations research in functional areas of management.
Linear Programming-formulation, solution by graphical and simplex methods, Special cases. Dual
simplex method. Principles of Duality. Sensitivity Analysis.
PART- A
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Define Operations Research (OR). Level 1 Remembering
2. Differentiate between Simplex and Big M Method Level 2 Understanding
3. How do you show your understanding unbounded solution? Level 3 Applying
4. Categorize the forms of LPP. Level 4 Analysing
5.
Discuss why is two phase method is better than Big M
method?
Level 5 Evaluating
6. Interpret the usage of Sensitivity Analysis in LPP. Level 6 Creating
7. What are the assumptions and requirements of LPP? Level 1 Remembering
8. Compare Dual Simplex and Duality. Level 2 Understanding
9. Identify the Advantages of duality. Level 3 Applying
10. What do you think about Infeasible solution? Level 4 Analysing
11. How will you solve LPP graphically? Level 5 Evaluating
12.
Conclude your understanding on the mathematical
formulation of LPP.
Level 6 Creating
13. Define basic variables and artificial variables. Level 1 Remembering
14. Compare Slack variable & Surplus Variable. Level 2 Understanding
15.
Give some example for the role of Surplus variable & Slack
Variable in the simplex method
Level 3 Applying
16. How would you apply Artificial variable? Level 4 Analysing
17. What is Big M Method? Level 1 Remembering
18. Distinguish simplex and Big M method Level 2 Understanding
19.
What do you mean by Duality? List the Rules for primal and
dual.
Level 1 Remembering
20. What is Shadow price? Level 1 Remembering
PART- B
S.NO
QUESTIONS
BT
LEVEL
COMPETENCE
1.
(i)
Maximise Z=3x+4y subject to
2x+5y ?60,
4x+2y ?40.
x, y >0. Solve by Graphical Method
Plot the graph
(8)
Level 1 Remembering
(ii) Which one is the best solution? (5)
2.
(i)
Min Z= 20x
1
+10 x
2
subject to
x
1
+2x
2
? 40,
3x
1
+x
2
? 30,
4x
1
+3x
2
? 60,
x
1
,x
2
? 0.
Solve by Graphical Method,
Plot the graph
(8)
Level 2 Understanding
(ii) Predict the value of x & y. (5)
3 Max Z= 5x1+4x2 subject to
x
1
-2x
2
? 1,
x
1
+2x
2
?3,
x
1
,x
2
? 0. Solve Graphically. Which one is the best
solution?
Level 3 Applying
4.
(i)
A Plant Manufacturer 2 Product A & B. The Profit Contribution
of each product has been estimated as Rs.300 for product A
and Rs.400 for Product B. Each Product passes through 3
departments of the plant. The time required for each product
and total time available in each department is as follows.
Department Hours
Required
Hours
Required
Available
Hours
during
month
Product
A
Product
B
I 2 3 1600
II 3 2 1500
III 1 1 700
The company has a contract to supply atleast 300 units of
Product B per month.
Formulate the LPP
(5)
Level 4
Analysing
(ii) Solve through Graphical Method
(8)
5. Solve the following LPP by graphical method.
Maximize Z= 3x
1
+2x
2
Subject t o
- 2x
1
+x
2
?1,
x
1
? 2,
x
1
+ x
2
? 3
and x
1
,x
2
? 0
Level 5 Evaluating
6. (i) Max Z= 1000x
1
+4000x
2
+5000x
3
Subject to 3x1+3x
3
?22,
x1+2x2+3x
3
? 14,
3x1+2x2 ? 14
& x1,x2 ? 0
Develop a Simplex Table
(5)
Level 6 Creating
(ii) Analyse and find the value of x
1
, x
2
? (8)
7. Analyze the following LPP by Simplex Method:
Min Z = -10y
1
-15y
2
-20y
3
Subject to 2y
1
+4y
2
+6y
3
? 24,
3y
1
+9y
2
+6y
3
? 30,
& y
1
, y
2
, y
3
? 0.
Level 1 Remembering
(i)
Develop a Simplex Table (5)
(ii) Solve and find the value of y1 ,y2 and y3
(8)
8.
Solve By Graphical Method
Minimize Z= 40x
1
+24x
2
Subject to, 20x
1
+50 x
2
> 4,800
80 x
1
+50x
2
> 7,200
x
1
,x
2
>0
Level 2 Understanding
9. Solve the following LPP by simplex method:
Minimize Z= 8x
1
-2x
2
Subject to -4x
1
+2x
2
?1,
5x
1
-4x
2
?3,
and x
1
,x
2
? 0
Level 3 Applying
10. Solve the following LPP by simplex method:
Maximize Z= 3x1+2x
2
Subject to
2x
1
+x
2
?2,
3x
1
+4x
2
?12,
x
1
,x
2
? 0
Level 4 Analyzing
11. Review the LPP and solve by simplex method
Max Z= 25x+10y
Subject to the constraints
x+0.5y? 20
x+y? 50
x,y ? 0
Level 1 Remembering
12. A firm produces three products. These products are
processors on 3 different machines. The time required for
manufacturing one unit of cost of the products and the daily
capacity of the three machines is given in the table below.
Analyse and find the optimum solution.
Mac
hine
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Machine
Capacity
Min /Day
Product1 Product 2 Product 3
M1 2 8 2 940
M2 4 - 8 970
M3 2 5 - 430
It is required to determine the daily no. of units to be
manufactured for each product. The profit for unit for
Level 2 Understanding
product 1,2,3 is Rs.4,Rs.8,Rs.6 respectively. It is assumed
that all the amount produced are consumed in the market
13. Using dual simplex method , solve and find the optimum
solution for the given LPP.
Maximize Z=6x
1
+4x
2
+4x
3
Subject to 3x
1
,x
2
+2x
3
? 2
2x
1
+x
2
-x
3
? 1
-x
1
+x
2
+2x
3
? 1 &
x
1
,x
2
,x
3
? 0
Level 4 Analysing
14.
(i)
Evaluate by using dual simplex method and solve the LPP.
Minimize Z=2x
1
+x
2
Subject to 3x
1
+2x
2
? 3
4x
1
+3x
2
? 6
x
1
+x
2
? 5 & x
1
,x
2
?
Determine the dual simplex table
(5)
Level 1 Remembering
(ii)
Find the value of x
1
, x
2
(8)
PART - C
S.No Questions BT
LEVEL
COMPETENCE
1.
Max Z=300x+400y subject to
2x+3y ? 1600,
3x+2y ? 1500,
x+y ? 700,
y ? 300, x,y ? 0 Solve by Graphical Method, choose the
value of x & y which maximizes profit.
Level 1 Remembering
2. Solve the following LPP by graphical method.
Minimize Z= 6000x1+4000x
2
Subject t o
3x+x
2
? 40,
x
1
+2.5 x
2
? 22
3x
1
+3 x
2
? 40
and x
1
,x
2
? 0
Level 2 Understanding
3. Develop a Simplex Table and Solve
Max Z = 3 x1+2 x2,
Subject to
x1+ x2 ?4,
x1- x2 ? 2;
x1, x2 ?0.
Level 3 Applying
4. Solve by using Simplex Method.
Maximize Z= 3x+5y
Subject to the constraints
x+y? 60
x? 40
y ? 30
x,y ? 0
Level 1 Remembering
UNIT - II LINEAR PROGRAMMING EXTENSIONS
SYLLABUS: Transportation Models (Minimizing and Maximizing Problems) ? Balanced and unbalanced
Problems ? Initial Basic feasible solution by N-W Corner Rule, Least cost and Vogel?s approximation methods.
Check for optimality. Solution by MODI /. Case of Degeneracy. Trans-shipment Models. Assignment Models
(Minimising and Maximising Problems) ? Balanced and Unbalanced Problems. Solution by Hungarian and
Branch and Bound Algorithms. Travelling Salesman problem.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define Transportation & Transhipment. Level 1 Remembering
2. Differentiate balanced transportation problem & Unbalanced
Transportation Problem.
Level 2 Understanding
3. How would you show your understanding on unbalanced
transportation problem?
Level 3 Applying
4. Categorize the Phases of transportation model. Level 4 Analysing
5. Construct the basic feasible solution for the following
transportation problem.
1 2 3 4 SUPPLY
1 2 3 11 7 6
2 1 0 6 1 1
3 5 8 15 9 10
DEMAN D 7 5 3 2
Level 5 Evaluating
6 Interpret the need for Optimum solution in transportation. Level 6 Creating
7. What do you mean by Least cost method (LCM)? Level 1 Remembering
8. Compare Vogel approximation method (VAM) & Least Cost
Method.
Level 2 Understanding
9. How do you represent a travelling salesman problem
through mathematical formulation?
Level 3 Applying
10. Analyse the rules of travelling salesman Problem. Level 4 Analysing
11. Discuss the meaning of Assignment Level 5 Evaluating
12. Compare Balanced assignment problem & Unbalanced
Assignment Problem.
Level 6 Creating
13. What example can you give for Unbalanced assignment
problem?
Level 1 Remembering
14. How will you resolve degeneracy in Transportation Problem? Level 2 Understanding
15. Classify transportation problem. Level 3 Applying
16. Examine the Steps in Hungarian algorithm. Level 4 Analysing
17. What is Branch and bound algorithm in Assignment? Level 1 Remembering
18. Compare Assignment and transportation Problem. Level 2 Understanding
19. What do you mean by Travelling Salesman Problem? Level 1 Remembering
20. What is Restricted Assignment? Level 1 Remembering
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Solve and find the Transportation Problem and Which method will
you select if you want toMinimize Cost?
Destination Supply
1 2 3 4
I 21 16 25 13 11
II 17 18 14 23 13
III 32 27 18 41 19
Demand 6 10 12 15
Level 1 Remembering
2. Find the Initial Basic Feasible solution for following TP. Using NW
Rule, LCM, and VAM. Which method will you select if you want to
Minimize Cost?
D1 D2 D3 Supply
S1 7 3 2 2
S2 2 1 3 3
S3 3 4 6 5
Demand 4 1 5 10
Level 2 Understanding
3.
(i)
Analyze the transportation problem with unit transportation
costs,demand, and supply as given below:
Destination
Supply
Source
D1 D2 D3 D4
S1
6 1 9 3
70
11 5 2 8
S2 55
10 12 4 7
S3
70
Demand 85 35 50 45
Apply VAM for Initial solution.
(5)
Level 3 Applying
(ii)
Construct the final Solution by using MODIMethod.
(8)
4.
(i)
Analyze & solve the following transportation problem to maximize
profit.
A B C D Supply
1
Source 2
3
Demand
15 51 42 33 23
80 42 26 81 44
90 40 66 60 33
23
31
16
30
100
Examine Initial solution using VAM.
(5)
Level 4 Analysing
(ii)
Analyze and find out the final Solution by using MODI Method.
(8)
5. Solve the following transportation problem using Vogel?s
method
Factory? Warehouse ?Available
A B C D E F
1 9 12 9 6 9 10 5
2 7 3 7 7 5 5 6
3 6 5 9 11 3 11 2
4 6 8 11 2 2 10 9
4 4 6 2 4 2
Requirement?
(5)
Level 5 Evaluating
6. (i) Solve the transportation problem and decide using VAM for initial
solution.
(5) Level 6 Creating
(ii) Evaluate using NWC and Least Cost method for initial solution?
Destination Supply
I 2 1 25 13 11
II 1 1 14 23 13
III 3 2 18 41 19
Demand 6 1 22 15
(8)
7.
Maximize profit from the following transportationproblem.
A B C D Supply
I 40 25 22 33 100
SourceII 44 35 30 30 30
III 38 38 28 30 70
Demand 40 20 60 30
Level 1 Remembering
(i) How will you convert maximization problem to minimization.
Find the maximum profit
(8)
(ii) Explain stepping stone method for checking the
solution for optimality transportation problems.
(5)
8. A company has one surplus truck in each of the cities A, B, C, D, &
E and one deficit trucks in each of the cities 1,2,3,4,5,6. The
distance between the cities in kms is shown in the matrix below.
Can you select the assignment of trucks from cities in surplus to
cities in deficiency .so that total distance covered by the vehicles is
minimum?
1 2 3 4 5 6
A 12 10 15 22 18 8
B 10 18 25 15 16 12
C 11 10 3 8 5 9
D 6 4 10 13 13 12
E 8 12 11 7 13 10
Level 2 Understanding
9.
Consider the problem of assigning five jobs to five persons. The
assignment costs are given as follows:
PERSONS?JOBS ?
1 2 3 4 5
A 8 4 2 6 1
B 0 9 5 5 4
C 3 8 9 2 6
D 4 3 1 0 3
Level 3 Applying
E 9 5 8 9 5
Determine the optimum assignment schedule.
10. The assignment cost of assigning any one operator to any one
machine is given in the following table.
MACHINE?OPERATORS ?
I II III IV
A 10 5 13 15
B 3 9 18 3
C 10 7 3 2
D 5 11 9 7
Find the optimal assignment by Hungarian method.
Level 4 Analysing
11. A machine shop purchased a drilling machine and two lathes of
different capacities. The Positioning of the machines among 4
possible locations on the shop floor is important forms the
standard of materials handling. Given the cost estimate per unit
time of materials below, find the optimum location of the
machines.
LOCATIONS
1 2 3 4
Lathe 1 12 9 12 9
Drill 15 Not
suitable
13 20
Lathe 2 4 8 10 6
Level 1 Remembering
12.
Solve the assignment problem for maximization given profit
matrix(profit in rupees).
Machines
P Q R S
JOB
51 53 54 50
47 50 48 50
49 50 60 61
63 64 60 60
Level 2 Understanding
PART - C
S.No Questions Marks BT
Level
Competence
1.
a
Assume that you are an OR specialist. Identify the procedure
for each of the following Method to the employees in order to
help them achieve solution to Transportation Problems.
Northwest Corner Cell Method
(3)
Level 1 Remembering
b Least Cost cell Method (4)
c Vogel?s Approximation Method (4)
d U V Method. (4)
13. The processing time in hours for the jobs when allocated to the
different machines is indicated below. Select the best assignment
of the machines for the jobs so that the total processing time is
Minimum.
Machines
M1 M2 M3 M4 M5
J1 9 22 58 11 19
JOB J2 43 78 72 50 63
J3 41 28 91 37 45
J4 74 42 27 49 39
J5 36 11 57 22 25
Level 4 Analysing
14. For the given travelling salesman problem, Minimize the total cost.
To
1 2 3 4
From A - 46 16 40
B 41 - 50 40
C 82 32 - 60
D 40 40 36 -
Level 1 Remembering
(i) Observe the above travelling salesman
problem and find out minimize the cost per
cycle.
(8)
(ii) Find whether path is satisfied. (5)
2.
Solve the following transportation problem, in which a
i
is the
availability at Origin
O
i
and b
j
is the requirement at the destination D
j
and cell entries
are unit costs of transportation from any origin to any
destination:
D1 D2 D3 D4 D5 a
j
O1 4 7 3 8 2 4
O2 1 4 7 3 8 7
O3 7 2 4 7 7 9
O4 4 8 2 4 7 2
b
j
8 3 7 2 2
Predict the allocation to minimize the cost.
Level 2 Understanding
3. A company has a team of 4 Salesman and the company wants to
do in 4 districts. Considering the capabilities of salesmen
and nature of the district, the company has estimated the profit per
day in Rs. For each salesmen in each district as follows.
District
s
Salesmen 1 2 3 4
A 16 10 14 11
B 14 11 15 15
C 15 15 13 12
D 13 12 14 15
Develop the best assignment schedule and analyze the total cost.
Level 3 Applying
4. Five operators have to be assigned to Five Machines. The
assignment costs are given in thetablebelow.
Analyse using Hungarian algorithm & find out the assignment to
minimize the cost.
Machine
I II III IV V
Operator
A 5 5 - 2 6
B 7 4 2 3 4
C 9 3 5 - 3
D 7 2 6 7 2
E 6 5 7 9 1
Level 4 Analyzing
UNIT ? III ? INTEGER PROGRAMMING AND GAME THEORY
SYLLABUS: Integer Programming ? Introduction and types - Game Theory-Two-person Zero sum
games-Saddle point, Dominance Rule, graphical and LP solutions, Nash Equilibrium
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. What do you mean by integer programming problem?
Level 1 Remembering
2. In what respect a mixed IPP differs from pure IPP?
Level 2 Understanding
3. What is Nash Equilibrium?
Level 3 Applying
4. Classify the different types of strategy.
Level 4 Analysing
5. Compile the Characteristics of game.
Level 5 Evaluating
6. Can you assess the applications of integer
programming?
Level 6 Creating
7. Define Game.
Level 1 Remembering
8. Compare Mixed Strategy and Pure Strategy.
Level 2 Understanding
9. How would you make use of the concept of Game theory
in Managerial Decision Making?
Level 3 Applying
10. Conclude your understanding about Payoff Matrix.
Level 4 Analysing
11. How will you find the optimal strategies and value of the
following game?
Player B
Player
A
H T
H 2 -1
T -1 0
Level 5 Evaluating
12. Interpret the concept of two person zero sum game.
Level 6 Creating
13. What is Saddle point?
Level 1 Remembering
14. Compare Dominance Principle of Rows and Columns.
Level 2 Understanding
15. Identify the basic assumptions of the Game.
Level 3 Applying
16. Conclude the advantages of Game theory.
Level 4 Analysing
17. What are the Methods of Matrices?
Level 1 Remembering
18. Summarize how graphs and LP solution are used in
Game theory.
Level 2 Understanding
19. What is a Decision Tree?
Level 1 Remembering
20. Define Dominance principle.
Level 1 Remembering
S.N
O
PART - B QUESTIONS MA
RK
S
BT
LEVEL
COMPETENCE
1. (i) What do you mean by Pure IPP? (3) Level 1 Remembering
(ii) What do you mean by Mixed IPP? (5)
(iii)
List out the difference between Pure and Mixed IPP.
(5)
2. (i) For what value of ?,the game with the following
matrix is strictly determined
B
1
B
2
B
3
A
1
? 6 2
A
2
-1 ? -7
A
3
-2 4 ?
(8) Level 2 Understanding
(ii) Write down the assumptions of game theory. (5)
3. (i) Solve the game whose pay-off matrix is given by
B
1
B
2
B
3
A
1
1 3 1
A
2
0 -4 -3
A
3
1 5 -1
(8)
Level 3 Applying
(ii) Explain the concept of Nash Equilibrium. (5)
4.
Analyze the Value of the game graphically
B1 B2
A1 4 4
A2 2 7
A3 5 3
A4 6 2
Level 4 Analysing
5.
What inference can be made using Dominance
Principle to reduce the following game and estimate
the game value?
B1 B2 B3 B4
A1 3 2 4 0
A2 3 4 2 4
A3 4 2 2 0
A4 2 1 6 3
Level 5 Evaluating
6.
How would you evaluate the following game whose
Pay-Off matrix is Given Below?
9 3 1 8 0
6 5 4 6 7
2 4 3 3 8
5 6 2 2 1
Level 6 Creating
7.
(i)
Two players A&B match coins. If the coins match
then A wins one unit value, if the coins do not
match then B wins one unit of value.
Determine pay-off matrix which strategy is to be
chosen
(5)
Level 1 Remembering
(ii)
Find the value of game. (8)
8.
Predict the Value of the Game given above Pay
OffMatrix.
Player B
B1 B2 B3
A1 -2 5 -3
Player A A2 1 3 5
A3 -3 -7 11
Level 2 Understanding
9.
Apply graphical analysis to Solve the game.
A/
B
B1 B2 B3 B4
A1 3 3 4 0
A2 5 4 3 7
Level 3 Applying
10. Solve the following game by graphical method.
Player B
1 2 3
1 6 4 3
Player A 2 2 4 8
Level 4 Analysing
11.
(i)
A and B play a Match(Game) in which each has 3
coins 5 paise, 10 paise and 20 paise. Each player
selects a coin without the knowledge of others
choice. IF the sum is even, B wins A?s Coin. If sum
is Odd, A wins B?s coin.
How will you find the pay-off matrix ?
(5)
Level 1
Remembering
(ii)
Find the Best Strategy & value of the Game. (8)
12.
Consider the Pay Off Matrix of player A as shown in
the table below and solve it optimally using the
graphical method .
Player A
Player
B
1 2 3 4 5
1 3 6 8 4 4
2 -7 4 2 10 2
Level 2 Understanding
FirstRanker.com - FirstRanker's Choice
(An
?
DEPARTMENT OF MANAGEMENT STUDIES
QUESTION BANK
II SEMESTER
1915201? APPLIED OPERATIONS RESEACH
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Dr. Radha Ganesh Kumar ? Asst. Professor (Sel.G) and HOD
Mr.B. Sam Paul ? Asst. Professor (OG)
(An
? .
DEPARTMENT OFMANAGEMENT STUDIES
QUESTION BANK
SUBJECT :1915201 ?APPLIED OPERATIONS RESEACH
SEM / YEAR : IISemester / IYear
UNIT ? I ?INTRODUCTION TO LINEAR PROGRAMMING (LP)
SYLLABUS: Introduction to applications of operations research in functional areas of management.
Linear Programming-formulation, solution by graphical and simplex methods, Special cases. Dual
simplex method. Principles of Duality. Sensitivity Analysis.
PART- A
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Define Operations Research (OR). Level 1 Remembering
2. Differentiate between Simplex and Big M Method Level 2 Understanding
3. How do you show your understanding unbounded solution? Level 3 Applying
4. Categorize the forms of LPP. Level 4 Analysing
5.
Discuss why is two phase method is better than Big M
method?
Level 5 Evaluating
6. Interpret the usage of Sensitivity Analysis in LPP. Level 6 Creating
7. What are the assumptions and requirements of LPP? Level 1 Remembering
8. Compare Dual Simplex and Duality. Level 2 Understanding
9. Identify the Advantages of duality. Level 3 Applying
10. What do you think about Infeasible solution? Level 4 Analysing
11. How will you solve LPP graphically? Level 5 Evaluating
12.
Conclude your understanding on the mathematical
formulation of LPP.
Level 6 Creating
13. Define basic variables and artificial variables. Level 1 Remembering
14. Compare Slack variable & Surplus Variable. Level 2 Understanding
15.
Give some example for the role of Surplus variable & Slack
Variable in the simplex method
Level 3 Applying
16. How would you apply Artificial variable? Level 4 Analysing
17. What is Big M Method? Level 1 Remembering
18. Distinguish simplex and Big M method Level 2 Understanding
19.
What do you mean by Duality? List the Rules for primal and
dual.
Level 1 Remembering
20. What is Shadow price? Level 1 Remembering
PART- B
S.NO
QUESTIONS
BT
LEVEL
COMPETENCE
1.
(i)
Maximise Z=3x+4y subject to
2x+5y ?60,
4x+2y ?40.
x, y >0. Solve by Graphical Method
Plot the graph
(8)
Level 1 Remembering
(ii) Which one is the best solution? (5)
2.
(i)
Min Z= 20x
1
+10 x
2
subject to
x
1
+2x
2
? 40,
3x
1
+x
2
? 30,
4x
1
+3x
2
? 60,
x
1
,x
2
? 0.
Solve by Graphical Method,
Plot the graph
(8)
Level 2 Understanding
(ii) Predict the value of x & y. (5)
3 Max Z= 5x1+4x2 subject to
x
1
-2x
2
? 1,
x
1
+2x
2
?3,
x
1
,x
2
? 0. Solve Graphically. Which one is the best
solution?
Level 3 Applying
4.
(i)
A Plant Manufacturer 2 Product A & B. The Profit Contribution
of each product has been estimated as Rs.300 for product A
and Rs.400 for Product B. Each Product passes through 3
departments of the plant. The time required for each product
and total time available in each department is as follows.
Department Hours
Required
Hours
Required
Available
Hours
during
month
Product
A
Product
B
I 2 3 1600
II 3 2 1500
III 1 1 700
The company has a contract to supply atleast 300 units of
Product B per month.
Formulate the LPP
(5)
Level 4
Analysing
(ii) Solve through Graphical Method
(8)
5. Solve the following LPP by graphical method.
Maximize Z= 3x
1
+2x
2
Subject t o
- 2x
1
+x
2
?1,
x
1
? 2,
x
1
+ x
2
? 3
and x
1
,x
2
? 0
Level 5 Evaluating
6. (i) Max Z= 1000x
1
+4000x
2
+5000x
3
Subject to 3x1+3x
3
?22,
x1+2x2+3x
3
? 14,
3x1+2x2 ? 14
& x1,x2 ? 0
Develop a Simplex Table
(5)
Level 6 Creating
(ii) Analyse and find the value of x
1
, x
2
? (8)
7. Analyze the following LPP by Simplex Method:
Min Z = -10y
1
-15y
2
-20y
3
Subject to 2y
1
+4y
2
+6y
3
? 24,
3y
1
+9y
2
+6y
3
? 30,
& y
1
, y
2
, y
3
? 0.
Level 1 Remembering
(i)
Develop a Simplex Table (5)
(ii) Solve and find the value of y1 ,y2 and y3
(8)
8.
Solve By Graphical Method
Minimize Z= 40x
1
+24x
2
Subject to, 20x
1
+50 x
2
> 4,800
80 x
1
+50x
2
> 7,200
x
1
,x
2
>0
Level 2 Understanding
9. Solve the following LPP by simplex method:
Minimize Z= 8x
1
-2x
2
Subject to -4x
1
+2x
2
?1,
5x
1
-4x
2
?3,
and x
1
,x
2
? 0
Level 3 Applying
10. Solve the following LPP by simplex method:
Maximize Z= 3x1+2x
2
Subject to
2x
1
+x
2
?2,
3x
1
+4x
2
?12,
x
1
,x
2
? 0
Level 4 Analyzing
11. Review the LPP and solve by simplex method
Max Z= 25x+10y
Subject to the constraints
x+0.5y? 20
x+y? 50
x,y ? 0
Level 1 Remembering
12. A firm produces three products. These products are
processors on 3 different machines. The time required for
manufacturing one unit of cost of the products and the daily
capacity of the three machines is given in the table below.
Analyse and find the optimum solution.
Mac
hine
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Machine
Capacity
Min /Day
Product1 Product 2 Product 3
M1 2 8 2 940
M2 4 - 8 970
M3 2 5 - 430
It is required to determine the daily no. of units to be
manufactured for each product. The profit for unit for
Level 2 Understanding
product 1,2,3 is Rs.4,Rs.8,Rs.6 respectively. It is assumed
that all the amount produced are consumed in the market
13. Using dual simplex method , solve and find the optimum
solution for the given LPP.
Maximize Z=6x
1
+4x
2
+4x
3
Subject to 3x
1
,x
2
+2x
3
? 2
2x
1
+x
2
-x
3
? 1
-x
1
+x
2
+2x
3
? 1 &
x
1
,x
2
,x
3
? 0
Level 4 Analysing
14.
(i)
Evaluate by using dual simplex method and solve the LPP.
Minimize Z=2x
1
+x
2
Subject to 3x
1
+2x
2
? 3
4x
1
+3x
2
? 6
x
1
+x
2
? 5 & x
1
,x
2
?
Determine the dual simplex table
(5)
Level 1 Remembering
(ii)
Find the value of x
1
, x
2
(8)
PART - C
S.No Questions BT
LEVEL
COMPETENCE
1.
Max Z=300x+400y subject to
2x+3y ? 1600,
3x+2y ? 1500,
x+y ? 700,
y ? 300, x,y ? 0 Solve by Graphical Method, choose the
value of x & y which maximizes profit.
Level 1 Remembering
2. Solve the following LPP by graphical method.
Minimize Z= 6000x1+4000x
2
Subject t o
3x+x
2
? 40,
x
1
+2.5 x
2
? 22
3x
1
+3 x
2
? 40
and x
1
,x
2
? 0
Level 2 Understanding
3. Develop a Simplex Table and Solve
Max Z = 3 x1+2 x2,
Subject to
x1+ x2 ?4,
x1- x2 ? 2;
x1, x2 ?0.
Level 3 Applying
4. Solve by using Simplex Method.
Maximize Z= 3x+5y
Subject to the constraints
x+y? 60
x? 40
y ? 30
x,y ? 0
Level 1 Remembering
UNIT - II LINEAR PROGRAMMING EXTENSIONS
SYLLABUS: Transportation Models (Minimizing and Maximizing Problems) ? Balanced and unbalanced
Problems ? Initial Basic feasible solution by N-W Corner Rule, Least cost and Vogel?s approximation methods.
Check for optimality. Solution by MODI /. Case of Degeneracy. Trans-shipment Models. Assignment Models
(Minimising and Maximising Problems) ? Balanced and Unbalanced Problems. Solution by Hungarian and
Branch and Bound Algorithms. Travelling Salesman problem.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define Transportation & Transhipment. Level 1 Remembering
2. Differentiate balanced transportation problem & Unbalanced
Transportation Problem.
Level 2 Understanding
3. How would you show your understanding on unbalanced
transportation problem?
Level 3 Applying
4. Categorize the Phases of transportation model. Level 4 Analysing
5. Construct the basic feasible solution for the following
transportation problem.
1 2 3 4 SUPPLY
1 2 3 11 7 6
2 1 0 6 1 1
3 5 8 15 9 10
DEMAN D 7 5 3 2
Level 5 Evaluating
6 Interpret the need for Optimum solution in transportation. Level 6 Creating
7. What do you mean by Least cost method (LCM)? Level 1 Remembering
8. Compare Vogel approximation method (VAM) & Least Cost
Method.
Level 2 Understanding
9. How do you represent a travelling salesman problem
through mathematical formulation?
Level 3 Applying
10. Analyse the rules of travelling salesman Problem. Level 4 Analysing
11. Discuss the meaning of Assignment Level 5 Evaluating
12. Compare Balanced assignment problem & Unbalanced
Assignment Problem.
Level 6 Creating
13. What example can you give for Unbalanced assignment
problem?
Level 1 Remembering
14. How will you resolve degeneracy in Transportation Problem? Level 2 Understanding
15. Classify transportation problem. Level 3 Applying
16. Examine the Steps in Hungarian algorithm. Level 4 Analysing
17. What is Branch and bound algorithm in Assignment? Level 1 Remembering
18. Compare Assignment and transportation Problem. Level 2 Understanding
19. What do you mean by Travelling Salesman Problem? Level 1 Remembering
20. What is Restricted Assignment? Level 1 Remembering
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Solve and find the Transportation Problem and Which method will
you select if you want toMinimize Cost?
Destination Supply
1 2 3 4
I 21 16 25 13 11
II 17 18 14 23 13
III 32 27 18 41 19
Demand 6 10 12 15
Level 1 Remembering
2. Find the Initial Basic Feasible solution for following TP. Using NW
Rule, LCM, and VAM. Which method will you select if you want to
Minimize Cost?
D1 D2 D3 Supply
S1 7 3 2 2
S2 2 1 3 3
S3 3 4 6 5
Demand 4 1 5 10
Level 2 Understanding
3.
(i)
Analyze the transportation problem with unit transportation
costs,demand, and supply as given below:
Destination
Supply
Source
D1 D2 D3 D4
S1
6 1 9 3
70
11 5 2 8
S2 55
10 12 4 7
S3
70
Demand 85 35 50 45
Apply VAM for Initial solution.
(5)
Level 3 Applying
(ii)
Construct the final Solution by using MODIMethod.
(8)
4.
(i)
Analyze & solve the following transportation problem to maximize
profit.
A B C D Supply
1
Source 2
3
Demand
15 51 42 33 23
80 42 26 81 44
90 40 66 60 33
23
31
16
30
100
Examine Initial solution using VAM.
(5)
Level 4 Analysing
(ii)
Analyze and find out the final Solution by using MODI Method.
(8)
5. Solve the following transportation problem using Vogel?s
method
Factory? Warehouse ?Available
A B C D E F
1 9 12 9 6 9 10 5
2 7 3 7 7 5 5 6
3 6 5 9 11 3 11 2
4 6 8 11 2 2 10 9
4 4 6 2 4 2
Requirement?
(5)
Level 5 Evaluating
6. (i) Solve the transportation problem and decide using VAM for initial
solution.
(5) Level 6 Creating
(ii) Evaluate using NWC and Least Cost method for initial solution?
Destination Supply
I 2 1 25 13 11
II 1 1 14 23 13
III 3 2 18 41 19
Demand 6 1 22 15
(8)
7.
Maximize profit from the following transportationproblem.
A B C D Supply
I 40 25 22 33 100
SourceII 44 35 30 30 30
III 38 38 28 30 70
Demand 40 20 60 30
Level 1 Remembering
(i) How will you convert maximization problem to minimization.
Find the maximum profit
(8)
(ii) Explain stepping stone method for checking the
solution for optimality transportation problems.
(5)
8. A company has one surplus truck in each of the cities A, B, C, D, &
E and one deficit trucks in each of the cities 1,2,3,4,5,6. The
distance between the cities in kms is shown in the matrix below.
Can you select the assignment of trucks from cities in surplus to
cities in deficiency .so that total distance covered by the vehicles is
minimum?
1 2 3 4 5 6
A 12 10 15 22 18 8
B 10 18 25 15 16 12
C 11 10 3 8 5 9
D 6 4 10 13 13 12
E 8 12 11 7 13 10
Level 2 Understanding
9.
Consider the problem of assigning five jobs to five persons. The
assignment costs are given as follows:
PERSONS?JOBS ?
1 2 3 4 5
A 8 4 2 6 1
B 0 9 5 5 4
C 3 8 9 2 6
D 4 3 1 0 3
Level 3 Applying
E 9 5 8 9 5
Determine the optimum assignment schedule.
10. The assignment cost of assigning any one operator to any one
machine is given in the following table.
MACHINE?OPERATORS ?
I II III IV
A 10 5 13 15
B 3 9 18 3
C 10 7 3 2
D 5 11 9 7
Find the optimal assignment by Hungarian method.
Level 4 Analysing
11. A machine shop purchased a drilling machine and two lathes of
different capacities. The Positioning of the machines among 4
possible locations on the shop floor is important forms the
standard of materials handling. Given the cost estimate per unit
time of materials below, find the optimum location of the
machines.
LOCATIONS
1 2 3 4
Lathe 1 12 9 12 9
Drill 15 Not
suitable
13 20
Lathe 2 4 8 10 6
Level 1 Remembering
12.
Solve the assignment problem for maximization given profit
matrix(profit in rupees).
Machines
P Q R S
JOB
51 53 54 50
47 50 48 50
49 50 60 61
63 64 60 60
Level 2 Understanding
PART - C
S.No Questions Marks BT
Level
Competence
1.
a
Assume that you are an OR specialist. Identify the procedure
for each of the following Method to the employees in order to
help them achieve solution to Transportation Problems.
Northwest Corner Cell Method
(3)
Level 1 Remembering
b Least Cost cell Method (4)
c Vogel?s Approximation Method (4)
d U V Method. (4)
13. The processing time in hours for the jobs when allocated to the
different machines is indicated below. Select the best assignment
of the machines for the jobs so that the total processing time is
Minimum.
Machines
M1 M2 M3 M4 M5
J1 9 22 58 11 19
JOB J2 43 78 72 50 63
J3 41 28 91 37 45
J4 74 42 27 49 39
J5 36 11 57 22 25
Level 4 Analysing
14. For the given travelling salesman problem, Minimize the total cost.
To
1 2 3 4
From A - 46 16 40
B 41 - 50 40
C 82 32 - 60
D 40 40 36 -
Level 1 Remembering
(i) Observe the above travelling salesman
problem and find out minimize the cost per
cycle.
(8)
(ii) Find whether path is satisfied. (5)
2.
Solve the following transportation problem, in which a
i
is the
availability at Origin
O
i
and b
j
is the requirement at the destination D
j
and cell entries
are unit costs of transportation from any origin to any
destination:
D1 D2 D3 D4 D5 a
j
O1 4 7 3 8 2 4
O2 1 4 7 3 8 7
O3 7 2 4 7 7 9
O4 4 8 2 4 7 2
b
j
8 3 7 2 2
Predict the allocation to minimize the cost.
Level 2 Understanding
3. A company has a team of 4 Salesman and the company wants to
do in 4 districts. Considering the capabilities of salesmen
and nature of the district, the company has estimated the profit per
day in Rs. For each salesmen in each district as follows.
District
s
Salesmen 1 2 3 4
A 16 10 14 11
B 14 11 15 15
C 15 15 13 12
D 13 12 14 15
Develop the best assignment schedule and analyze the total cost.
Level 3 Applying
4. Five operators have to be assigned to Five Machines. The
assignment costs are given in thetablebelow.
Analyse using Hungarian algorithm & find out the assignment to
minimize the cost.
Machine
I II III IV V
Operator
A 5 5 - 2 6
B 7 4 2 3 4
C 9 3 5 - 3
D 7 2 6 7 2
E 6 5 7 9 1
Level 4 Analyzing
UNIT ? III ? INTEGER PROGRAMMING AND GAME THEORY
SYLLABUS: Integer Programming ? Introduction and types - Game Theory-Two-person Zero sum
games-Saddle point, Dominance Rule, graphical and LP solutions, Nash Equilibrium
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. What do you mean by integer programming problem?
Level 1 Remembering
2. In what respect a mixed IPP differs from pure IPP?
Level 2 Understanding
3. What is Nash Equilibrium?
Level 3 Applying
4. Classify the different types of strategy.
Level 4 Analysing
5. Compile the Characteristics of game.
Level 5 Evaluating
6. Can you assess the applications of integer
programming?
Level 6 Creating
7. Define Game.
Level 1 Remembering
8. Compare Mixed Strategy and Pure Strategy.
Level 2 Understanding
9. How would you make use of the concept of Game theory
in Managerial Decision Making?
Level 3 Applying
10. Conclude your understanding about Payoff Matrix.
Level 4 Analysing
11. How will you find the optimal strategies and value of the
following game?
Player B
Player
A
H T
H 2 -1
T -1 0
Level 5 Evaluating
12. Interpret the concept of two person zero sum game.
Level 6 Creating
13. What is Saddle point?
Level 1 Remembering
14. Compare Dominance Principle of Rows and Columns.
Level 2 Understanding
15. Identify the basic assumptions of the Game.
Level 3 Applying
16. Conclude the advantages of Game theory.
Level 4 Analysing
17. What are the Methods of Matrices?
Level 1 Remembering
18. Summarize how graphs and LP solution are used in
Game theory.
Level 2 Understanding
19. What is a Decision Tree?
Level 1 Remembering
20. Define Dominance principle.
Level 1 Remembering
S.N
O
PART - B QUESTIONS MA
RK
S
BT
LEVEL
COMPETENCE
1. (i) What do you mean by Pure IPP? (3) Level 1 Remembering
(ii) What do you mean by Mixed IPP? (5)
(iii)
List out the difference between Pure and Mixed IPP.
(5)
2. (i) For what value of ?,the game with the following
matrix is strictly determined
B
1
B
2
B
3
A
1
? 6 2
A
2
-1 ? -7
A
3
-2 4 ?
(8) Level 2 Understanding
(ii) Write down the assumptions of game theory. (5)
3. (i) Solve the game whose pay-off matrix is given by
B
1
B
2
B
3
A
1
1 3 1
A
2
0 -4 -3
A
3
1 5 -1
(8)
Level 3 Applying
(ii) Explain the concept of Nash Equilibrium. (5)
4.
Analyze the Value of the game graphically
B1 B2
A1 4 4
A2 2 7
A3 5 3
A4 6 2
Level 4 Analysing
5.
What inference can be made using Dominance
Principle to reduce the following game and estimate
the game value?
B1 B2 B3 B4
A1 3 2 4 0
A2 3 4 2 4
A3 4 2 2 0
A4 2 1 6 3
Level 5 Evaluating
6.
How would you evaluate the following game whose
Pay-Off matrix is Given Below?
9 3 1 8 0
6 5 4 6 7
2 4 3 3 8
5 6 2 2 1
Level 6 Creating
7.
(i)
Two players A&B match coins. If the coins match
then A wins one unit value, if the coins do not
match then B wins one unit of value.
Determine pay-off matrix which strategy is to be
chosen
(5)
Level 1 Remembering
(ii)
Find the value of game. (8)
8.
Predict the Value of the Game given above Pay
OffMatrix.
Player B
B1 B2 B3
A1 -2 5 -3
Player A A2 1 3 5
A3 -3 -7 11
Level 2 Understanding
9.
Apply graphical analysis to Solve the game.
A/
B
B1 B2 B3 B4
A1 3 3 4 0
A2 5 4 3 7
Level 3 Applying
10. Solve the following game by graphical method.
Player B
1 2 3
1 6 4 3
Player A 2 2 4 8
Level 4 Analysing
11.
(i)
A and B play a Match(Game) in which each has 3
coins 5 paise, 10 paise and 20 paise. Each player
selects a coin without the knowledge of others
choice. IF the sum is even, B wins A?s Coin. If sum
is Odd, A wins B?s coin.
How will you find the pay-off matrix ?
(5)
Level 1
Remembering
(ii)
Find the Best Strategy & value of the Game. (8)
12.
Consider the Pay Off Matrix of player A as shown in
the table below and solve it optimally using the
graphical method .
Player A
Player
B
1 2 3 4 5
1 3 6 8 4 4
2 -7 4 2 10 2
Level 2 Understanding
13.
(i)
Analyze the Game Graphically:
Player A
Player
A
B1 B2
A1 -3 1
A2 5 3
A3 6 -1
A4 1 4
A5 2 2
A6 0 -5
Plot the graph
(5)
Level 4 Analysing
(ii)
Analyse and find the value of the game.
(8)
14.
Which one is the best strategy using Dominance
Principle?
B1 B2 B3 B4 B5 B6
A1
4 2 0 2 1 1
A2
4 3 1 3 2 2
A3
4 3 7 -5 1 2
A4
4 3 4 -1 2 2
A5
4 3 3 -2 2 2
Level 1 Remembering
PART-C
S.No Questions BT
Level
Competence
1.
Using Dominance property Solve.
B
A
I II IIIIV
1 -5 3 1 20
2 5 5 4 6
3 -4 -2 0 -5
Level 1 Remembering
2. Examine the 2 * n Game by the Method of Sub Game:
B1 B2 B3
A1 1 3 11
A2 8 5 2
Level 2 Understanding
FirstRanker.com - FirstRanker's Choice
(An
?
DEPARTMENT OF MANAGEMENT STUDIES
QUESTION BANK
II SEMESTER
1915201? APPLIED OPERATIONS RESEACH
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Dr. Radha Ganesh Kumar ? Asst. Professor (Sel.G) and HOD
Mr.B. Sam Paul ? Asst. Professor (OG)
(An
? .
DEPARTMENT OFMANAGEMENT STUDIES
QUESTION BANK
SUBJECT :1915201 ?APPLIED OPERATIONS RESEACH
SEM / YEAR : IISemester / IYear
UNIT ? I ?INTRODUCTION TO LINEAR PROGRAMMING (LP)
SYLLABUS: Introduction to applications of operations research in functional areas of management.
Linear Programming-formulation, solution by graphical and simplex methods, Special cases. Dual
simplex method. Principles of Duality. Sensitivity Analysis.
PART- A
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Define Operations Research (OR). Level 1 Remembering
2. Differentiate between Simplex and Big M Method Level 2 Understanding
3. How do you show your understanding unbounded solution? Level 3 Applying
4. Categorize the forms of LPP. Level 4 Analysing
5.
Discuss why is two phase method is better than Big M
method?
Level 5 Evaluating
6. Interpret the usage of Sensitivity Analysis in LPP. Level 6 Creating
7. What are the assumptions and requirements of LPP? Level 1 Remembering
8. Compare Dual Simplex and Duality. Level 2 Understanding
9. Identify the Advantages of duality. Level 3 Applying
10. What do you think about Infeasible solution? Level 4 Analysing
11. How will you solve LPP graphically? Level 5 Evaluating
12.
Conclude your understanding on the mathematical
formulation of LPP.
Level 6 Creating
13. Define basic variables and artificial variables. Level 1 Remembering
14. Compare Slack variable & Surplus Variable. Level 2 Understanding
15.
Give some example for the role of Surplus variable & Slack
Variable in the simplex method
Level 3 Applying
16. How would you apply Artificial variable? Level 4 Analysing
17. What is Big M Method? Level 1 Remembering
18. Distinguish simplex and Big M method Level 2 Understanding
19.
What do you mean by Duality? List the Rules for primal and
dual.
Level 1 Remembering
20. What is Shadow price? Level 1 Remembering
PART- B
S.NO
QUESTIONS
BT
LEVEL
COMPETENCE
1.
(i)
Maximise Z=3x+4y subject to
2x+5y ?60,
4x+2y ?40.
x, y >0. Solve by Graphical Method
Plot the graph
(8)
Level 1 Remembering
(ii) Which one is the best solution? (5)
2.
(i)
Min Z= 20x
1
+10 x
2
subject to
x
1
+2x
2
? 40,
3x
1
+x
2
? 30,
4x
1
+3x
2
? 60,
x
1
,x
2
? 0.
Solve by Graphical Method,
Plot the graph
(8)
Level 2 Understanding
(ii) Predict the value of x & y. (5)
3 Max Z= 5x1+4x2 subject to
x
1
-2x
2
? 1,
x
1
+2x
2
?3,
x
1
,x
2
? 0. Solve Graphically. Which one is the best
solution?
Level 3 Applying
4.
(i)
A Plant Manufacturer 2 Product A & B. The Profit Contribution
of each product has been estimated as Rs.300 for product A
and Rs.400 for Product B. Each Product passes through 3
departments of the plant. The time required for each product
and total time available in each department is as follows.
Department Hours
Required
Hours
Required
Available
Hours
during
month
Product
A
Product
B
I 2 3 1600
II 3 2 1500
III 1 1 700
The company has a contract to supply atleast 300 units of
Product B per month.
Formulate the LPP
(5)
Level 4
Analysing
(ii) Solve through Graphical Method
(8)
5. Solve the following LPP by graphical method.
Maximize Z= 3x
1
+2x
2
Subject t o
- 2x
1
+x
2
?1,
x
1
? 2,
x
1
+ x
2
? 3
and x
1
,x
2
? 0
Level 5 Evaluating
6. (i) Max Z= 1000x
1
+4000x
2
+5000x
3
Subject to 3x1+3x
3
?22,
x1+2x2+3x
3
? 14,
3x1+2x2 ? 14
& x1,x2 ? 0
Develop a Simplex Table
(5)
Level 6 Creating
(ii) Analyse and find the value of x
1
, x
2
? (8)
7. Analyze the following LPP by Simplex Method:
Min Z = -10y
1
-15y
2
-20y
3
Subject to 2y
1
+4y
2
+6y
3
? 24,
3y
1
+9y
2
+6y
3
? 30,
& y
1
, y
2
, y
3
? 0.
Level 1 Remembering
(i)
Develop a Simplex Table (5)
(ii) Solve and find the value of y1 ,y2 and y3
(8)
8.
Solve By Graphical Method
Minimize Z= 40x
1
+24x
2
Subject to, 20x
1
+50 x
2
> 4,800
80 x
1
+50x
2
> 7,200
x
1
,x
2
>0
Level 2 Understanding
9. Solve the following LPP by simplex method:
Minimize Z= 8x
1
-2x
2
Subject to -4x
1
+2x
2
?1,
5x
1
-4x
2
?3,
and x
1
,x
2
? 0
Level 3 Applying
10. Solve the following LPP by simplex method:
Maximize Z= 3x1+2x
2
Subject to
2x
1
+x
2
?2,
3x
1
+4x
2
?12,
x
1
,x
2
? 0
Level 4 Analyzing
11. Review the LPP and solve by simplex method
Max Z= 25x+10y
Subject to the constraints
x+0.5y? 20
x+y? 50
x,y ? 0
Level 1 Remembering
12. A firm produces three products. These products are
processors on 3 different machines. The time required for
manufacturing one unit of cost of the products and the daily
capacity of the three machines is given in the table below.
Analyse and find the optimum solution.
Mac
hine
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Machine
Capacity
Min /Day
Product1 Product 2 Product 3
M1 2 8 2 940
M2 4 - 8 970
M3 2 5 - 430
It is required to determine the daily no. of units to be
manufactured for each product. The profit for unit for
Level 2 Understanding
product 1,2,3 is Rs.4,Rs.8,Rs.6 respectively. It is assumed
that all the amount produced are consumed in the market
13. Using dual simplex method , solve and find the optimum
solution for the given LPP.
Maximize Z=6x
1
+4x
2
+4x
3
Subject to 3x
1
,x
2
+2x
3
? 2
2x
1
+x
2
-x
3
? 1
-x
1
+x
2
+2x
3
? 1 &
x
1
,x
2
,x
3
? 0
Level 4 Analysing
14.
(i)
Evaluate by using dual simplex method and solve the LPP.
Minimize Z=2x
1
+x
2
Subject to 3x
1
+2x
2
? 3
4x
1
+3x
2
? 6
x
1
+x
2
? 5 & x
1
,x
2
?
Determine the dual simplex table
(5)
Level 1 Remembering
(ii)
Find the value of x
1
, x
2
(8)
PART - C
S.No Questions BT
LEVEL
COMPETENCE
1.
Max Z=300x+400y subject to
2x+3y ? 1600,
3x+2y ? 1500,
x+y ? 700,
y ? 300, x,y ? 0 Solve by Graphical Method, choose the
value of x & y which maximizes profit.
Level 1 Remembering
2. Solve the following LPP by graphical method.
Minimize Z= 6000x1+4000x
2
Subject t o
3x+x
2
? 40,
x
1
+2.5 x
2
? 22
3x
1
+3 x
2
? 40
and x
1
,x
2
? 0
Level 2 Understanding
3. Develop a Simplex Table and Solve
Max Z = 3 x1+2 x2,
Subject to
x1+ x2 ?4,
x1- x2 ? 2;
x1, x2 ?0.
Level 3 Applying
4. Solve by using Simplex Method.
Maximize Z= 3x+5y
Subject to the constraints
x+y? 60
x? 40
y ? 30
x,y ? 0
Level 1 Remembering
UNIT - II LINEAR PROGRAMMING EXTENSIONS
SYLLABUS: Transportation Models (Minimizing and Maximizing Problems) ? Balanced and unbalanced
Problems ? Initial Basic feasible solution by N-W Corner Rule, Least cost and Vogel?s approximation methods.
Check for optimality. Solution by MODI /. Case of Degeneracy. Trans-shipment Models. Assignment Models
(Minimising and Maximising Problems) ? Balanced and Unbalanced Problems. Solution by Hungarian and
Branch and Bound Algorithms. Travelling Salesman problem.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define Transportation & Transhipment. Level 1 Remembering
2. Differentiate balanced transportation problem & Unbalanced
Transportation Problem.
Level 2 Understanding
3. How would you show your understanding on unbalanced
transportation problem?
Level 3 Applying
4. Categorize the Phases of transportation model. Level 4 Analysing
5. Construct the basic feasible solution for the following
transportation problem.
1 2 3 4 SUPPLY
1 2 3 11 7 6
2 1 0 6 1 1
3 5 8 15 9 10
DEMAN D 7 5 3 2
Level 5 Evaluating
6 Interpret the need for Optimum solution in transportation. Level 6 Creating
7. What do you mean by Least cost method (LCM)? Level 1 Remembering
8. Compare Vogel approximation method (VAM) & Least Cost
Method.
Level 2 Understanding
9. How do you represent a travelling salesman problem
through mathematical formulation?
Level 3 Applying
10. Analyse the rules of travelling salesman Problem. Level 4 Analysing
11. Discuss the meaning of Assignment Level 5 Evaluating
12. Compare Balanced assignment problem & Unbalanced
Assignment Problem.
Level 6 Creating
13. What example can you give for Unbalanced assignment
problem?
Level 1 Remembering
14. How will you resolve degeneracy in Transportation Problem? Level 2 Understanding
15. Classify transportation problem. Level 3 Applying
16. Examine the Steps in Hungarian algorithm. Level 4 Analysing
17. What is Branch and bound algorithm in Assignment? Level 1 Remembering
18. Compare Assignment and transportation Problem. Level 2 Understanding
19. What do you mean by Travelling Salesman Problem? Level 1 Remembering
20. What is Restricted Assignment? Level 1 Remembering
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Solve and find the Transportation Problem and Which method will
you select if you want toMinimize Cost?
Destination Supply
1 2 3 4
I 21 16 25 13 11
II 17 18 14 23 13
III 32 27 18 41 19
Demand 6 10 12 15
Level 1 Remembering
2. Find the Initial Basic Feasible solution for following TP. Using NW
Rule, LCM, and VAM. Which method will you select if you want to
Minimize Cost?
D1 D2 D3 Supply
S1 7 3 2 2
S2 2 1 3 3
S3 3 4 6 5
Demand 4 1 5 10
Level 2 Understanding
3.
(i)
Analyze the transportation problem with unit transportation
costs,demand, and supply as given below:
Destination
Supply
Source
D1 D2 D3 D4
S1
6 1 9 3
70
11 5 2 8
S2 55
10 12 4 7
S3
70
Demand 85 35 50 45
Apply VAM for Initial solution.
(5)
Level 3 Applying
(ii)
Construct the final Solution by using MODIMethod.
(8)
4.
(i)
Analyze & solve the following transportation problem to maximize
profit.
A B C D Supply
1
Source 2
3
Demand
15 51 42 33 23
80 42 26 81 44
90 40 66 60 33
23
31
16
30
100
Examine Initial solution using VAM.
(5)
Level 4 Analysing
(ii)
Analyze and find out the final Solution by using MODI Method.
(8)
5. Solve the following transportation problem using Vogel?s
method
Factory? Warehouse ?Available
A B C D E F
1 9 12 9 6 9 10 5
2 7 3 7 7 5 5 6
3 6 5 9 11 3 11 2
4 6 8 11 2 2 10 9
4 4 6 2 4 2
Requirement?
(5)
Level 5 Evaluating
6. (i) Solve the transportation problem and decide using VAM for initial
solution.
(5) Level 6 Creating
(ii) Evaluate using NWC and Least Cost method for initial solution?
Destination Supply
I 2 1 25 13 11
II 1 1 14 23 13
III 3 2 18 41 19
Demand 6 1 22 15
(8)
7.
Maximize profit from the following transportationproblem.
A B C D Supply
I 40 25 22 33 100
SourceII 44 35 30 30 30
III 38 38 28 30 70
Demand 40 20 60 30
Level 1 Remembering
(i) How will you convert maximization problem to minimization.
Find the maximum profit
(8)
(ii) Explain stepping stone method for checking the
solution for optimality transportation problems.
(5)
8. A company has one surplus truck in each of the cities A, B, C, D, &
E and one deficit trucks in each of the cities 1,2,3,4,5,6. The
distance between the cities in kms is shown in the matrix below.
Can you select the assignment of trucks from cities in surplus to
cities in deficiency .so that total distance covered by the vehicles is
minimum?
1 2 3 4 5 6
A 12 10 15 22 18 8
B 10 18 25 15 16 12
C 11 10 3 8 5 9
D 6 4 10 13 13 12
E 8 12 11 7 13 10
Level 2 Understanding
9.
Consider the problem of assigning five jobs to five persons. The
assignment costs are given as follows:
PERSONS?JOBS ?
1 2 3 4 5
A 8 4 2 6 1
B 0 9 5 5 4
C 3 8 9 2 6
D 4 3 1 0 3
Level 3 Applying
E 9 5 8 9 5
Determine the optimum assignment schedule.
10. The assignment cost of assigning any one operator to any one
machine is given in the following table.
MACHINE?OPERATORS ?
I II III IV
A 10 5 13 15
B 3 9 18 3
C 10 7 3 2
D 5 11 9 7
Find the optimal assignment by Hungarian method.
Level 4 Analysing
11. A machine shop purchased a drilling machine and two lathes of
different capacities. The Positioning of the machines among 4
possible locations on the shop floor is important forms the
standard of materials handling. Given the cost estimate per unit
time of materials below, find the optimum location of the
machines.
LOCATIONS
1 2 3 4
Lathe 1 12 9 12 9
Drill 15 Not
suitable
13 20
Lathe 2 4 8 10 6
Level 1 Remembering
12.
Solve the assignment problem for maximization given profit
matrix(profit in rupees).
Machines
P Q R S
JOB
51 53 54 50
47 50 48 50
49 50 60 61
63 64 60 60
Level 2 Understanding
PART - C
S.No Questions Marks BT
Level
Competence
1.
a
Assume that you are an OR specialist. Identify the procedure
for each of the following Method to the employees in order to
help them achieve solution to Transportation Problems.
Northwest Corner Cell Method
(3)
Level 1 Remembering
b Least Cost cell Method (4)
c Vogel?s Approximation Method (4)
d U V Method. (4)
13. The processing time in hours for the jobs when allocated to the
different machines is indicated below. Select the best assignment
of the machines for the jobs so that the total processing time is
Minimum.
Machines
M1 M2 M3 M4 M5
J1 9 22 58 11 19
JOB J2 43 78 72 50 63
J3 41 28 91 37 45
J4 74 42 27 49 39
J5 36 11 57 22 25
Level 4 Analysing
14. For the given travelling salesman problem, Minimize the total cost.
To
1 2 3 4
From A - 46 16 40
B 41 - 50 40
C 82 32 - 60
D 40 40 36 -
Level 1 Remembering
(i) Observe the above travelling salesman
problem and find out minimize the cost per
cycle.
(8)
(ii) Find whether path is satisfied. (5)
2.
Solve the following transportation problem, in which a
i
is the
availability at Origin
O
i
and b
j
is the requirement at the destination D
j
and cell entries
are unit costs of transportation from any origin to any
destination:
D1 D2 D3 D4 D5 a
j
O1 4 7 3 8 2 4
O2 1 4 7 3 8 7
O3 7 2 4 7 7 9
O4 4 8 2 4 7 2
b
j
8 3 7 2 2
Predict the allocation to minimize the cost.
Level 2 Understanding
3. A company has a team of 4 Salesman and the company wants to
do in 4 districts. Considering the capabilities of salesmen
and nature of the district, the company has estimated the profit per
day in Rs. For each salesmen in each district as follows.
District
s
Salesmen 1 2 3 4
A 16 10 14 11
B 14 11 15 15
C 15 15 13 12
D 13 12 14 15
Develop the best assignment schedule and analyze the total cost.
Level 3 Applying
4. Five operators have to be assigned to Five Machines. The
assignment costs are given in thetablebelow.
Analyse using Hungarian algorithm & find out the assignment to
minimize the cost.
Machine
I II III IV V
Operator
A 5 5 - 2 6
B 7 4 2 3 4
C 9 3 5 - 3
D 7 2 6 7 2
E 6 5 7 9 1
Level 4 Analyzing
UNIT ? III ? INTEGER PROGRAMMING AND GAME THEORY
SYLLABUS: Integer Programming ? Introduction and types - Game Theory-Two-person Zero sum
games-Saddle point, Dominance Rule, graphical and LP solutions, Nash Equilibrium
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. What do you mean by integer programming problem?
Level 1 Remembering
2. In what respect a mixed IPP differs from pure IPP?
Level 2 Understanding
3. What is Nash Equilibrium?
Level 3 Applying
4. Classify the different types of strategy.
Level 4 Analysing
5. Compile the Characteristics of game.
Level 5 Evaluating
6. Can you assess the applications of integer
programming?
Level 6 Creating
7. Define Game.
Level 1 Remembering
8. Compare Mixed Strategy and Pure Strategy.
Level 2 Understanding
9. How would you make use of the concept of Game theory
in Managerial Decision Making?
Level 3 Applying
10. Conclude your understanding about Payoff Matrix.
Level 4 Analysing
11. How will you find the optimal strategies and value of the
following game?
Player B
Player
A
H T
H 2 -1
T -1 0
Level 5 Evaluating
12. Interpret the concept of two person zero sum game.
Level 6 Creating
13. What is Saddle point?
Level 1 Remembering
14. Compare Dominance Principle of Rows and Columns.
Level 2 Understanding
15. Identify the basic assumptions of the Game.
Level 3 Applying
16. Conclude the advantages of Game theory.
Level 4 Analysing
17. What are the Methods of Matrices?
Level 1 Remembering
18. Summarize how graphs and LP solution are used in
Game theory.
Level 2 Understanding
19. What is a Decision Tree?
Level 1 Remembering
20. Define Dominance principle.
Level 1 Remembering
S.N
O
PART - B QUESTIONS MA
RK
S
BT
LEVEL
COMPETENCE
1. (i) What do you mean by Pure IPP? (3) Level 1 Remembering
(ii) What do you mean by Mixed IPP? (5)
(iii)
List out the difference between Pure and Mixed IPP.
(5)
2. (i) For what value of ?,the game with the following
matrix is strictly determined
B
1
B
2
B
3
A
1
? 6 2
A
2
-1 ? -7
A
3
-2 4 ?
(8) Level 2 Understanding
(ii) Write down the assumptions of game theory. (5)
3. (i) Solve the game whose pay-off matrix is given by
B
1
B
2
B
3
A
1
1 3 1
A
2
0 -4 -3
A
3
1 5 -1
(8)
Level 3 Applying
(ii) Explain the concept of Nash Equilibrium. (5)
4.
Analyze the Value of the game graphically
B1 B2
A1 4 4
A2 2 7
A3 5 3
A4 6 2
Level 4 Analysing
5.
What inference can be made using Dominance
Principle to reduce the following game and estimate
the game value?
B1 B2 B3 B4
A1 3 2 4 0
A2 3 4 2 4
A3 4 2 2 0
A4 2 1 6 3
Level 5 Evaluating
6.
How would you evaluate the following game whose
Pay-Off matrix is Given Below?
9 3 1 8 0
6 5 4 6 7
2 4 3 3 8
5 6 2 2 1
Level 6 Creating
7.
(i)
Two players A&B match coins. If the coins match
then A wins one unit value, if the coins do not
match then B wins one unit of value.
Determine pay-off matrix which strategy is to be
chosen
(5)
Level 1 Remembering
(ii)
Find the value of game. (8)
8.
Predict the Value of the Game given above Pay
OffMatrix.
Player B
B1 B2 B3
A1 -2 5 -3
Player A A2 1 3 5
A3 -3 -7 11
Level 2 Understanding
9.
Apply graphical analysis to Solve the game.
A/
B
B1 B2 B3 B4
A1 3 3 4 0
A2 5 4 3 7
Level 3 Applying
10. Solve the following game by graphical method.
Player B
1 2 3
1 6 4 3
Player A 2 2 4 8
Level 4 Analysing
11.
(i)
A and B play a Match(Game) in which each has 3
coins 5 paise, 10 paise and 20 paise. Each player
selects a coin without the knowledge of others
choice. IF the sum is even, B wins A?s Coin. If sum
is Odd, A wins B?s coin.
How will you find the pay-off matrix ?
(5)
Level 1
Remembering
(ii)
Find the Best Strategy & value of the Game. (8)
12.
Consider the Pay Off Matrix of player A as shown in
the table below and solve it optimally using the
graphical method .
Player A
Player
B
1 2 3 4 5
1 3 6 8 4 4
2 -7 4 2 10 2
Level 2 Understanding
13.
(i)
Analyze the Game Graphically:
Player A
Player
A
B1 B2
A1 -3 1
A2 5 3
A3 6 -1
A4 1 4
A5 2 2
A6 0 -5
Plot the graph
(5)
Level 4 Analysing
(ii)
Analyse and find the value of the game.
(8)
14.
Which one is the best strategy using Dominance
Principle?
B1 B2 B3 B4 B5 B6
A1
4 2 0 2 1 1
A2
4 3 1 3 2 2
A3
4 3 7 -5 1 2
A4
4 3 4 -1 2 2
A5
4 3 3 -2 2 2
Level 1 Remembering
PART-C
S.No Questions BT
Level
Competence
1.
Using Dominance property Solve.
B
A
I II IIIIV
1 -5 3 1 20
2 5 5 4 6
3 -4 -2 0 -5
Level 1 Remembering
2. Examine the 2 * n Game by the Method of Sub Game:
B1 B2 B3
A1 1 3 11
A2 8 5 2
Level 2 Understanding
3. In a game of matching coins with 2 players, A wins 1 unit value
when there are 2 heads, wins nothing when there are 2 tails
and looses ? unit value when there are one head and one tail.
Develop Pay Off matrix and value of the game.
Level 3 Applying
4.
i
ii
iii
Assume you have to choice of 3 strategies for advertising
and you have one major
Analyse the theory on Two-person sum games competitor
with 3 strategies.
(5)
Level 4 Analysing
What are the assumptions of Game? (5)
Find value of game.
B1 B2 B3
A1 80 70 60
A2 90 80 100
A3 40 30 40
(5)
UNIT - IV INVENTORY MODELS, SIMULATION AND DECISION THEORY
SYLLABUS: Inventory Models ? EOQ and EBQ Models (With and without shortages), Quantity Discount
Models. Decision making under risk ? Decision trees ? Decision making under uncertainty. Monte-carlo
simulation.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define inventory. Level 1 Remembering
2.
Classify the Forms of inventory.
Level 2 Understanding
3.
Identify the Objectives/significance of inventory model.
Level 3 Applying
4.
Highlight the importance of Reorder level.
Level 4 Analysing
5.
Discuss the concept of Lead time.
Level 5 Evaluate
6.
Interpret the Types of stock replenishment.
Level 1 Remembering
7.
List the Basic inventory models.
Level 2 Understanding
8.
Compare Ordering Cost and Carrying Cost.
Level 3 Appyling
9.
Identify when shortage cost and stock out cost arises?
Level 5 Evaluating
10.
Analyze why safety stock is maintained.
Level 1 Remembering
11.
Discuss the concept of Quantity Discount Model.
Level 2 Understanding
12.
Interpret the meaning of EOQ & EBQ.
Level 3 Applying
13.
What are random and pseudo random numbers?
Level 4 Analysing
14.
Explain Monte Carlo Method.
Level 5 Evaluating
15.
Summarize the concept of EMV.
Level 1 Remembering
16.
What inference can you make about holding cost ?
Level 2 Understanding
FirstRanker.com - FirstRanker's Choice
(An
?
DEPARTMENT OF MANAGEMENT STUDIES
QUESTION BANK
II SEMESTER
1915201? APPLIED OPERATIONS RESEACH
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Dr. Radha Ganesh Kumar ? Asst. Professor (Sel.G) and HOD
Mr.B. Sam Paul ? Asst. Professor (OG)
(An
? .
DEPARTMENT OFMANAGEMENT STUDIES
QUESTION BANK
SUBJECT :1915201 ?APPLIED OPERATIONS RESEACH
SEM / YEAR : IISemester / IYear
UNIT ? I ?INTRODUCTION TO LINEAR PROGRAMMING (LP)
SYLLABUS: Introduction to applications of operations research in functional areas of management.
Linear Programming-formulation, solution by graphical and simplex methods, Special cases. Dual
simplex method. Principles of Duality. Sensitivity Analysis.
PART- A
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Define Operations Research (OR). Level 1 Remembering
2. Differentiate between Simplex and Big M Method Level 2 Understanding
3. How do you show your understanding unbounded solution? Level 3 Applying
4. Categorize the forms of LPP. Level 4 Analysing
5.
Discuss why is two phase method is better than Big M
method?
Level 5 Evaluating
6. Interpret the usage of Sensitivity Analysis in LPP. Level 6 Creating
7. What are the assumptions and requirements of LPP? Level 1 Remembering
8. Compare Dual Simplex and Duality. Level 2 Understanding
9. Identify the Advantages of duality. Level 3 Applying
10. What do you think about Infeasible solution? Level 4 Analysing
11. How will you solve LPP graphically? Level 5 Evaluating
12.
Conclude your understanding on the mathematical
formulation of LPP.
Level 6 Creating
13. Define basic variables and artificial variables. Level 1 Remembering
14. Compare Slack variable & Surplus Variable. Level 2 Understanding
15.
Give some example for the role of Surplus variable & Slack
Variable in the simplex method
Level 3 Applying
16. How would you apply Artificial variable? Level 4 Analysing
17. What is Big M Method? Level 1 Remembering
18. Distinguish simplex and Big M method Level 2 Understanding
19.
What do you mean by Duality? List the Rules for primal and
dual.
Level 1 Remembering
20. What is Shadow price? Level 1 Remembering
PART- B
S.NO
QUESTIONS
BT
LEVEL
COMPETENCE
1.
(i)
Maximise Z=3x+4y subject to
2x+5y ?60,
4x+2y ?40.
x, y >0. Solve by Graphical Method
Plot the graph
(8)
Level 1 Remembering
(ii) Which one is the best solution? (5)
2.
(i)
Min Z= 20x
1
+10 x
2
subject to
x
1
+2x
2
? 40,
3x
1
+x
2
? 30,
4x
1
+3x
2
? 60,
x
1
,x
2
? 0.
Solve by Graphical Method,
Plot the graph
(8)
Level 2 Understanding
(ii) Predict the value of x & y. (5)
3 Max Z= 5x1+4x2 subject to
x
1
-2x
2
? 1,
x
1
+2x
2
?3,
x
1
,x
2
? 0. Solve Graphically. Which one is the best
solution?
Level 3 Applying
4.
(i)
A Plant Manufacturer 2 Product A & B. The Profit Contribution
of each product has been estimated as Rs.300 for product A
and Rs.400 for Product B. Each Product passes through 3
departments of the plant. The time required for each product
and total time available in each department is as follows.
Department Hours
Required
Hours
Required
Available
Hours
during
month
Product
A
Product
B
I 2 3 1600
II 3 2 1500
III 1 1 700
The company has a contract to supply atleast 300 units of
Product B per month.
Formulate the LPP
(5)
Level 4
Analysing
(ii) Solve through Graphical Method
(8)
5. Solve the following LPP by graphical method.
Maximize Z= 3x
1
+2x
2
Subject t o
- 2x
1
+x
2
?1,
x
1
? 2,
x
1
+ x
2
? 3
and x
1
,x
2
? 0
Level 5 Evaluating
6. (i) Max Z= 1000x
1
+4000x
2
+5000x
3
Subject to 3x1+3x
3
?22,
x1+2x2+3x
3
? 14,
3x1+2x2 ? 14
& x1,x2 ? 0
Develop a Simplex Table
(5)
Level 6 Creating
(ii) Analyse and find the value of x
1
, x
2
? (8)
7. Analyze the following LPP by Simplex Method:
Min Z = -10y
1
-15y
2
-20y
3
Subject to 2y
1
+4y
2
+6y
3
? 24,
3y
1
+9y
2
+6y
3
? 30,
& y
1
, y
2
, y
3
? 0.
Level 1 Remembering
(i)
Develop a Simplex Table (5)
(ii) Solve and find the value of y1 ,y2 and y3
(8)
8.
Solve By Graphical Method
Minimize Z= 40x
1
+24x
2
Subject to, 20x
1
+50 x
2
> 4,800
80 x
1
+50x
2
> 7,200
x
1
,x
2
>0
Level 2 Understanding
9. Solve the following LPP by simplex method:
Minimize Z= 8x
1
-2x
2
Subject to -4x
1
+2x
2
?1,
5x
1
-4x
2
?3,
and x
1
,x
2
? 0
Level 3 Applying
10. Solve the following LPP by simplex method:
Maximize Z= 3x1+2x
2
Subject to
2x
1
+x
2
?2,
3x
1
+4x
2
?12,
x
1
,x
2
? 0
Level 4 Analyzing
11. Review the LPP and solve by simplex method
Max Z= 25x+10y
Subject to the constraints
x+0.5y? 20
x+y? 50
x,y ? 0
Level 1 Remembering
12. A firm produces three products. These products are
processors on 3 different machines. The time required for
manufacturing one unit of cost of the products and the daily
capacity of the three machines is given in the table below.
Analyse and find the optimum solution.
Mac
hine
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Machine
Capacity
Min /Day
Product1 Product 2 Product 3
M1 2 8 2 940
M2 4 - 8 970
M3 2 5 - 430
It is required to determine the daily no. of units to be
manufactured for each product. The profit for unit for
Level 2 Understanding
product 1,2,3 is Rs.4,Rs.8,Rs.6 respectively. It is assumed
that all the amount produced are consumed in the market
13. Using dual simplex method , solve and find the optimum
solution for the given LPP.
Maximize Z=6x
1
+4x
2
+4x
3
Subject to 3x
1
,x
2
+2x
3
? 2
2x
1
+x
2
-x
3
? 1
-x
1
+x
2
+2x
3
? 1 &
x
1
,x
2
,x
3
? 0
Level 4 Analysing
14.
(i)
Evaluate by using dual simplex method and solve the LPP.
Minimize Z=2x
1
+x
2
Subject to 3x
1
+2x
2
? 3
4x
1
+3x
2
? 6
x
1
+x
2
? 5 & x
1
,x
2
?
Determine the dual simplex table
(5)
Level 1 Remembering
(ii)
Find the value of x
1
, x
2
(8)
PART - C
S.No Questions BT
LEVEL
COMPETENCE
1.
Max Z=300x+400y subject to
2x+3y ? 1600,
3x+2y ? 1500,
x+y ? 700,
y ? 300, x,y ? 0 Solve by Graphical Method, choose the
value of x & y which maximizes profit.
Level 1 Remembering
2. Solve the following LPP by graphical method.
Minimize Z= 6000x1+4000x
2
Subject t o
3x+x
2
? 40,
x
1
+2.5 x
2
? 22
3x
1
+3 x
2
? 40
and x
1
,x
2
? 0
Level 2 Understanding
3. Develop a Simplex Table and Solve
Max Z = 3 x1+2 x2,
Subject to
x1+ x2 ?4,
x1- x2 ? 2;
x1, x2 ?0.
Level 3 Applying
4. Solve by using Simplex Method.
Maximize Z= 3x+5y
Subject to the constraints
x+y? 60
x? 40
y ? 30
x,y ? 0
Level 1 Remembering
UNIT - II LINEAR PROGRAMMING EXTENSIONS
SYLLABUS: Transportation Models (Minimizing and Maximizing Problems) ? Balanced and unbalanced
Problems ? Initial Basic feasible solution by N-W Corner Rule, Least cost and Vogel?s approximation methods.
Check for optimality. Solution by MODI /. Case of Degeneracy. Trans-shipment Models. Assignment Models
(Minimising and Maximising Problems) ? Balanced and Unbalanced Problems. Solution by Hungarian and
Branch and Bound Algorithms. Travelling Salesman problem.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define Transportation & Transhipment. Level 1 Remembering
2. Differentiate balanced transportation problem & Unbalanced
Transportation Problem.
Level 2 Understanding
3. How would you show your understanding on unbalanced
transportation problem?
Level 3 Applying
4. Categorize the Phases of transportation model. Level 4 Analysing
5. Construct the basic feasible solution for the following
transportation problem.
1 2 3 4 SUPPLY
1 2 3 11 7 6
2 1 0 6 1 1
3 5 8 15 9 10
DEMAN D 7 5 3 2
Level 5 Evaluating
6 Interpret the need for Optimum solution in transportation. Level 6 Creating
7. What do you mean by Least cost method (LCM)? Level 1 Remembering
8. Compare Vogel approximation method (VAM) & Least Cost
Method.
Level 2 Understanding
9. How do you represent a travelling salesman problem
through mathematical formulation?
Level 3 Applying
10. Analyse the rules of travelling salesman Problem. Level 4 Analysing
11. Discuss the meaning of Assignment Level 5 Evaluating
12. Compare Balanced assignment problem & Unbalanced
Assignment Problem.
Level 6 Creating
13. What example can you give for Unbalanced assignment
problem?
Level 1 Remembering
14. How will you resolve degeneracy in Transportation Problem? Level 2 Understanding
15. Classify transportation problem. Level 3 Applying
16. Examine the Steps in Hungarian algorithm. Level 4 Analysing
17. What is Branch and bound algorithm in Assignment? Level 1 Remembering
18. Compare Assignment and transportation Problem. Level 2 Understanding
19. What do you mean by Travelling Salesman Problem? Level 1 Remembering
20. What is Restricted Assignment? Level 1 Remembering
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Solve and find the Transportation Problem and Which method will
you select if you want toMinimize Cost?
Destination Supply
1 2 3 4
I 21 16 25 13 11
II 17 18 14 23 13
III 32 27 18 41 19
Demand 6 10 12 15
Level 1 Remembering
2. Find the Initial Basic Feasible solution for following TP. Using NW
Rule, LCM, and VAM. Which method will you select if you want to
Minimize Cost?
D1 D2 D3 Supply
S1 7 3 2 2
S2 2 1 3 3
S3 3 4 6 5
Demand 4 1 5 10
Level 2 Understanding
3.
(i)
Analyze the transportation problem with unit transportation
costs,demand, and supply as given below:
Destination
Supply
Source
D1 D2 D3 D4
S1
6 1 9 3
70
11 5 2 8
S2 55
10 12 4 7
S3
70
Demand 85 35 50 45
Apply VAM for Initial solution.
(5)
Level 3 Applying
(ii)
Construct the final Solution by using MODIMethod.
(8)
4.
(i)
Analyze & solve the following transportation problem to maximize
profit.
A B C D Supply
1
Source 2
3
Demand
15 51 42 33 23
80 42 26 81 44
90 40 66 60 33
23
31
16
30
100
Examine Initial solution using VAM.
(5)
Level 4 Analysing
(ii)
Analyze and find out the final Solution by using MODI Method.
(8)
5. Solve the following transportation problem using Vogel?s
method
Factory? Warehouse ?Available
A B C D E F
1 9 12 9 6 9 10 5
2 7 3 7 7 5 5 6
3 6 5 9 11 3 11 2
4 6 8 11 2 2 10 9
4 4 6 2 4 2
Requirement?
(5)
Level 5 Evaluating
6. (i) Solve the transportation problem and decide using VAM for initial
solution.
(5) Level 6 Creating
(ii) Evaluate using NWC and Least Cost method for initial solution?
Destination Supply
I 2 1 25 13 11
II 1 1 14 23 13
III 3 2 18 41 19
Demand 6 1 22 15
(8)
7.
Maximize profit from the following transportationproblem.
A B C D Supply
I 40 25 22 33 100
SourceII 44 35 30 30 30
III 38 38 28 30 70
Demand 40 20 60 30
Level 1 Remembering
(i) How will you convert maximization problem to minimization.
Find the maximum profit
(8)
(ii) Explain stepping stone method for checking the
solution for optimality transportation problems.
(5)
8. A company has one surplus truck in each of the cities A, B, C, D, &
E and one deficit trucks in each of the cities 1,2,3,4,5,6. The
distance between the cities in kms is shown in the matrix below.
Can you select the assignment of trucks from cities in surplus to
cities in deficiency .so that total distance covered by the vehicles is
minimum?
1 2 3 4 5 6
A 12 10 15 22 18 8
B 10 18 25 15 16 12
C 11 10 3 8 5 9
D 6 4 10 13 13 12
E 8 12 11 7 13 10
Level 2 Understanding
9.
Consider the problem of assigning five jobs to five persons. The
assignment costs are given as follows:
PERSONS?JOBS ?
1 2 3 4 5
A 8 4 2 6 1
B 0 9 5 5 4
C 3 8 9 2 6
D 4 3 1 0 3
Level 3 Applying
E 9 5 8 9 5
Determine the optimum assignment schedule.
10. The assignment cost of assigning any one operator to any one
machine is given in the following table.
MACHINE?OPERATORS ?
I II III IV
A 10 5 13 15
B 3 9 18 3
C 10 7 3 2
D 5 11 9 7
Find the optimal assignment by Hungarian method.
Level 4 Analysing
11. A machine shop purchased a drilling machine and two lathes of
different capacities. The Positioning of the machines among 4
possible locations on the shop floor is important forms the
standard of materials handling. Given the cost estimate per unit
time of materials below, find the optimum location of the
machines.
LOCATIONS
1 2 3 4
Lathe 1 12 9 12 9
Drill 15 Not
suitable
13 20
Lathe 2 4 8 10 6
Level 1 Remembering
12.
Solve the assignment problem for maximization given profit
matrix(profit in rupees).
Machines
P Q R S
JOB
51 53 54 50
47 50 48 50
49 50 60 61
63 64 60 60
Level 2 Understanding
PART - C
S.No Questions Marks BT
Level
Competence
1.
a
Assume that you are an OR specialist. Identify the procedure
for each of the following Method to the employees in order to
help them achieve solution to Transportation Problems.
Northwest Corner Cell Method
(3)
Level 1 Remembering
b Least Cost cell Method (4)
c Vogel?s Approximation Method (4)
d U V Method. (4)
13. The processing time in hours for the jobs when allocated to the
different machines is indicated below. Select the best assignment
of the machines for the jobs so that the total processing time is
Minimum.
Machines
M1 M2 M3 M4 M5
J1 9 22 58 11 19
JOB J2 43 78 72 50 63
J3 41 28 91 37 45
J4 74 42 27 49 39
J5 36 11 57 22 25
Level 4 Analysing
14. For the given travelling salesman problem, Minimize the total cost.
To
1 2 3 4
From A - 46 16 40
B 41 - 50 40
C 82 32 - 60
D 40 40 36 -
Level 1 Remembering
(i) Observe the above travelling salesman
problem and find out minimize the cost per
cycle.
(8)
(ii) Find whether path is satisfied. (5)
2.
Solve the following transportation problem, in which a
i
is the
availability at Origin
O
i
and b
j
is the requirement at the destination D
j
and cell entries
are unit costs of transportation from any origin to any
destination:
D1 D2 D3 D4 D5 a
j
O1 4 7 3 8 2 4
O2 1 4 7 3 8 7
O3 7 2 4 7 7 9
O4 4 8 2 4 7 2
b
j
8 3 7 2 2
Predict the allocation to minimize the cost.
Level 2 Understanding
3. A company has a team of 4 Salesman and the company wants to
do in 4 districts. Considering the capabilities of salesmen
and nature of the district, the company has estimated the profit per
day in Rs. For each salesmen in each district as follows.
District
s
Salesmen 1 2 3 4
A 16 10 14 11
B 14 11 15 15
C 15 15 13 12
D 13 12 14 15
Develop the best assignment schedule and analyze the total cost.
Level 3 Applying
4. Five operators have to be assigned to Five Machines. The
assignment costs are given in thetablebelow.
Analyse using Hungarian algorithm & find out the assignment to
minimize the cost.
Machine
I II III IV V
Operator
A 5 5 - 2 6
B 7 4 2 3 4
C 9 3 5 - 3
D 7 2 6 7 2
E 6 5 7 9 1
Level 4 Analyzing
UNIT ? III ? INTEGER PROGRAMMING AND GAME THEORY
SYLLABUS: Integer Programming ? Introduction and types - Game Theory-Two-person Zero sum
games-Saddle point, Dominance Rule, graphical and LP solutions, Nash Equilibrium
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. What do you mean by integer programming problem?
Level 1 Remembering
2. In what respect a mixed IPP differs from pure IPP?
Level 2 Understanding
3. What is Nash Equilibrium?
Level 3 Applying
4. Classify the different types of strategy.
Level 4 Analysing
5. Compile the Characteristics of game.
Level 5 Evaluating
6. Can you assess the applications of integer
programming?
Level 6 Creating
7. Define Game.
Level 1 Remembering
8. Compare Mixed Strategy and Pure Strategy.
Level 2 Understanding
9. How would you make use of the concept of Game theory
in Managerial Decision Making?
Level 3 Applying
10. Conclude your understanding about Payoff Matrix.
Level 4 Analysing
11. How will you find the optimal strategies and value of the
following game?
Player B
Player
A
H T
H 2 -1
T -1 0
Level 5 Evaluating
12. Interpret the concept of two person zero sum game.
Level 6 Creating
13. What is Saddle point?
Level 1 Remembering
14. Compare Dominance Principle of Rows and Columns.
Level 2 Understanding
15. Identify the basic assumptions of the Game.
Level 3 Applying
16. Conclude the advantages of Game theory.
Level 4 Analysing
17. What are the Methods of Matrices?
Level 1 Remembering
18. Summarize how graphs and LP solution are used in
Game theory.
Level 2 Understanding
19. What is a Decision Tree?
Level 1 Remembering
20. Define Dominance principle.
Level 1 Remembering
S.N
O
PART - B QUESTIONS MA
RK
S
BT
LEVEL
COMPETENCE
1. (i) What do you mean by Pure IPP? (3) Level 1 Remembering
(ii) What do you mean by Mixed IPP? (5)
(iii)
List out the difference between Pure and Mixed IPP.
(5)
2. (i) For what value of ?,the game with the following
matrix is strictly determined
B
1
B
2
B
3
A
1
? 6 2
A
2
-1 ? -7
A
3
-2 4 ?
(8) Level 2 Understanding
(ii) Write down the assumptions of game theory. (5)
3. (i) Solve the game whose pay-off matrix is given by
B
1
B
2
B
3
A
1
1 3 1
A
2
0 -4 -3
A
3
1 5 -1
(8)
Level 3 Applying
(ii) Explain the concept of Nash Equilibrium. (5)
4.
Analyze the Value of the game graphically
B1 B2
A1 4 4
A2 2 7
A3 5 3
A4 6 2
Level 4 Analysing
5.
What inference can be made using Dominance
Principle to reduce the following game and estimate
the game value?
B1 B2 B3 B4
A1 3 2 4 0
A2 3 4 2 4
A3 4 2 2 0
A4 2 1 6 3
Level 5 Evaluating
6.
How would you evaluate the following game whose
Pay-Off matrix is Given Below?
9 3 1 8 0
6 5 4 6 7
2 4 3 3 8
5 6 2 2 1
Level 6 Creating
7.
(i)
Two players A&B match coins. If the coins match
then A wins one unit value, if the coins do not
match then B wins one unit of value.
Determine pay-off matrix which strategy is to be
chosen
(5)
Level 1 Remembering
(ii)
Find the value of game. (8)
8.
Predict the Value of the Game given above Pay
OffMatrix.
Player B
B1 B2 B3
A1 -2 5 -3
Player A A2 1 3 5
A3 -3 -7 11
Level 2 Understanding
9.
Apply graphical analysis to Solve the game.
A/
B
B1 B2 B3 B4
A1 3 3 4 0
A2 5 4 3 7
Level 3 Applying
10. Solve the following game by graphical method.
Player B
1 2 3
1 6 4 3
Player A 2 2 4 8
Level 4 Analysing
11.
(i)
A and B play a Match(Game) in which each has 3
coins 5 paise, 10 paise and 20 paise. Each player
selects a coin without the knowledge of others
choice. IF the sum is even, B wins A?s Coin. If sum
is Odd, A wins B?s coin.
How will you find the pay-off matrix ?
(5)
Level 1
Remembering
(ii)
Find the Best Strategy & value of the Game. (8)
12.
Consider the Pay Off Matrix of player A as shown in
the table below and solve it optimally using the
graphical method .
Player A
Player
B
1 2 3 4 5
1 3 6 8 4 4
2 -7 4 2 10 2
Level 2 Understanding
13.
(i)
Analyze the Game Graphically:
Player A
Player
A
B1 B2
A1 -3 1
A2 5 3
A3 6 -1
A4 1 4
A5 2 2
A6 0 -5
Plot the graph
(5)
Level 4 Analysing
(ii)
Analyse and find the value of the game.
(8)
14.
Which one is the best strategy using Dominance
Principle?
B1 B2 B3 B4 B5 B6
A1
4 2 0 2 1 1
A2
4 3 1 3 2 2
A3
4 3 7 -5 1 2
A4
4 3 4 -1 2 2
A5
4 3 3 -2 2 2
Level 1 Remembering
PART-C
S.No Questions BT
Level
Competence
1.
Using Dominance property Solve.
B
A
I II IIIIV
1 -5 3 1 20
2 5 5 4 6
3 -4 -2 0 -5
Level 1 Remembering
2. Examine the 2 * n Game by the Method of Sub Game:
B1 B2 B3
A1 1 3 11
A2 8 5 2
Level 2 Understanding
3. In a game of matching coins with 2 players, A wins 1 unit value
when there are 2 heads, wins nothing when there are 2 tails
and looses ? unit value when there are one head and one tail.
Develop Pay Off matrix and value of the game.
Level 3 Applying
4.
i
ii
iii
Assume you have to choice of 3 strategies for advertising
and you have one major
Analyse the theory on Two-person sum games competitor
with 3 strategies.
(5)
Level 4 Analysing
What are the assumptions of Game? (5)
Find value of game.
B1 B2 B3
A1 80 70 60
A2 90 80 100
A3 40 30 40
(5)
UNIT - IV INVENTORY MODELS, SIMULATION AND DECISION THEORY
SYLLABUS: Inventory Models ? EOQ and EBQ Models (With and without shortages), Quantity Discount
Models. Decision making under risk ? Decision trees ? Decision making under uncertainty. Monte-carlo
simulation.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define inventory. Level 1 Remembering
2.
Classify the Forms of inventory.
Level 2 Understanding
3.
Identify the Objectives/significance of inventory model.
Level 3 Applying
4.
Highlight the importance of Reorder level.
Level 4 Analysing
5.
Discuss the concept of Lead time.
Level 5 Evaluate
6.
Interpret the Types of stock replenishment.
Level 1 Remembering
7.
List the Basic inventory models.
Level 2 Understanding
8.
Compare Ordering Cost and Carrying Cost.
Level 3 Appyling
9.
Identify when shortage cost and stock out cost arises?
Level 5 Evaluating
10.
Analyze why safety stock is maintained.
Level 1 Remembering
11.
Discuss the concept of Quantity Discount Model.
Level 2 Understanding
12.
Interpret the meaning of EOQ & EBQ.
Level 3 Applying
13.
What are random and pseudo random numbers?
Level 4 Analysing
14.
Explain Monte Carlo Method.
Level 5 Evaluating
15.
Summarize the concept of EMV.
Level 1 Remembering
16.
What inference can you make about holding cost ?
Level 2 Understanding
17.
What is Shortage Cost?
Level 3 Applying
18. Classify and explain the various conditions under which
decisions are made.
Level 1 Remembering
19. What is meant by the following terms in inventory
management: i)Carrying cost ii) shortage costs
Level 2 Understanding
20. What is Decision theory? List the problems that can be solved
by Simulation.
Level 3 Applying
S.NO PART - B QUESTIONS Marks BT
LEVEL
COMPETENCE
1.
(i)
Alpha industry needs 5400 units per year of a bought out
component which will be
used in its main product. The ordering cost is Rs.250
per order and the carrying cost per unit per year is
Rs.30.
Which is the best order quantity?
(8)
Level 1 Remembering
(ii)
Find the number of order per year and Frequency of
orders?
(5)
2.
(i)
A stockiest has to supply 12000 units of a product per
year to his customer. Demand is
fixed and known. Shortage cost is assumed to be
infinite. Inventory holding cost is 20 paise per unit per
month. Ordering Cost is Rs. 250 and purchase price
is Rs.10 per unit.
Estimate the EOQ
(8)
Level 2 Understanding
(ii)
Find the Frequency of orders and total inventory cost. (5)
3.
ABC manufacturing company purchases 9000 parts of a
machine for its annual requirement. Each part costs
Rs.20. The ordering cost per order is Rs.15 and the
carrying charges are 15% of the average inventory per
year. Apply EOQ formulae and find out EOQ, No of
orders ,Total Inventory Cost and total cost.
Level 3 Applying
FirstRanker.com - FirstRanker's Choice
(An
?
DEPARTMENT OF MANAGEMENT STUDIES
QUESTION BANK
II SEMESTER
1915201? APPLIED OPERATIONS RESEACH
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Dr. Radha Ganesh Kumar ? Asst. Professor (Sel.G) and HOD
Mr.B. Sam Paul ? Asst. Professor (OG)
(An
? .
DEPARTMENT OFMANAGEMENT STUDIES
QUESTION BANK
SUBJECT :1915201 ?APPLIED OPERATIONS RESEACH
SEM / YEAR : IISemester / IYear
UNIT ? I ?INTRODUCTION TO LINEAR PROGRAMMING (LP)
SYLLABUS: Introduction to applications of operations research in functional areas of management.
Linear Programming-formulation, solution by graphical and simplex methods, Special cases. Dual
simplex method. Principles of Duality. Sensitivity Analysis.
PART- A
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Define Operations Research (OR). Level 1 Remembering
2. Differentiate between Simplex and Big M Method Level 2 Understanding
3. How do you show your understanding unbounded solution? Level 3 Applying
4. Categorize the forms of LPP. Level 4 Analysing
5.
Discuss why is two phase method is better than Big M
method?
Level 5 Evaluating
6. Interpret the usage of Sensitivity Analysis in LPP. Level 6 Creating
7. What are the assumptions and requirements of LPP? Level 1 Remembering
8. Compare Dual Simplex and Duality. Level 2 Understanding
9. Identify the Advantages of duality. Level 3 Applying
10. What do you think about Infeasible solution? Level 4 Analysing
11. How will you solve LPP graphically? Level 5 Evaluating
12.
Conclude your understanding on the mathematical
formulation of LPP.
Level 6 Creating
13. Define basic variables and artificial variables. Level 1 Remembering
14. Compare Slack variable & Surplus Variable. Level 2 Understanding
15.
Give some example for the role of Surplus variable & Slack
Variable in the simplex method
Level 3 Applying
16. How would you apply Artificial variable? Level 4 Analysing
17. What is Big M Method? Level 1 Remembering
18. Distinguish simplex and Big M method Level 2 Understanding
19.
What do you mean by Duality? List the Rules for primal and
dual.
Level 1 Remembering
20. What is Shadow price? Level 1 Remembering
PART- B
S.NO
QUESTIONS
BT
LEVEL
COMPETENCE
1.
(i)
Maximise Z=3x+4y subject to
2x+5y ?60,
4x+2y ?40.
x, y >0. Solve by Graphical Method
Plot the graph
(8)
Level 1 Remembering
(ii) Which one is the best solution? (5)
2.
(i)
Min Z= 20x
1
+10 x
2
subject to
x
1
+2x
2
? 40,
3x
1
+x
2
? 30,
4x
1
+3x
2
? 60,
x
1
,x
2
? 0.
Solve by Graphical Method,
Plot the graph
(8)
Level 2 Understanding
(ii) Predict the value of x & y. (5)
3 Max Z= 5x1+4x2 subject to
x
1
-2x
2
? 1,
x
1
+2x
2
?3,
x
1
,x
2
? 0. Solve Graphically. Which one is the best
solution?
Level 3 Applying
4.
(i)
A Plant Manufacturer 2 Product A & B. The Profit Contribution
of each product has been estimated as Rs.300 for product A
and Rs.400 for Product B. Each Product passes through 3
departments of the plant. The time required for each product
and total time available in each department is as follows.
Department Hours
Required
Hours
Required
Available
Hours
during
month
Product
A
Product
B
I 2 3 1600
II 3 2 1500
III 1 1 700
The company has a contract to supply atleast 300 units of
Product B per month.
Formulate the LPP
(5)
Level 4
Analysing
(ii) Solve through Graphical Method
(8)
5. Solve the following LPP by graphical method.
Maximize Z= 3x
1
+2x
2
Subject t o
- 2x
1
+x
2
?1,
x
1
? 2,
x
1
+ x
2
? 3
and x
1
,x
2
? 0
Level 5 Evaluating
6. (i) Max Z= 1000x
1
+4000x
2
+5000x
3
Subject to 3x1+3x
3
?22,
x1+2x2+3x
3
? 14,
3x1+2x2 ? 14
& x1,x2 ? 0
Develop a Simplex Table
(5)
Level 6 Creating
(ii) Analyse and find the value of x
1
, x
2
? (8)
7. Analyze the following LPP by Simplex Method:
Min Z = -10y
1
-15y
2
-20y
3
Subject to 2y
1
+4y
2
+6y
3
? 24,
3y
1
+9y
2
+6y
3
? 30,
& y
1
, y
2
, y
3
? 0.
Level 1 Remembering
(i)
Develop a Simplex Table (5)
(ii) Solve and find the value of y1 ,y2 and y3
(8)
8.
Solve By Graphical Method
Minimize Z= 40x
1
+24x
2
Subject to, 20x
1
+50 x
2
> 4,800
80 x
1
+50x
2
> 7,200
x
1
,x
2
>0
Level 2 Understanding
9. Solve the following LPP by simplex method:
Minimize Z= 8x
1
-2x
2
Subject to -4x
1
+2x
2
?1,
5x
1
-4x
2
?3,
and x
1
,x
2
? 0
Level 3 Applying
10. Solve the following LPP by simplex method:
Maximize Z= 3x1+2x
2
Subject to
2x
1
+x
2
?2,
3x
1
+4x
2
?12,
x
1
,x
2
? 0
Level 4 Analyzing
11. Review the LPP and solve by simplex method
Max Z= 25x+10y
Subject to the constraints
x+0.5y? 20
x+y? 50
x,y ? 0
Level 1 Remembering
12. A firm produces three products. These products are
processors on 3 different machines. The time required for
manufacturing one unit of cost of the products and the daily
capacity of the three machines is given in the table below.
Analyse and find the optimum solution.
Mac
hine
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Machine
Capacity
Min /Day
Product1 Product 2 Product 3
M1 2 8 2 940
M2 4 - 8 970
M3 2 5 - 430
It is required to determine the daily no. of units to be
manufactured for each product. The profit for unit for
Level 2 Understanding
product 1,2,3 is Rs.4,Rs.8,Rs.6 respectively. It is assumed
that all the amount produced are consumed in the market
13. Using dual simplex method , solve and find the optimum
solution for the given LPP.
Maximize Z=6x
1
+4x
2
+4x
3
Subject to 3x
1
,x
2
+2x
3
? 2
2x
1
+x
2
-x
3
? 1
-x
1
+x
2
+2x
3
? 1 &
x
1
,x
2
,x
3
? 0
Level 4 Analysing
14.
(i)
Evaluate by using dual simplex method and solve the LPP.
Minimize Z=2x
1
+x
2
Subject to 3x
1
+2x
2
? 3
4x
1
+3x
2
? 6
x
1
+x
2
? 5 & x
1
,x
2
?
Determine the dual simplex table
(5)
Level 1 Remembering
(ii)
Find the value of x
1
, x
2
(8)
PART - C
S.No Questions BT
LEVEL
COMPETENCE
1.
Max Z=300x+400y subject to
2x+3y ? 1600,
3x+2y ? 1500,
x+y ? 700,
y ? 300, x,y ? 0 Solve by Graphical Method, choose the
value of x & y which maximizes profit.
Level 1 Remembering
2. Solve the following LPP by graphical method.
Minimize Z= 6000x1+4000x
2
Subject t o
3x+x
2
? 40,
x
1
+2.5 x
2
? 22
3x
1
+3 x
2
? 40
and x
1
,x
2
? 0
Level 2 Understanding
3. Develop a Simplex Table and Solve
Max Z = 3 x1+2 x2,
Subject to
x1+ x2 ?4,
x1- x2 ? 2;
x1, x2 ?0.
Level 3 Applying
4. Solve by using Simplex Method.
Maximize Z= 3x+5y
Subject to the constraints
x+y? 60
x? 40
y ? 30
x,y ? 0
Level 1 Remembering
UNIT - II LINEAR PROGRAMMING EXTENSIONS
SYLLABUS: Transportation Models (Minimizing and Maximizing Problems) ? Balanced and unbalanced
Problems ? Initial Basic feasible solution by N-W Corner Rule, Least cost and Vogel?s approximation methods.
Check for optimality. Solution by MODI /. Case of Degeneracy. Trans-shipment Models. Assignment Models
(Minimising and Maximising Problems) ? Balanced and Unbalanced Problems. Solution by Hungarian and
Branch and Bound Algorithms. Travelling Salesman problem.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define Transportation & Transhipment. Level 1 Remembering
2. Differentiate balanced transportation problem & Unbalanced
Transportation Problem.
Level 2 Understanding
3. How would you show your understanding on unbalanced
transportation problem?
Level 3 Applying
4. Categorize the Phases of transportation model. Level 4 Analysing
5. Construct the basic feasible solution for the following
transportation problem.
1 2 3 4 SUPPLY
1 2 3 11 7 6
2 1 0 6 1 1
3 5 8 15 9 10
DEMAN D 7 5 3 2
Level 5 Evaluating
6 Interpret the need for Optimum solution in transportation. Level 6 Creating
7. What do you mean by Least cost method (LCM)? Level 1 Remembering
8. Compare Vogel approximation method (VAM) & Least Cost
Method.
Level 2 Understanding
9. How do you represent a travelling salesman problem
through mathematical formulation?
Level 3 Applying
10. Analyse the rules of travelling salesman Problem. Level 4 Analysing
11. Discuss the meaning of Assignment Level 5 Evaluating
12. Compare Balanced assignment problem & Unbalanced
Assignment Problem.
Level 6 Creating
13. What example can you give for Unbalanced assignment
problem?
Level 1 Remembering
14. How will you resolve degeneracy in Transportation Problem? Level 2 Understanding
15. Classify transportation problem. Level 3 Applying
16. Examine the Steps in Hungarian algorithm. Level 4 Analysing
17. What is Branch and bound algorithm in Assignment? Level 1 Remembering
18. Compare Assignment and transportation Problem. Level 2 Understanding
19. What do you mean by Travelling Salesman Problem? Level 1 Remembering
20. What is Restricted Assignment? Level 1 Remembering
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Solve and find the Transportation Problem and Which method will
you select if you want toMinimize Cost?
Destination Supply
1 2 3 4
I 21 16 25 13 11
II 17 18 14 23 13
III 32 27 18 41 19
Demand 6 10 12 15
Level 1 Remembering
2. Find the Initial Basic Feasible solution for following TP. Using NW
Rule, LCM, and VAM. Which method will you select if you want to
Minimize Cost?
D1 D2 D3 Supply
S1 7 3 2 2
S2 2 1 3 3
S3 3 4 6 5
Demand 4 1 5 10
Level 2 Understanding
3.
(i)
Analyze the transportation problem with unit transportation
costs,demand, and supply as given below:
Destination
Supply
Source
D1 D2 D3 D4
S1
6 1 9 3
70
11 5 2 8
S2 55
10 12 4 7
S3
70
Demand 85 35 50 45
Apply VAM for Initial solution.
(5)
Level 3 Applying
(ii)
Construct the final Solution by using MODIMethod.
(8)
4.
(i)
Analyze & solve the following transportation problem to maximize
profit.
A B C D Supply
1
Source 2
3
Demand
15 51 42 33 23
80 42 26 81 44
90 40 66 60 33
23
31
16
30
100
Examine Initial solution using VAM.
(5)
Level 4 Analysing
(ii)
Analyze and find out the final Solution by using MODI Method.
(8)
5. Solve the following transportation problem using Vogel?s
method
Factory? Warehouse ?Available
A B C D E F
1 9 12 9 6 9 10 5
2 7 3 7 7 5 5 6
3 6 5 9 11 3 11 2
4 6 8 11 2 2 10 9
4 4 6 2 4 2
Requirement?
(5)
Level 5 Evaluating
6. (i) Solve the transportation problem and decide using VAM for initial
solution.
(5) Level 6 Creating
(ii) Evaluate using NWC and Least Cost method for initial solution?
Destination Supply
I 2 1 25 13 11
II 1 1 14 23 13
III 3 2 18 41 19
Demand 6 1 22 15
(8)
7.
Maximize profit from the following transportationproblem.
A B C D Supply
I 40 25 22 33 100
SourceII 44 35 30 30 30
III 38 38 28 30 70
Demand 40 20 60 30
Level 1 Remembering
(i) How will you convert maximization problem to minimization.
Find the maximum profit
(8)
(ii) Explain stepping stone method for checking the
solution for optimality transportation problems.
(5)
8. A company has one surplus truck in each of the cities A, B, C, D, &
E and one deficit trucks in each of the cities 1,2,3,4,5,6. The
distance between the cities in kms is shown in the matrix below.
Can you select the assignment of trucks from cities in surplus to
cities in deficiency .so that total distance covered by the vehicles is
minimum?
1 2 3 4 5 6
A 12 10 15 22 18 8
B 10 18 25 15 16 12
C 11 10 3 8 5 9
D 6 4 10 13 13 12
E 8 12 11 7 13 10
Level 2 Understanding
9.
Consider the problem of assigning five jobs to five persons. The
assignment costs are given as follows:
PERSONS?JOBS ?
1 2 3 4 5
A 8 4 2 6 1
B 0 9 5 5 4
C 3 8 9 2 6
D 4 3 1 0 3
Level 3 Applying
E 9 5 8 9 5
Determine the optimum assignment schedule.
10. The assignment cost of assigning any one operator to any one
machine is given in the following table.
MACHINE?OPERATORS ?
I II III IV
A 10 5 13 15
B 3 9 18 3
C 10 7 3 2
D 5 11 9 7
Find the optimal assignment by Hungarian method.
Level 4 Analysing
11. A machine shop purchased a drilling machine and two lathes of
different capacities. The Positioning of the machines among 4
possible locations on the shop floor is important forms the
standard of materials handling. Given the cost estimate per unit
time of materials below, find the optimum location of the
machines.
LOCATIONS
1 2 3 4
Lathe 1 12 9 12 9
Drill 15 Not
suitable
13 20
Lathe 2 4 8 10 6
Level 1 Remembering
12.
Solve the assignment problem for maximization given profit
matrix(profit in rupees).
Machines
P Q R S
JOB
51 53 54 50
47 50 48 50
49 50 60 61
63 64 60 60
Level 2 Understanding
PART - C
S.No Questions Marks BT
Level
Competence
1.
a
Assume that you are an OR specialist. Identify the procedure
for each of the following Method to the employees in order to
help them achieve solution to Transportation Problems.
Northwest Corner Cell Method
(3)
Level 1 Remembering
b Least Cost cell Method (4)
c Vogel?s Approximation Method (4)
d U V Method. (4)
13. The processing time in hours for the jobs when allocated to the
different machines is indicated below. Select the best assignment
of the machines for the jobs so that the total processing time is
Minimum.
Machines
M1 M2 M3 M4 M5
J1 9 22 58 11 19
JOB J2 43 78 72 50 63
J3 41 28 91 37 45
J4 74 42 27 49 39
J5 36 11 57 22 25
Level 4 Analysing
14. For the given travelling salesman problem, Minimize the total cost.
To
1 2 3 4
From A - 46 16 40
B 41 - 50 40
C 82 32 - 60
D 40 40 36 -
Level 1 Remembering
(i) Observe the above travelling salesman
problem and find out minimize the cost per
cycle.
(8)
(ii) Find whether path is satisfied. (5)
2.
Solve the following transportation problem, in which a
i
is the
availability at Origin
O
i
and b
j
is the requirement at the destination D
j
and cell entries
are unit costs of transportation from any origin to any
destination:
D1 D2 D3 D4 D5 a
j
O1 4 7 3 8 2 4
O2 1 4 7 3 8 7
O3 7 2 4 7 7 9
O4 4 8 2 4 7 2
b
j
8 3 7 2 2
Predict the allocation to minimize the cost.
Level 2 Understanding
3. A company has a team of 4 Salesman and the company wants to
do in 4 districts. Considering the capabilities of salesmen
and nature of the district, the company has estimated the profit per
day in Rs. For each salesmen in each district as follows.
District
s
Salesmen 1 2 3 4
A 16 10 14 11
B 14 11 15 15
C 15 15 13 12
D 13 12 14 15
Develop the best assignment schedule and analyze the total cost.
Level 3 Applying
4. Five operators have to be assigned to Five Machines. The
assignment costs are given in thetablebelow.
Analyse using Hungarian algorithm & find out the assignment to
minimize the cost.
Machine
I II III IV V
Operator
A 5 5 - 2 6
B 7 4 2 3 4
C 9 3 5 - 3
D 7 2 6 7 2
E 6 5 7 9 1
Level 4 Analyzing
UNIT ? III ? INTEGER PROGRAMMING AND GAME THEORY
SYLLABUS: Integer Programming ? Introduction and types - Game Theory-Two-person Zero sum
games-Saddle point, Dominance Rule, graphical and LP solutions, Nash Equilibrium
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. What do you mean by integer programming problem?
Level 1 Remembering
2. In what respect a mixed IPP differs from pure IPP?
Level 2 Understanding
3. What is Nash Equilibrium?
Level 3 Applying
4. Classify the different types of strategy.
Level 4 Analysing
5. Compile the Characteristics of game.
Level 5 Evaluating
6. Can you assess the applications of integer
programming?
Level 6 Creating
7. Define Game.
Level 1 Remembering
8. Compare Mixed Strategy and Pure Strategy.
Level 2 Understanding
9. How would you make use of the concept of Game theory
in Managerial Decision Making?
Level 3 Applying
10. Conclude your understanding about Payoff Matrix.
Level 4 Analysing
11. How will you find the optimal strategies and value of the
following game?
Player B
Player
A
H T
H 2 -1
T -1 0
Level 5 Evaluating
12. Interpret the concept of two person zero sum game.
Level 6 Creating
13. What is Saddle point?
Level 1 Remembering
14. Compare Dominance Principle of Rows and Columns.
Level 2 Understanding
15. Identify the basic assumptions of the Game.
Level 3 Applying
16. Conclude the advantages of Game theory.
Level 4 Analysing
17. What are the Methods of Matrices?
Level 1 Remembering
18. Summarize how graphs and LP solution are used in
Game theory.
Level 2 Understanding
19. What is a Decision Tree?
Level 1 Remembering
20. Define Dominance principle.
Level 1 Remembering
S.N
O
PART - B QUESTIONS MA
RK
S
BT
LEVEL
COMPETENCE
1. (i) What do you mean by Pure IPP? (3) Level 1 Remembering
(ii) What do you mean by Mixed IPP? (5)
(iii)
List out the difference between Pure and Mixed IPP.
(5)
2. (i) For what value of ?,the game with the following
matrix is strictly determined
B
1
B
2
B
3
A
1
? 6 2
A
2
-1 ? -7
A
3
-2 4 ?
(8) Level 2 Understanding
(ii) Write down the assumptions of game theory. (5)
3. (i) Solve the game whose pay-off matrix is given by
B
1
B
2
B
3
A
1
1 3 1
A
2
0 -4 -3
A
3
1 5 -1
(8)
Level 3 Applying
(ii) Explain the concept of Nash Equilibrium. (5)
4.
Analyze the Value of the game graphically
B1 B2
A1 4 4
A2 2 7
A3 5 3
A4 6 2
Level 4 Analysing
5.
What inference can be made using Dominance
Principle to reduce the following game and estimate
the game value?
B1 B2 B3 B4
A1 3 2 4 0
A2 3 4 2 4
A3 4 2 2 0
A4 2 1 6 3
Level 5 Evaluating
6.
How would you evaluate the following game whose
Pay-Off matrix is Given Below?
9 3 1 8 0
6 5 4 6 7
2 4 3 3 8
5 6 2 2 1
Level 6 Creating
7.
(i)
Two players A&B match coins. If the coins match
then A wins one unit value, if the coins do not
match then B wins one unit of value.
Determine pay-off matrix which strategy is to be
chosen
(5)
Level 1 Remembering
(ii)
Find the value of game. (8)
8.
Predict the Value of the Game given above Pay
OffMatrix.
Player B
B1 B2 B3
A1 -2 5 -3
Player A A2 1 3 5
A3 -3 -7 11
Level 2 Understanding
9.
Apply graphical analysis to Solve the game.
A/
B
B1 B2 B3 B4
A1 3 3 4 0
A2 5 4 3 7
Level 3 Applying
10. Solve the following game by graphical method.
Player B
1 2 3
1 6 4 3
Player A 2 2 4 8
Level 4 Analysing
11.
(i)
A and B play a Match(Game) in which each has 3
coins 5 paise, 10 paise and 20 paise. Each player
selects a coin without the knowledge of others
choice. IF the sum is even, B wins A?s Coin. If sum
is Odd, A wins B?s coin.
How will you find the pay-off matrix ?
(5)
Level 1
Remembering
(ii)
Find the Best Strategy & value of the Game. (8)
12.
Consider the Pay Off Matrix of player A as shown in
the table below and solve it optimally using the
graphical method .
Player A
Player
B
1 2 3 4 5
1 3 6 8 4 4
2 -7 4 2 10 2
Level 2 Understanding
13.
(i)
Analyze the Game Graphically:
Player A
Player
A
B1 B2
A1 -3 1
A2 5 3
A3 6 -1
A4 1 4
A5 2 2
A6 0 -5
Plot the graph
(5)
Level 4 Analysing
(ii)
Analyse and find the value of the game.
(8)
14.
Which one is the best strategy using Dominance
Principle?
B1 B2 B3 B4 B5 B6
A1
4 2 0 2 1 1
A2
4 3 1 3 2 2
A3
4 3 7 -5 1 2
A4
4 3 4 -1 2 2
A5
4 3 3 -2 2 2
Level 1 Remembering
PART-C
S.No Questions BT
Level
Competence
1.
Using Dominance property Solve.
B
A
I II IIIIV
1 -5 3 1 20
2 5 5 4 6
3 -4 -2 0 -5
Level 1 Remembering
2. Examine the 2 * n Game by the Method of Sub Game:
B1 B2 B3
A1 1 3 11
A2 8 5 2
Level 2 Understanding
3. In a game of matching coins with 2 players, A wins 1 unit value
when there are 2 heads, wins nothing when there are 2 tails
and looses ? unit value when there are one head and one tail.
Develop Pay Off matrix and value of the game.
Level 3 Applying
4.
i
ii
iii
Assume you have to choice of 3 strategies for advertising
and you have one major
Analyse the theory on Two-person sum games competitor
with 3 strategies.
(5)
Level 4 Analysing
What are the assumptions of Game? (5)
Find value of game.
B1 B2 B3
A1 80 70 60
A2 90 80 100
A3 40 30 40
(5)
UNIT - IV INVENTORY MODELS, SIMULATION AND DECISION THEORY
SYLLABUS: Inventory Models ? EOQ and EBQ Models (With and without shortages), Quantity Discount
Models. Decision making under risk ? Decision trees ? Decision making under uncertainty. Monte-carlo
simulation.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define inventory. Level 1 Remembering
2.
Classify the Forms of inventory.
Level 2 Understanding
3.
Identify the Objectives/significance of inventory model.
Level 3 Applying
4.
Highlight the importance of Reorder level.
Level 4 Analysing
5.
Discuss the concept of Lead time.
Level 5 Evaluate
6.
Interpret the Types of stock replenishment.
Level 1 Remembering
7.
List the Basic inventory models.
Level 2 Understanding
8.
Compare Ordering Cost and Carrying Cost.
Level 3 Appyling
9.
Identify when shortage cost and stock out cost arises?
Level 5 Evaluating
10.
Analyze why safety stock is maintained.
Level 1 Remembering
11.
Discuss the concept of Quantity Discount Model.
Level 2 Understanding
12.
Interpret the meaning of EOQ & EBQ.
Level 3 Applying
13.
What are random and pseudo random numbers?
Level 4 Analysing
14.
Explain Monte Carlo Method.
Level 5 Evaluating
15.
Summarize the concept of EMV.
Level 1 Remembering
16.
What inference can you make about holding cost ?
Level 2 Understanding
17.
What is Shortage Cost?
Level 3 Applying
18. Classify and explain the various conditions under which
decisions are made.
Level 1 Remembering
19. What is meant by the following terms in inventory
management: i)Carrying cost ii) shortage costs
Level 2 Understanding
20. What is Decision theory? List the problems that can be solved
by Simulation.
Level 3 Applying
S.NO PART - B QUESTIONS Marks BT
LEVEL
COMPETENCE
1.
(i)
Alpha industry needs 5400 units per year of a bought out
component which will be
used in its main product. The ordering cost is Rs.250
per order and the carrying cost per unit per year is
Rs.30.
Which is the best order quantity?
(8)
Level 1 Remembering
(ii)
Find the number of order per year and Frequency of
orders?
(5)
2.
(i)
A stockiest has to supply 12000 units of a product per
year to his customer. Demand is
fixed and known. Shortage cost is assumed to be
infinite. Inventory holding cost is 20 paise per unit per
month. Ordering Cost is Rs. 250 and purchase price
is Rs.10 per unit.
Estimate the EOQ
(8)
Level 2 Understanding
(ii)
Find the Frequency of orders and total inventory cost. (5)
3.
ABC manufacturing company purchases 9000 parts of a
machine for its annual requirement. Each part costs
Rs.20. The ordering cost per order is Rs.15 and the
carrying charges are 15% of the average inventory per
year. Apply EOQ formulae and find out EOQ, No of
orders ,Total Inventory Cost and total cost.
Level 3 Applying
4.
(i)
Demand for an item in a company is 18,000 units per
year. The company can produce the items at a rate of
3000 units per month. The Cost of one setup is Rs.500
and the holding cost of one unit per month is 15 paise.
Shortage cost of one unit is Rs.20 per year.
Analyze and find the optimum manufacturing quantity.
(8)
Level 4 Analysing
(ii)
Find the number of shortages and frequency of
Production run.
(5)
5. A company has a demand of 12000 units/year for an
item and it can produce 2000 units per month. The
cost of one setup is Rs.400 and the holding
cost/unit/month is 15 paise. Select the optimum lot
size and total cost per year assuming the cost of 1 unit
as Rs.4. Find EBQ, the number of set ups & total cost.
Level 5 Evaluating
6.
(i)
Find the optimal order quantity for a product when the
annual demand for the product is 500 units. The Cost of
storage per unit per year is 10% of the unit cost. Ordering
cost per order is Rs. 180.
Determine EOQ
(8)
Level 6 Creating
(ii)
Evaluate the Total Cost
(5)
The unit cost are given below:
Quantity Unit Cost(Rs.)
O
1500<=Q3<3000 24.60
3000<=Q4 24.40
7. (i)
Formulate the Optimal order quantity for a product for
which the price breaks are as follows
(8)
Level 1 Remembering
(ii)
Also find the Total cost.
Quantity Unit Cost(Rs.)
O
750<=Q 875
(5)
FirstRanker.com - FirstRanker's Choice
(An
?
DEPARTMENT OF MANAGEMENT STUDIES
QUESTION BANK
II SEMESTER
1915201? APPLIED OPERATIONS RESEACH
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Dr. Radha Ganesh Kumar ? Asst. Professor (Sel.G) and HOD
Mr.B. Sam Paul ? Asst. Professor (OG)
(An
? .
DEPARTMENT OFMANAGEMENT STUDIES
QUESTION BANK
SUBJECT :1915201 ?APPLIED OPERATIONS RESEACH
SEM / YEAR : IISemester / IYear
UNIT ? I ?INTRODUCTION TO LINEAR PROGRAMMING (LP)
SYLLABUS: Introduction to applications of operations research in functional areas of management.
Linear Programming-formulation, solution by graphical and simplex methods, Special cases. Dual
simplex method. Principles of Duality. Sensitivity Analysis.
PART- A
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Define Operations Research (OR). Level 1 Remembering
2. Differentiate between Simplex and Big M Method Level 2 Understanding
3. How do you show your understanding unbounded solution? Level 3 Applying
4. Categorize the forms of LPP. Level 4 Analysing
5.
Discuss why is two phase method is better than Big M
method?
Level 5 Evaluating
6. Interpret the usage of Sensitivity Analysis in LPP. Level 6 Creating
7. What are the assumptions and requirements of LPP? Level 1 Remembering
8. Compare Dual Simplex and Duality. Level 2 Understanding
9. Identify the Advantages of duality. Level 3 Applying
10. What do you think about Infeasible solution? Level 4 Analysing
11. How will you solve LPP graphically? Level 5 Evaluating
12.
Conclude your understanding on the mathematical
formulation of LPP.
Level 6 Creating
13. Define basic variables and artificial variables. Level 1 Remembering
14. Compare Slack variable & Surplus Variable. Level 2 Understanding
15.
Give some example for the role of Surplus variable & Slack
Variable in the simplex method
Level 3 Applying
16. How would you apply Artificial variable? Level 4 Analysing
17. What is Big M Method? Level 1 Remembering
18. Distinguish simplex and Big M method Level 2 Understanding
19.
What do you mean by Duality? List the Rules for primal and
dual.
Level 1 Remembering
20. What is Shadow price? Level 1 Remembering
PART- B
S.NO
QUESTIONS
BT
LEVEL
COMPETENCE
1.
(i)
Maximise Z=3x+4y subject to
2x+5y ?60,
4x+2y ?40.
x, y >0. Solve by Graphical Method
Plot the graph
(8)
Level 1 Remembering
(ii) Which one is the best solution? (5)
2.
(i)
Min Z= 20x
1
+10 x
2
subject to
x
1
+2x
2
? 40,
3x
1
+x
2
? 30,
4x
1
+3x
2
? 60,
x
1
,x
2
? 0.
Solve by Graphical Method,
Plot the graph
(8)
Level 2 Understanding
(ii) Predict the value of x & y. (5)
3 Max Z= 5x1+4x2 subject to
x
1
-2x
2
? 1,
x
1
+2x
2
?3,
x
1
,x
2
? 0. Solve Graphically. Which one is the best
solution?
Level 3 Applying
4.
(i)
A Plant Manufacturer 2 Product A & B. The Profit Contribution
of each product has been estimated as Rs.300 for product A
and Rs.400 for Product B. Each Product passes through 3
departments of the plant. The time required for each product
and total time available in each department is as follows.
Department Hours
Required
Hours
Required
Available
Hours
during
month
Product
A
Product
B
I 2 3 1600
II 3 2 1500
III 1 1 700
The company has a contract to supply atleast 300 units of
Product B per month.
Formulate the LPP
(5)
Level 4
Analysing
(ii) Solve through Graphical Method
(8)
5. Solve the following LPP by graphical method.
Maximize Z= 3x
1
+2x
2
Subject t o
- 2x
1
+x
2
?1,
x
1
? 2,
x
1
+ x
2
? 3
and x
1
,x
2
? 0
Level 5 Evaluating
6. (i) Max Z= 1000x
1
+4000x
2
+5000x
3
Subject to 3x1+3x
3
?22,
x1+2x2+3x
3
? 14,
3x1+2x2 ? 14
& x1,x2 ? 0
Develop a Simplex Table
(5)
Level 6 Creating
(ii) Analyse and find the value of x
1
, x
2
? (8)
7. Analyze the following LPP by Simplex Method:
Min Z = -10y
1
-15y
2
-20y
3
Subject to 2y
1
+4y
2
+6y
3
? 24,
3y
1
+9y
2
+6y
3
? 30,
& y
1
, y
2
, y
3
? 0.
Level 1 Remembering
(i)
Develop a Simplex Table (5)
(ii) Solve and find the value of y1 ,y2 and y3
(8)
8.
Solve By Graphical Method
Minimize Z= 40x
1
+24x
2
Subject to, 20x
1
+50 x
2
> 4,800
80 x
1
+50x
2
> 7,200
x
1
,x
2
>0
Level 2 Understanding
9. Solve the following LPP by simplex method:
Minimize Z= 8x
1
-2x
2
Subject to -4x
1
+2x
2
?1,
5x
1
-4x
2
?3,
and x
1
,x
2
? 0
Level 3 Applying
10. Solve the following LPP by simplex method:
Maximize Z= 3x1+2x
2
Subject to
2x
1
+x
2
?2,
3x
1
+4x
2
?12,
x
1
,x
2
? 0
Level 4 Analyzing
11. Review the LPP and solve by simplex method
Max Z= 25x+10y
Subject to the constraints
x+0.5y? 20
x+y? 50
x,y ? 0
Level 1 Remembering
12. A firm produces three products. These products are
processors on 3 different machines. The time required for
manufacturing one unit of cost of the products and the daily
capacity of the three machines is given in the table below.
Analyse and find the optimum solution.
Mac
hine
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Machine
Capacity
Min /Day
Product1 Product 2 Product 3
M1 2 8 2 940
M2 4 - 8 970
M3 2 5 - 430
It is required to determine the daily no. of units to be
manufactured for each product. The profit for unit for
Level 2 Understanding
product 1,2,3 is Rs.4,Rs.8,Rs.6 respectively. It is assumed
that all the amount produced are consumed in the market
13. Using dual simplex method , solve and find the optimum
solution for the given LPP.
Maximize Z=6x
1
+4x
2
+4x
3
Subject to 3x
1
,x
2
+2x
3
? 2
2x
1
+x
2
-x
3
? 1
-x
1
+x
2
+2x
3
? 1 &
x
1
,x
2
,x
3
? 0
Level 4 Analysing
14.
(i)
Evaluate by using dual simplex method and solve the LPP.
Minimize Z=2x
1
+x
2
Subject to 3x
1
+2x
2
? 3
4x
1
+3x
2
? 6
x
1
+x
2
? 5 & x
1
,x
2
?
Determine the dual simplex table
(5)
Level 1 Remembering
(ii)
Find the value of x
1
, x
2
(8)
PART - C
S.No Questions BT
LEVEL
COMPETENCE
1.
Max Z=300x+400y subject to
2x+3y ? 1600,
3x+2y ? 1500,
x+y ? 700,
y ? 300, x,y ? 0 Solve by Graphical Method, choose the
value of x & y which maximizes profit.
Level 1 Remembering
2. Solve the following LPP by graphical method.
Minimize Z= 6000x1+4000x
2
Subject t o
3x+x
2
? 40,
x
1
+2.5 x
2
? 22
3x
1
+3 x
2
? 40
and x
1
,x
2
? 0
Level 2 Understanding
3. Develop a Simplex Table and Solve
Max Z = 3 x1+2 x2,
Subject to
x1+ x2 ?4,
x1- x2 ? 2;
x1, x2 ?0.
Level 3 Applying
4. Solve by using Simplex Method.
Maximize Z= 3x+5y
Subject to the constraints
x+y? 60
x? 40
y ? 30
x,y ? 0
Level 1 Remembering
UNIT - II LINEAR PROGRAMMING EXTENSIONS
SYLLABUS: Transportation Models (Minimizing and Maximizing Problems) ? Balanced and unbalanced
Problems ? Initial Basic feasible solution by N-W Corner Rule, Least cost and Vogel?s approximation methods.
Check for optimality. Solution by MODI /. Case of Degeneracy. Trans-shipment Models. Assignment Models
(Minimising and Maximising Problems) ? Balanced and Unbalanced Problems. Solution by Hungarian and
Branch and Bound Algorithms. Travelling Salesman problem.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define Transportation & Transhipment. Level 1 Remembering
2. Differentiate balanced transportation problem & Unbalanced
Transportation Problem.
Level 2 Understanding
3. How would you show your understanding on unbalanced
transportation problem?
Level 3 Applying
4. Categorize the Phases of transportation model. Level 4 Analysing
5. Construct the basic feasible solution for the following
transportation problem.
1 2 3 4 SUPPLY
1 2 3 11 7 6
2 1 0 6 1 1
3 5 8 15 9 10
DEMAN D 7 5 3 2
Level 5 Evaluating
6 Interpret the need for Optimum solution in transportation. Level 6 Creating
7. What do you mean by Least cost method (LCM)? Level 1 Remembering
8. Compare Vogel approximation method (VAM) & Least Cost
Method.
Level 2 Understanding
9. How do you represent a travelling salesman problem
through mathematical formulation?
Level 3 Applying
10. Analyse the rules of travelling salesman Problem. Level 4 Analysing
11. Discuss the meaning of Assignment Level 5 Evaluating
12. Compare Balanced assignment problem & Unbalanced
Assignment Problem.
Level 6 Creating
13. What example can you give for Unbalanced assignment
problem?
Level 1 Remembering
14. How will you resolve degeneracy in Transportation Problem? Level 2 Understanding
15. Classify transportation problem. Level 3 Applying
16. Examine the Steps in Hungarian algorithm. Level 4 Analysing
17. What is Branch and bound algorithm in Assignment? Level 1 Remembering
18. Compare Assignment and transportation Problem. Level 2 Understanding
19. What do you mean by Travelling Salesman Problem? Level 1 Remembering
20. What is Restricted Assignment? Level 1 Remembering
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Solve and find the Transportation Problem and Which method will
you select if you want toMinimize Cost?
Destination Supply
1 2 3 4
I 21 16 25 13 11
II 17 18 14 23 13
III 32 27 18 41 19
Demand 6 10 12 15
Level 1 Remembering
2. Find the Initial Basic Feasible solution for following TP. Using NW
Rule, LCM, and VAM. Which method will you select if you want to
Minimize Cost?
D1 D2 D3 Supply
S1 7 3 2 2
S2 2 1 3 3
S3 3 4 6 5
Demand 4 1 5 10
Level 2 Understanding
3.
(i)
Analyze the transportation problem with unit transportation
costs,demand, and supply as given below:
Destination
Supply
Source
D1 D2 D3 D4
S1
6 1 9 3
70
11 5 2 8
S2 55
10 12 4 7
S3
70
Demand 85 35 50 45
Apply VAM for Initial solution.
(5)
Level 3 Applying
(ii)
Construct the final Solution by using MODIMethod.
(8)
4.
(i)
Analyze & solve the following transportation problem to maximize
profit.
A B C D Supply
1
Source 2
3
Demand
15 51 42 33 23
80 42 26 81 44
90 40 66 60 33
23
31
16
30
100
Examine Initial solution using VAM.
(5)
Level 4 Analysing
(ii)
Analyze and find out the final Solution by using MODI Method.
(8)
5. Solve the following transportation problem using Vogel?s
method
Factory? Warehouse ?Available
A B C D E F
1 9 12 9 6 9 10 5
2 7 3 7 7 5 5 6
3 6 5 9 11 3 11 2
4 6 8 11 2 2 10 9
4 4 6 2 4 2
Requirement?
(5)
Level 5 Evaluating
6. (i) Solve the transportation problem and decide using VAM for initial
solution.
(5) Level 6 Creating
(ii) Evaluate using NWC and Least Cost method for initial solution?
Destination Supply
I 2 1 25 13 11
II 1 1 14 23 13
III 3 2 18 41 19
Demand 6 1 22 15
(8)
7.
Maximize profit from the following transportationproblem.
A B C D Supply
I 40 25 22 33 100
SourceII 44 35 30 30 30
III 38 38 28 30 70
Demand 40 20 60 30
Level 1 Remembering
(i) How will you convert maximization problem to minimization.
Find the maximum profit
(8)
(ii) Explain stepping stone method for checking the
solution for optimality transportation problems.
(5)
8. A company has one surplus truck in each of the cities A, B, C, D, &
E and one deficit trucks in each of the cities 1,2,3,4,5,6. The
distance between the cities in kms is shown in the matrix below.
Can you select the assignment of trucks from cities in surplus to
cities in deficiency .so that total distance covered by the vehicles is
minimum?
1 2 3 4 5 6
A 12 10 15 22 18 8
B 10 18 25 15 16 12
C 11 10 3 8 5 9
D 6 4 10 13 13 12
E 8 12 11 7 13 10
Level 2 Understanding
9.
Consider the problem of assigning five jobs to five persons. The
assignment costs are given as follows:
PERSONS?JOBS ?
1 2 3 4 5
A 8 4 2 6 1
B 0 9 5 5 4
C 3 8 9 2 6
D 4 3 1 0 3
Level 3 Applying
E 9 5 8 9 5
Determine the optimum assignment schedule.
10. The assignment cost of assigning any one operator to any one
machine is given in the following table.
MACHINE?OPERATORS ?
I II III IV
A 10 5 13 15
B 3 9 18 3
C 10 7 3 2
D 5 11 9 7
Find the optimal assignment by Hungarian method.
Level 4 Analysing
11. A machine shop purchased a drilling machine and two lathes of
different capacities. The Positioning of the machines among 4
possible locations on the shop floor is important forms the
standard of materials handling. Given the cost estimate per unit
time of materials below, find the optimum location of the
machines.
LOCATIONS
1 2 3 4
Lathe 1 12 9 12 9
Drill 15 Not
suitable
13 20
Lathe 2 4 8 10 6
Level 1 Remembering
12.
Solve the assignment problem for maximization given profit
matrix(profit in rupees).
Machines
P Q R S
JOB
51 53 54 50
47 50 48 50
49 50 60 61
63 64 60 60
Level 2 Understanding
PART - C
S.No Questions Marks BT
Level
Competence
1.
a
Assume that you are an OR specialist. Identify the procedure
for each of the following Method to the employees in order to
help them achieve solution to Transportation Problems.
Northwest Corner Cell Method
(3)
Level 1 Remembering
b Least Cost cell Method (4)
c Vogel?s Approximation Method (4)
d U V Method. (4)
13. The processing time in hours for the jobs when allocated to the
different machines is indicated below. Select the best assignment
of the machines for the jobs so that the total processing time is
Minimum.
Machines
M1 M2 M3 M4 M5
J1 9 22 58 11 19
JOB J2 43 78 72 50 63
J3 41 28 91 37 45
J4 74 42 27 49 39
J5 36 11 57 22 25
Level 4 Analysing
14. For the given travelling salesman problem, Minimize the total cost.
To
1 2 3 4
From A - 46 16 40
B 41 - 50 40
C 82 32 - 60
D 40 40 36 -
Level 1 Remembering
(i) Observe the above travelling salesman
problem and find out minimize the cost per
cycle.
(8)
(ii) Find whether path is satisfied. (5)
2.
Solve the following transportation problem, in which a
i
is the
availability at Origin
O
i
and b
j
is the requirement at the destination D
j
and cell entries
are unit costs of transportation from any origin to any
destination:
D1 D2 D3 D4 D5 a
j
O1 4 7 3 8 2 4
O2 1 4 7 3 8 7
O3 7 2 4 7 7 9
O4 4 8 2 4 7 2
b
j
8 3 7 2 2
Predict the allocation to minimize the cost.
Level 2 Understanding
3. A company has a team of 4 Salesman and the company wants to
do in 4 districts. Considering the capabilities of salesmen
and nature of the district, the company has estimated the profit per
day in Rs. For each salesmen in each district as follows.
District
s
Salesmen 1 2 3 4
A 16 10 14 11
B 14 11 15 15
C 15 15 13 12
D 13 12 14 15
Develop the best assignment schedule and analyze the total cost.
Level 3 Applying
4. Five operators have to be assigned to Five Machines. The
assignment costs are given in thetablebelow.
Analyse using Hungarian algorithm & find out the assignment to
minimize the cost.
Machine
I II III IV V
Operator
A 5 5 - 2 6
B 7 4 2 3 4
C 9 3 5 - 3
D 7 2 6 7 2
E 6 5 7 9 1
Level 4 Analyzing
UNIT ? III ? INTEGER PROGRAMMING AND GAME THEORY
SYLLABUS: Integer Programming ? Introduction and types - Game Theory-Two-person Zero sum
games-Saddle point, Dominance Rule, graphical and LP solutions, Nash Equilibrium
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. What do you mean by integer programming problem?
Level 1 Remembering
2. In what respect a mixed IPP differs from pure IPP?
Level 2 Understanding
3. What is Nash Equilibrium?
Level 3 Applying
4. Classify the different types of strategy.
Level 4 Analysing
5. Compile the Characteristics of game.
Level 5 Evaluating
6. Can you assess the applications of integer
programming?
Level 6 Creating
7. Define Game.
Level 1 Remembering
8. Compare Mixed Strategy and Pure Strategy.
Level 2 Understanding
9. How would you make use of the concept of Game theory
in Managerial Decision Making?
Level 3 Applying
10. Conclude your understanding about Payoff Matrix.
Level 4 Analysing
11. How will you find the optimal strategies and value of the
following game?
Player B
Player
A
H T
H 2 -1
T -1 0
Level 5 Evaluating
12. Interpret the concept of two person zero sum game.
Level 6 Creating
13. What is Saddle point?
Level 1 Remembering
14. Compare Dominance Principle of Rows and Columns.
Level 2 Understanding
15. Identify the basic assumptions of the Game.
Level 3 Applying
16. Conclude the advantages of Game theory.
Level 4 Analysing
17. What are the Methods of Matrices?
Level 1 Remembering
18. Summarize how graphs and LP solution are used in
Game theory.
Level 2 Understanding
19. What is a Decision Tree?
Level 1 Remembering
20. Define Dominance principle.
Level 1 Remembering
S.N
O
PART - B QUESTIONS MA
RK
S
BT
LEVEL
COMPETENCE
1. (i) What do you mean by Pure IPP? (3) Level 1 Remembering
(ii) What do you mean by Mixed IPP? (5)
(iii)
List out the difference between Pure and Mixed IPP.
(5)
2. (i) For what value of ?,the game with the following
matrix is strictly determined
B
1
B
2
B
3
A
1
? 6 2
A
2
-1 ? -7
A
3
-2 4 ?
(8) Level 2 Understanding
(ii) Write down the assumptions of game theory. (5)
3. (i) Solve the game whose pay-off matrix is given by
B
1
B
2
B
3
A
1
1 3 1
A
2
0 -4 -3
A
3
1 5 -1
(8)
Level 3 Applying
(ii) Explain the concept of Nash Equilibrium. (5)
4.
Analyze the Value of the game graphically
B1 B2
A1 4 4
A2 2 7
A3 5 3
A4 6 2
Level 4 Analysing
5.
What inference can be made using Dominance
Principle to reduce the following game and estimate
the game value?
B1 B2 B3 B4
A1 3 2 4 0
A2 3 4 2 4
A3 4 2 2 0
A4 2 1 6 3
Level 5 Evaluating
6.
How would you evaluate the following game whose
Pay-Off matrix is Given Below?
9 3 1 8 0
6 5 4 6 7
2 4 3 3 8
5 6 2 2 1
Level 6 Creating
7.
(i)
Two players A&B match coins. If the coins match
then A wins one unit value, if the coins do not
match then B wins one unit of value.
Determine pay-off matrix which strategy is to be
chosen
(5)
Level 1 Remembering
(ii)
Find the value of game. (8)
8.
Predict the Value of the Game given above Pay
OffMatrix.
Player B
B1 B2 B3
A1 -2 5 -3
Player A A2 1 3 5
A3 -3 -7 11
Level 2 Understanding
9.
Apply graphical analysis to Solve the game.
A/
B
B1 B2 B3 B4
A1 3 3 4 0
A2 5 4 3 7
Level 3 Applying
10. Solve the following game by graphical method.
Player B
1 2 3
1 6 4 3
Player A 2 2 4 8
Level 4 Analysing
11.
(i)
A and B play a Match(Game) in which each has 3
coins 5 paise, 10 paise and 20 paise. Each player
selects a coin without the knowledge of others
choice. IF the sum is even, B wins A?s Coin. If sum
is Odd, A wins B?s coin.
How will you find the pay-off matrix ?
(5)
Level 1
Remembering
(ii)
Find the Best Strategy & value of the Game. (8)
12.
Consider the Pay Off Matrix of player A as shown in
the table below and solve it optimally using the
graphical method .
Player A
Player
B
1 2 3 4 5
1 3 6 8 4 4
2 -7 4 2 10 2
Level 2 Understanding
13.
(i)
Analyze the Game Graphically:
Player A
Player
A
B1 B2
A1 -3 1
A2 5 3
A3 6 -1
A4 1 4
A5 2 2
A6 0 -5
Plot the graph
(5)
Level 4 Analysing
(ii)
Analyse and find the value of the game.
(8)
14.
Which one is the best strategy using Dominance
Principle?
B1 B2 B3 B4 B5 B6
A1
4 2 0 2 1 1
A2
4 3 1 3 2 2
A3
4 3 7 -5 1 2
A4
4 3 4 -1 2 2
A5
4 3 3 -2 2 2
Level 1 Remembering
PART-C
S.No Questions BT
Level
Competence
1.
Using Dominance property Solve.
B
A
I II IIIIV
1 -5 3 1 20
2 5 5 4 6
3 -4 -2 0 -5
Level 1 Remembering
2. Examine the 2 * n Game by the Method of Sub Game:
B1 B2 B3
A1 1 3 11
A2 8 5 2
Level 2 Understanding
3. In a game of matching coins with 2 players, A wins 1 unit value
when there are 2 heads, wins nothing when there are 2 tails
and looses ? unit value when there are one head and one tail.
Develop Pay Off matrix and value of the game.
Level 3 Applying
4.
i
ii
iii
Assume you have to choice of 3 strategies for advertising
and you have one major
Analyse the theory on Two-person sum games competitor
with 3 strategies.
(5)
Level 4 Analysing
What are the assumptions of Game? (5)
Find value of game.
B1 B2 B3
A1 80 70 60
A2 90 80 100
A3 40 30 40
(5)
UNIT - IV INVENTORY MODELS, SIMULATION AND DECISION THEORY
SYLLABUS: Inventory Models ? EOQ and EBQ Models (With and without shortages), Quantity Discount
Models. Decision making under risk ? Decision trees ? Decision making under uncertainty. Monte-carlo
simulation.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define inventory. Level 1 Remembering
2.
Classify the Forms of inventory.
Level 2 Understanding
3.
Identify the Objectives/significance of inventory model.
Level 3 Applying
4.
Highlight the importance of Reorder level.
Level 4 Analysing
5.
Discuss the concept of Lead time.
Level 5 Evaluate
6.
Interpret the Types of stock replenishment.
Level 1 Remembering
7.
List the Basic inventory models.
Level 2 Understanding
8.
Compare Ordering Cost and Carrying Cost.
Level 3 Appyling
9.
Identify when shortage cost and stock out cost arises?
Level 5 Evaluating
10.
Analyze why safety stock is maintained.
Level 1 Remembering
11.
Discuss the concept of Quantity Discount Model.
Level 2 Understanding
12.
Interpret the meaning of EOQ & EBQ.
Level 3 Applying
13.
What are random and pseudo random numbers?
Level 4 Analysing
14.
Explain Monte Carlo Method.
Level 5 Evaluating
15.
Summarize the concept of EMV.
Level 1 Remembering
16.
What inference can you make about holding cost ?
Level 2 Understanding
17.
What is Shortage Cost?
Level 3 Applying
18. Classify and explain the various conditions under which
decisions are made.
Level 1 Remembering
19. What is meant by the following terms in inventory
management: i)Carrying cost ii) shortage costs
Level 2 Understanding
20. What is Decision theory? List the problems that can be solved
by Simulation.
Level 3 Applying
S.NO PART - B QUESTIONS Marks BT
LEVEL
COMPETENCE
1.
(i)
Alpha industry needs 5400 units per year of a bought out
component which will be
used in its main product. The ordering cost is Rs.250
per order and the carrying cost per unit per year is
Rs.30.
Which is the best order quantity?
(8)
Level 1 Remembering
(ii)
Find the number of order per year and Frequency of
orders?
(5)
2.
(i)
A stockiest has to supply 12000 units of a product per
year to his customer. Demand is
fixed and known. Shortage cost is assumed to be
infinite. Inventory holding cost is 20 paise per unit per
month. Ordering Cost is Rs. 250 and purchase price
is Rs.10 per unit.
Estimate the EOQ
(8)
Level 2 Understanding
(ii)
Find the Frequency of orders and total inventory cost. (5)
3.
ABC manufacturing company purchases 9000 parts of a
machine for its annual requirement. Each part costs
Rs.20. The ordering cost per order is Rs.15 and the
carrying charges are 15% of the average inventory per
year. Apply EOQ formulae and find out EOQ, No of
orders ,Total Inventory Cost and total cost.
Level 3 Applying
4.
(i)
Demand for an item in a company is 18,000 units per
year. The company can produce the items at a rate of
3000 units per month. The Cost of one setup is Rs.500
and the holding cost of one unit per month is 15 paise.
Shortage cost of one unit is Rs.20 per year.
Analyze and find the optimum manufacturing quantity.
(8)
Level 4 Analysing
(ii)
Find the number of shortages and frequency of
Production run.
(5)
5. A company has a demand of 12000 units/year for an
item and it can produce 2000 units per month. The
cost of one setup is Rs.400 and the holding
cost/unit/month is 15 paise. Select the optimum lot
size and total cost per year assuming the cost of 1 unit
as Rs.4. Find EBQ, the number of set ups & total cost.
Level 5 Evaluating
6.
(i)
Find the optimal order quantity for a product when the
annual demand for the product is 500 units. The Cost of
storage per unit per year is 10% of the unit cost. Ordering
cost per order is Rs. 180.
Determine EOQ
(8)
Level 6 Creating
(ii)
Evaluate the Total Cost
(5)
The unit cost are given below:
Quantity Unit Cost(Rs.)
O
1500<=Q3<3000 24.60
3000<=Q4 24.40
7. (i)
Formulate the Optimal order quantity for a product for
which the price breaks are as follows
(8)
Level 1 Remembering
(ii)
Also find the Total cost.
Quantity Unit Cost(Rs.)
O
750<=Q 875
(5)
8.
Compute the EOQ and the total variable cost for the
following:
Annual demand: 25 units
Unit price: Rs.2.50
Order cost: Rs.4.00
Storage rate: 1% per year
Level 2 Understand
9.
(i)
Identify the profit under three states of nature & three
decision alternative.
State of
Nature
State of
Nature
State of
Nature
N1 N2 N3
Decision
Naking
D1 150 250 300
Decision
Naking
D2 450 250 200
Decision
Naking
D3 100 180 290
Hurwitz criterion for alpha=0.5
(3)
Level 3 Applying
(ii)
Laplace condition
(5)
(iii)
Minimax Condition
(5)
10.
A Bakery keeps a stock of particular brand of cake. Daily
demand of past experience.
Daily
demand
0 15 25 35 45 50
Probability 0.01 0.15 0.20 0.50 0.12 0.02
Consider the following sequence of random numbers.
48 78 9 51 56 77 15 14 68 9
Using this sequence simulate the demand for next 10
days.
Find the stock situation if the owner makes 35 cakes
every day. Examine the daily average demand.
Level 1 Remembering
11.
Given above is the following pay off matrix.
Using EMV criterion . Decide which of the act can be
chosen at the best. FindEVPI & EOL.
Nature
Probability
Don?t
Expand
Expand
200
Expand
400
High
Demand
0.4 2500 3500 5000
Medium
Demand
0.4 2500 3500 2500
Low
Demand
0.2 2500 1500 1000
Level 2 Understanding
FirstRanker.com - FirstRanker's Choice
(An
?
DEPARTMENT OF MANAGEMENT STUDIES
QUESTION BANK
II SEMESTER
1915201? APPLIED OPERATIONS RESEACH
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Dr. Radha Ganesh Kumar ? Asst. Professor (Sel.G) and HOD
Mr.B. Sam Paul ? Asst. Professor (OG)
(An
? .
DEPARTMENT OFMANAGEMENT STUDIES
QUESTION BANK
SUBJECT :1915201 ?APPLIED OPERATIONS RESEACH
SEM / YEAR : IISemester / IYear
UNIT ? I ?INTRODUCTION TO LINEAR PROGRAMMING (LP)
SYLLABUS: Introduction to applications of operations research in functional areas of management.
Linear Programming-formulation, solution by graphical and simplex methods, Special cases. Dual
simplex method. Principles of Duality. Sensitivity Analysis.
PART- A
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Define Operations Research (OR). Level 1 Remembering
2. Differentiate between Simplex and Big M Method Level 2 Understanding
3. How do you show your understanding unbounded solution? Level 3 Applying
4. Categorize the forms of LPP. Level 4 Analysing
5.
Discuss why is two phase method is better than Big M
method?
Level 5 Evaluating
6. Interpret the usage of Sensitivity Analysis in LPP. Level 6 Creating
7. What are the assumptions and requirements of LPP? Level 1 Remembering
8. Compare Dual Simplex and Duality. Level 2 Understanding
9. Identify the Advantages of duality. Level 3 Applying
10. What do you think about Infeasible solution? Level 4 Analysing
11. How will you solve LPP graphically? Level 5 Evaluating
12.
Conclude your understanding on the mathematical
formulation of LPP.
Level 6 Creating
13. Define basic variables and artificial variables. Level 1 Remembering
14. Compare Slack variable & Surplus Variable. Level 2 Understanding
15.
Give some example for the role of Surplus variable & Slack
Variable in the simplex method
Level 3 Applying
16. How would you apply Artificial variable? Level 4 Analysing
17. What is Big M Method? Level 1 Remembering
18. Distinguish simplex and Big M method Level 2 Understanding
19.
What do you mean by Duality? List the Rules for primal and
dual.
Level 1 Remembering
20. What is Shadow price? Level 1 Remembering
PART- B
S.NO
QUESTIONS
BT
LEVEL
COMPETENCE
1.
(i)
Maximise Z=3x+4y subject to
2x+5y ?60,
4x+2y ?40.
x, y >0. Solve by Graphical Method
Plot the graph
(8)
Level 1 Remembering
(ii) Which one is the best solution? (5)
2.
(i)
Min Z= 20x
1
+10 x
2
subject to
x
1
+2x
2
? 40,
3x
1
+x
2
? 30,
4x
1
+3x
2
? 60,
x
1
,x
2
? 0.
Solve by Graphical Method,
Plot the graph
(8)
Level 2 Understanding
(ii) Predict the value of x & y. (5)
3 Max Z= 5x1+4x2 subject to
x
1
-2x
2
? 1,
x
1
+2x
2
?3,
x
1
,x
2
? 0. Solve Graphically. Which one is the best
solution?
Level 3 Applying
4.
(i)
A Plant Manufacturer 2 Product A & B. The Profit Contribution
of each product has been estimated as Rs.300 for product A
and Rs.400 for Product B. Each Product passes through 3
departments of the plant. The time required for each product
and total time available in each department is as follows.
Department Hours
Required
Hours
Required
Available
Hours
during
month
Product
A
Product
B
I 2 3 1600
II 3 2 1500
III 1 1 700
The company has a contract to supply atleast 300 units of
Product B per month.
Formulate the LPP
(5)
Level 4
Analysing
(ii) Solve through Graphical Method
(8)
5. Solve the following LPP by graphical method.
Maximize Z= 3x
1
+2x
2
Subject t o
- 2x
1
+x
2
?1,
x
1
? 2,
x
1
+ x
2
? 3
and x
1
,x
2
? 0
Level 5 Evaluating
6. (i) Max Z= 1000x
1
+4000x
2
+5000x
3
Subject to 3x1+3x
3
?22,
x1+2x2+3x
3
? 14,
3x1+2x2 ? 14
& x1,x2 ? 0
Develop a Simplex Table
(5)
Level 6 Creating
(ii) Analyse and find the value of x
1
, x
2
? (8)
7. Analyze the following LPP by Simplex Method:
Min Z = -10y
1
-15y
2
-20y
3
Subject to 2y
1
+4y
2
+6y
3
? 24,
3y
1
+9y
2
+6y
3
? 30,
& y
1
, y
2
, y
3
? 0.
Level 1 Remembering
(i)
Develop a Simplex Table (5)
(ii) Solve and find the value of y1 ,y2 and y3
(8)
8.
Solve By Graphical Method
Minimize Z= 40x
1
+24x
2
Subject to, 20x
1
+50 x
2
> 4,800
80 x
1
+50x
2
> 7,200
x
1
,x
2
>0
Level 2 Understanding
9. Solve the following LPP by simplex method:
Minimize Z= 8x
1
-2x
2
Subject to -4x
1
+2x
2
?1,
5x
1
-4x
2
?3,
and x
1
,x
2
? 0
Level 3 Applying
10. Solve the following LPP by simplex method:
Maximize Z= 3x1+2x
2
Subject to
2x
1
+x
2
?2,
3x
1
+4x
2
?12,
x
1
,x
2
? 0
Level 4 Analyzing
11. Review the LPP and solve by simplex method
Max Z= 25x+10y
Subject to the constraints
x+0.5y? 20
x+y? 50
x,y ? 0
Level 1 Remembering
12. A firm produces three products. These products are
processors on 3 different machines. The time required for
manufacturing one unit of cost of the products and the daily
capacity of the three machines is given in the table below.
Analyse and find the optimum solution.
Mac
hine
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Machine
Capacity
Min /Day
Product1 Product 2 Product 3
M1 2 8 2 940
M2 4 - 8 970
M3 2 5 - 430
It is required to determine the daily no. of units to be
manufactured for each product. The profit for unit for
Level 2 Understanding
product 1,2,3 is Rs.4,Rs.8,Rs.6 respectively. It is assumed
that all the amount produced are consumed in the market
13. Using dual simplex method , solve and find the optimum
solution for the given LPP.
Maximize Z=6x
1
+4x
2
+4x
3
Subject to 3x
1
,x
2
+2x
3
? 2
2x
1
+x
2
-x
3
? 1
-x
1
+x
2
+2x
3
? 1 &
x
1
,x
2
,x
3
? 0
Level 4 Analysing
14.
(i)
Evaluate by using dual simplex method and solve the LPP.
Minimize Z=2x
1
+x
2
Subject to 3x
1
+2x
2
? 3
4x
1
+3x
2
? 6
x
1
+x
2
? 5 & x
1
,x
2
?
Determine the dual simplex table
(5)
Level 1 Remembering
(ii)
Find the value of x
1
, x
2
(8)
PART - C
S.No Questions BT
LEVEL
COMPETENCE
1.
Max Z=300x+400y subject to
2x+3y ? 1600,
3x+2y ? 1500,
x+y ? 700,
y ? 300, x,y ? 0 Solve by Graphical Method, choose the
value of x & y which maximizes profit.
Level 1 Remembering
2. Solve the following LPP by graphical method.
Minimize Z= 6000x1+4000x
2
Subject t o
3x+x
2
? 40,
x
1
+2.5 x
2
? 22
3x
1
+3 x
2
? 40
and x
1
,x
2
? 0
Level 2 Understanding
3. Develop a Simplex Table and Solve
Max Z = 3 x1+2 x2,
Subject to
x1+ x2 ?4,
x1- x2 ? 2;
x1, x2 ?0.
Level 3 Applying
4. Solve by using Simplex Method.
Maximize Z= 3x+5y
Subject to the constraints
x+y? 60
x? 40
y ? 30
x,y ? 0
Level 1 Remembering
UNIT - II LINEAR PROGRAMMING EXTENSIONS
SYLLABUS: Transportation Models (Minimizing and Maximizing Problems) ? Balanced and unbalanced
Problems ? Initial Basic feasible solution by N-W Corner Rule, Least cost and Vogel?s approximation methods.
Check for optimality. Solution by MODI /. Case of Degeneracy. Trans-shipment Models. Assignment Models
(Minimising and Maximising Problems) ? Balanced and Unbalanced Problems. Solution by Hungarian and
Branch and Bound Algorithms. Travelling Salesman problem.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define Transportation & Transhipment. Level 1 Remembering
2. Differentiate balanced transportation problem & Unbalanced
Transportation Problem.
Level 2 Understanding
3. How would you show your understanding on unbalanced
transportation problem?
Level 3 Applying
4. Categorize the Phases of transportation model. Level 4 Analysing
5. Construct the basic feasible solution for the following
transportation problem.
1 2 3 4 SUPPLY
1 2 3 11 7 6
2 1 0 6 1 1
3 5 8 15 9 10
DEMAN D 7 5 3 2
Level 5 Evaluating
6 Interpret the need for Optimum solution in transportation. Level 6 Creating
7. What do you mean by Least cost method (LCM)? Level 1 Remembering
8. Compare Vogel approximation method (VAM) & Least Cost
Method.
Level 2 Understanding
9. How do you represent a travelling salesman problem
through mathematical formulation?
Level 3 Applying
10. Analyse the rules of travelling salesman Problem. Level 4 Analysing
11. Discuss the meaning of Assignment Level 5 Evaluating
12. Compare Balanced assignment problem & Unbalanced
Assignment Problem.
Level 6 Creating
13. What example can you give for Unbalanced assignment
problem?
Level 1 Remembering
14. How will you resolve degeneracy in Transportation Problem? Level 2 Understanding
15. Classify transportation problem. Level 3 Applying
16. Examine the Steps in Hungarian algorithm. Level 4 Analysing
17. What is Branch and bound algorithm in Assignment? Level 1 Remembering
18. Compare Assignment and transportation Problem. Level 2 Understanding
19. What do you mean by Travelling Salesman Problem? Level 1 Remembering
20. What is Restricted Assignment? Level 1 Remembering
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Solve and find the Transportation Problem and Which method will
you select if you want toMinimize Cost?
Destination Supply
1 2 3 4
I 21 16 25 13 11
II 17 18 14 23 13
III 32 27 18 41 19
Demand 6 10 12 15
Level 1 Remembering
2. Find the Initial Basic Feasible solution for following TP. Using NW
Rule, LCM, and VAM. Which method will you select if you want to
Minimize Cost?
D1 D2 D3 Supply
S1 7 3 2 2
S2 2 1 3 3
S3 3 4 6 5
Demand 4 1 5 10
Level 2 Understanding
3.
(i)
Analyze the transportation problem with unit transportation
costs,demand, and supply as given below:
Destination
Supply
Source
D1 D2 D3 D4
S1
6 1 9 3
70
11 5 2 8
S2 55
10 12 4 7
S3
70
Demand 85 35 50 45
Apply VAM for Initial solution.
(5)
Level 3 Applying
(ii)
Construct the final Solution by using MODIMethod.
(8)
4.
(i)
Analyze & solve the following transportation problem to maximize
profit.
A B C D Supply
1
Source 2
3
Demand
15 51 42 33 23
80 42 26 81 44
90 40 66 60 33
23
31
16
30
100
Examine Initial solution using VAM.
(5)
Level 4 Analysing
(ii)
Analyze and find out the final Solution by using MODI Method.
(8)
5. Solve the following transportation problem using Vogel?s
method
Factory? Warehouse ?Available
A B C D E F
1 9 12 9 6 9 10 5
2 7 3 7 7 5 5 6
3 6 5 9 11 3 11 2
4 6 8 11 2 2 10 9
4 4 6 2 4 2
Requirement?
(5)
Level 5 Evaluating
6. (i) Solve the transportation problem and decide using VAM for initial
solution.
(5) Level 6 Creating
(ii) Evaluate using NWC and Least Cost method for initial solution?
Destination Supply
I 2 1 25 13 11
II 1 1 14 23 13
III 3 2 18 41 19
Demand 6 1 22 15
(8)
7.
Maximize profit from the following transportationproblem.
A B C D Supply
I 40 25 22 33 100
SourceII 44 35 30 30 30
III 38 38 28 30 70
Demand 40 20 60 30
Level 1 Remembering
(i) How will you convert maximization problem to minimization.
Find the maximum profit
(8)
(ii) Explain stepping stone method for checking the
solution for optimality transportation problems.
(5)
8. A company has one surplus truck in each of the cities A, B, C, D, &
E and one deficit trucks in each of the cities 1,2,3,4,5,6. The
distance between the cities in kms is shown in the matrix below.
Can you select the assignment of trucks from cities in surplus to
cities in deficiency .so that total distance covered by the vehicles is
minimum?
1 2 3 4 5 6
A 12 10 15 22 18 8
B 10 18 25 15 16 12
C 11 10 3 8 5 9
D 6 4 10 13 13 12
E 8 12 11 7 13 10
Level 2 Understanding
9.
Consider the problem of assigning five jobs to five persons. The
assignment costs are given as follows:
PERSONS?JOBS ?
1 2 3 4 5
A 8 4 2 6 1
B 0 9 5 5 4
C 3 8 9 2 6
D 4 3 1 0 3
Level 3 Applying
E 9 5 8 9 5
Determine the optimum assignment schedule.
10. The assignment cost of assigning any one operator to any one
machine is given in the following table.
MACHINE?OPERATORS ?
I II III IV
A 10 5 13 15
B 3 9 18 3
C 10 7 3 2
D 5 11 9 7
Find the optimal assignment by Hungarian method.
Level 4 Analysing
11. A machine shop purchased a drilling machine and two lathes of
different capacities. The Positioning of the machines among 4
possible locations on the shop floor is important forms the
standard of materials handling. Given the cost estimate per unit
time of materials below, find the optimum location of the
machines.
LOCATIONS
1 2 3 4
Lathe 1 12 9 12 9
Drill 15 Not
suitable
13 20
Lathe 2 4 8 10 6
Level 1 Remembering
12.
Solve the assignment problem for maximization given profit
matrix(profit in rupees).
Machines
P Q R S
JOB
51 53 54 50
47 50 48 50
49 50 60 61
63 64 60 60
Level 2 Understanding
PART - C
S.No Questions Marks BT
Level
Competence
1.
a
Assume that you are an OR specialist. Identify the procedure
for each of the following Method to the employees in order to
help them achieve solution to Transportation Problems.
Northwest Corner Cell Method
(3)
Level 1 Remembering
b Least Cost cell Method (4)
c Vogel?s Approximation Method (4)
d U V Method. (4)
13. The processing time in hours for the jobs when allocated to the
different machines is indicated below. Select the best assignment
of the machines for the jobs so that the total processing time is
Minimum.
Machines
M1 M2 M3 M4 M5
J1 9 22 58 11 19
JOB J2 43 78 72 50 63
J3 41 28 91 37 45
J4 74 42 27 49 39
J5 36 11 57 22 25
Level 4 Analysing
14. For the given travelling salesman problem, Minimize the total cost.
To
1 2 3 4
From A - 46 16 40
B 41 - 50 40
C 82 32 - 60
D 40 40 36 -
Level 1 Remembering
(i) Observe the above travelling salesman
problem and find out minimize the cost per
cycle.
(8)
(ii) Find whether path is satisfied. (5)
2.
Solve the following transportation problem, in which a
i
is the
availability at Origin
O
i
and b
j
is the requirement at the destination D
j
and cell entries
are unit costs of transportation from any origin to any
destination:
D1 D2 D3 D4 D5 a
j
O1 4 7 3 8 2 4
O2 1 4 7 3 8 7
O3 7 2 4 7 7 9
O4 4 8 2 4 7 2
b
j
8 3 7 2 2
Predict the allocation to minimize the cost.
Level 2 Understanding
3. A company has a team of 4 Salesman and the company wants to
do in 4 districts. Considering the capabilities of salesmen
and nature of the district, the company has estimated the profit per
day in Rs. For each salesmen in each district as follows.
District
s
Salesmen 1 2 3 4
A 16 10 14 11
B 14 11 15 15
C 15 15 13 12
D 13 12 14 15
Develop the best assignment schedule and analyze the total cost.
Level 3 Applying
4. Five operators have to be assigned to Five Machines. The
assignment costs are given in thetablebelow.
Analyse using Hungarian algorithm & find out the assignment to
minimize the cost.
Machine
I II III IV V
Operator
A 5 5 - 2 6
B 7 4 2 3 4
C 9 3 5 - 3
D 7 2 6 7 2
E 6 5 7 9 1
Level 4 Analyzing
UNIT ? III ? INTEGER PROGRAMMING AND GAME THEORY
SYLLABUS: Integer Programming ? Introduction and types - Game Theory-Two-person Zero sum
games-Saddle point, Dominance Rule, graphical and LP solutions, Nash Equilibrium
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. What do you mean by integer programming problem?
Level 1 Remembering
2. In what respect a mixed IPP differs from pure IPP?
Level 2 Understanding
3. What is Nash Equilibrium?
Level 3 Applying
4. Classify the different types of strategy.
Level 4 Analysing
5. Compile the Characteristics of game.
Level 5 Evaluating
6. Can you assess the applications of integer
programming?
Level 6 Creating
7. Define Game.
Level 1 Remembering
8. Compare Mixed Strategy and Pure Strategy.
Level 2 Understanding
9. How would you make use of the concept of Game theory
in Managerial Decision Making?
Level 3 Applying
10. Conclude your understanding about Payoff Matrix.
Level 4 Analysing
11. How will you find the optimal strategies and value of the
following game?
Player B
Player
A
H T
H 2 -1
T -1 0
Level 5 Evaluating
12. Interpret the concept of two person zero sum game.
Level 6 Creating
13. What is Saddle point?
Level 1 Remembering
14. Compare Dominance Principle of Rows and Columns.
Level 2 Understanding
15. Identify the basic assumptions of the Game.
Level 3 Applying
16. Conclude the advantages of Game theory.
Level 4 Analysing
17. What are the Methods of Matrices?
Level 1 Remembering
18. Summarize how graphs and LP solution are used in
Game theory.
Level 2 Understanding
19. What is a Decision Tree?
Level 1 Remembering
20. Define Dominance principle.
Level 1 Remembering
S.N
O
PART - B QUESTIONS MA
RK
S
BT
LEVEL
COMPETENCE
1. (i) What do you mean by Pure IPP? (3) Level 1 Remembering
(ii) What do you mean by Mixed IPP? (5)
(iii)
List out the difference between Pure and Mixed IPP.
(5)
2. (i) For what value of ?,the game with the following
matrix is strictly determined
B
1
B
2
B
3
A
1
? 6 2
A
2
-1 ? -7
A
3
-2 4 ?
(8) Level 2 Understanding
(ii) Write down the assumptions of game theory. (5)
3. (i) Solve the game whose pay-off matrix is given by
B
1
B
2
B
3
A
1
1 3 1
A
2
0 -4 -3
A
3
1 5 -1
(8)
Level 3 Applying
(ii) Explain the concept of Nash Equilibrium. (5)
4.
Analyze the Value of the game graphically
B1 B2
A1 4 4
A2 2 7
A3 5 3
A4 6 2
Level 4 Analysing
5.
What inference can be made using Dominance
Principle to reduce the following game and estimate
the game value?
B1 B2 B3 B4
A1 3 2 4 0
A2 3 4 2 4
A3 4 2 2 0
A4 2 1 6 3
Level 5 Evaluating
6.
How would you evaluate the following game whose
Pay-Off matrix is Given Below?
9 3 1 8 0
6 5 4 6 7
2 4 3 3 8
5 6 2 2 1
Level 6 Creating
7.
(i)
Two players A&B match coins. If the coins match
then A wins one unit value, if the coins do not
match then B wins one unit of value.
Determine pay-off matrix which strategy is to be
chosen
(5)
Level 1 Remembering
(ii)
Find the value of game. (8)
8.
Predict the Value of the Game given above Pay
OffMatrix.
Player B
B1 B2 B3
A1 -2 5 -3
Player A A2 1 3 5
A3 -3 -7 11
Level 2 Understanding
9.
Apply graphical analysis to Solve the game.
A/
B
B1 B2 B3 B4
A1 3 3 4 0
A2 5 4 3 7
Level 3 Applying
10. Solve the following game by graphical method.
Player B
1 2 3
1 6 4 3
Player A 2 2 4 8
Level 4 Analysing
11.
(i)
A and B play a Match(Game) in which each has 3
coins 5 paise, 10 paise and 20 paise. Each player
selects a coin without the knowledge of others
choice. IF the sum is even, B wins A?s Coin. If sum
is Odd, A wins B?s coin.
How will you find the pay-off matrix ?
(5)
Level 1
Remembering
(ii)
Find the Best Strategy & value of the Game. (8)
12.
Consider the Pay Off Matrix of player A as shown in
the table below and solve it optimally using the
graphical method .
Player A
Player
B
1 2 3 4 5
1 3 6 8 4 4
2 -7 4 2 10 2
Level 2 Understanding
13.
(i)
Analyze the Game Graphically:
Player A
Player
A
B1 B2
A1 -3 1
A2 5 3
A3 6 -1
A4 1 4
A5 2 2
A6 0 -5
Plot the graph
(5)
Level 4 Analysing
(ii)
Analyse and find the value of the game.
(8)
14.
Which one is the best strategy using Dominance
Principle?
B1 B2 B3 B4 B5 B6
A1
4 2 0 2 1 1
A2
4 3 1 3 2 2
A3
4 3 7 -5 1 2
A4
4 3 4 -1 2 2
A5
4 3 3 -2 2 2
Level 1 Remembering
PART-C
S.No Questions BT
Level
Competence
1.
Using Dominance property Solve.
B
A
I II IIIIV
1 -5 3 1 20
2 5 5 4 6
3 -4 -2 0 -5
Level 1 Remembering
2. Examine the 2 * n Game by the Method of Sub Game:
B1 B2 B3
A1 1 3 11
A2 8 5 2
Level 2 Understanding
3. In a game of matching coins with 2 players, A wins 1 unit value
when there are 2 heads, wins nothing when there are 2 tails
and looses ? unit value when there are one head and one tail.
Develop Pay Off matrix and value of the game.
Level 3 Applying
4.
i
ii
iii
Assume you have to choice of 3 strategies for advertising
and you have one major
Analyse the theory on Two-person sum games competitor
with 3 strategies.
(5)
Level 4 Analysing
What are the assumptions of Game? (5)
Find value of game.
B1 B2 B3
A1 80 70 60
A2 90 80 100
A3 40 30 40
(5)
UNIT - IV INVENTORY MODELS, SIMULATION AND DECISION THEORY
SYLLABUS: Inventory Models ? EOQ and EBQ Models (With and without shortages), Quantity Discount
Models. Decision making under risk ? Decision trees ? Decision making under uncertainty. Monte-carlo
simulation.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define inventory. Level 1 Remembering
2.
Classify the Forms of inventory.
Level 2 Understanding
3.
Identify the Objectives/significance of inventory model.
Level 3 Applying
4.
Highlight the importance of Reorder level.
Level 4 Analysing
5.
Discuss the concept of Lead time.
Level 5 Evaluate
6.
Interpret the Types of stock replenishment.
Level 1 Remembering
7.
List the Basic inventory models.
Level 2 Understanding
8.
Compare Ordering Cost and Carrying Cost.
Level 3 Appyling
9.
Identify when shortage cost and stock out cost arises?
Level 5 Evaluating
10.
Analyze why safety stock is maintained.
Level 1 Remembering
11.
Discuss the concept of Quantity Discount Model.
Level 2 Understanding
12.
Interpret the meaning of EOQ & EBQ.
Level 3 Applying
13.
What are random and pseudo random numbers?
Level 4 Analysing
14.
Explain Monte Carlo Method.
Level 5 Evaluating
15.
Summarize the concept of EMV.
Level 1 Remembering
16.
What inference can you make about holding cost ?
Level 2 Understanding
17.
What is Shortage Cost?
Level 3 Applying
18. Classify and explain the various conditions under which
decisions are made.
Level 1 Remembering
19. What is meant by the following terms in inventory
management: i)Carrying cost ii) shortage costs
Level 2 Understanding
20. What is Decision theory? List the problems that can be solved
by Simulation.
Level 3 Applying
S.NO PART - B QUESTIONS Marks BT
LEVEL
COMPETENCE
1.
(i)
Alpha industry needs 5400 units per year of a bought out
component which will be
used in its main product. The ordering cost is Rs.250
per order and the carrying cost per unit per year is
Rs.30.
Which is the best order quantity?
(8)
Level 1 Remembering
(ii)
Find the number of order per year and Frequency of
orders?
(5)
2.
(i)
A stockiest has to supply 12000 units of a product per
year to his customer. Demand is
fixed and known. Shortage cost is assumed to be
infinite. Inventory holding cost is 20 paise per unit per
month. Ordering Cost is Rs. 250 and purchase price
is Rs.10 per unit.
Estimate the EOQ
(8)
Level 2 Understanding
(ii)
Find the Frequency of orders and total inventory cost. (5)
3.
ABC manufacturing company purchases 9000 parts of a
machine for its annual requirement. Each part costs
Rs.20. The ordering cost per order is Rs.15 and the
carrying charges are 15% of the average inventory per
year. Apply EOQ formulae and find out EOQ, No of
orders ,Total Inventory Cost and total cost.
Level 3 Applying
4.
(i)
Demand for an item in a company is 18,000 units per
year. The company can produce the items at a rate of
3000 units per month. The Cost of one setup is Rs.500
and the holding cost of one unit per month is 15 paise.
Shortage cost of one unit is Rs.20 per year.
Analyze and find the optimum manufacturing quantity.
(8)
Level 4 Analysing
(ii)
Find the number of shortages and frequency of
Production run.
(5)
5. A company has a demand of 12000 units/year for an
item and it can produce 2000 units per month. The
cost of one setup is Rs.400 and the holding
cost/unit/month is 15 paise. Select the optimum lot
size and total cost per year assuming the cost of 1 unit
as Rs.4. Find EBQ, the number of set ups & total cost.
Level 5 Evaluating
6.
(i)
Find the optimal order quantity for a product when the
annual demand for the product is 500 units. The Cost of
storage per unit per year is 10% of the unit cost. Ordering
cost per order is Rs. 180.
Determine EOQ
(8)
Level 6 Creating
(ii)
Evaluate the Total Cost
(5)
The unit cost are given below:
Quantity Unit Cost(Rs.)
O
1500<=Q3<3000 24.60
3000<=Q4 24.40
7. (i)
Formulate the Optimal order quantity for a product for
which the price breaks are as follows
(8)
Level 1 Remembering
(ii)
Also find the Total cost.
Quantity Unit Cost(Rs.)
O
750<=Q 875
(5)
8.
Compute the EOQ and the total variable cost for the
following:
Annual demand: 25 units
Unit price: Rs.2.50
Order cost: Rs.4.00
Storage rate: 1% per year
Level 2 Understand
9.
(i)
Identify the profit under three states of nature & three
decision alternative.
State of
Nature
State of
Nature
State of
Nature
N1 N2 N3
Decision
Naking
D1 150 250 300
Decision
Naking
D2 450 250 200
Decision
Naking
D3 100 180 290
Hurwitz criterion for alpha=0.5
(3)
Level 3 Applying
(ii)
Laplace condition
(5)
(iii)
Minimax Condition
(5)
10.
A Bakery keeps a stock of particular brand of cake. Daily
demand of past experience.
Daily
demand
0 15 25 35 45 50
Probability 0.01 0.15 0.20 0.50 0.12 0.02
Consider the following sequence of random numbers.
48 78 9 51 56 77 15 14 68 9
Using this sequence simulate the demand for next 10
days.
Find the stock situation if the owner makes 35 cakes
every day. Examine the daily average demand.
Level 1 Remembering
11.
Given above is the following pay off matrix.
Using EMV criterion . Decide which of the act can be
chosen at the best. FindEVPI & EOL.
Nature
Probability
Don?t
Expand
Expand
200
Expand
400
High
Demand
0.4 2500 3500 5000
Medium
Demand
0.4 2500 3500 2500
Low
Demand
0.2 2500 1500 1000
Level 2 Understanding
12.
A sample of 100 arrivals of customers at a retail sales
depot is according to the following distribution.
Time between arrivals(mins) Frequency
0.5 2
1.0 6
1.5 10
2.0 25
2.5 20
3.0 14
3.5 4
4.0 7
4.5 4
5.0 2
Use random numbers and predict the average time
between arrivals.
48 78 9 51 56 77 15 14 68 9
Level 3 Applying
13.
(i)
A departmental store purchases sprays which can be
ordered only in lots of 10. Each spray cost Rs.75 and
sells at Rs.90 each. Used sprays, however have \no
salvage value.
Demand 10 20 30 40 50
Probability 0.2 0.35 0.25 0.15 0.05
The probability distribution obtained from analysis of past
sales data is given below.
Analyse the payoff table.
(5)
Level 4 Analysing
(ii) How much quantity should the departmental store buy to
maximize its profit?
(8)
14. (i)
A company uses annually 50,000 units of an item each
costing Rs.1.20. Each order costs Rs.45 and inventory
carrying costs are 15% of the annual average inventory
value.
Find EOQ.
(3)
Level 2 Understanding
(ii) If the company operates 250 days a year and the
procurement time is 10 days and safety stock is 500
units, find reorder level, maximum, minimum and
average inventory
(10)
FirstRanker.com - FirstRanker's Choice
(An
?
DEPARTMENT OF MANAGEMENT STUDIES
QUESTION BANK
II SEMESTER
1915201? APPLIED OPERATIONS RESEACH
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Dr. Radha Ganesh Kumar ? Asst. Professor (Sel.G) and HOD
Mr.B. Sam Paul ? Asst. Professor (OG)
(An
? .
DEPARTMENT OFMANAGEMENT STUDIES
QUESTION BANK
SUBJECT :1915201 ?APPLIED OPERATIONS RESEACH
SEM / YEAR : IISemester / IYear
UNIT ? I ?INTRODUCTION TO LINEAR PROGRAMMING (LP)
SYLLABUS: Introduction to applications of operations research in functional areas of management.
Linear Programming-formulation, solution by graphical and simplex methods, Special cases. Dual
simplex method. Principles of Duality. Sensitivity Analysis.
PART- A
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Define Operations Research (OR). Level 1 Remembering
2. Differentiate between Simplex and Big M Method Level 2 Understanding
3. How do you show your understanding unbounded solution? Level 3 Applying
4. Categorize the forms of LPP. Level 4 Analysing
5.
Discuss why is two phase method is better than Big M
method?
Level 5 Evaluating
6. Interpret the usage of Sensitivity Analysis in LPP. Level 6 Creating
7. What are the assumptions and requirements of LPP? Level 1 Remembering
8. Compare Dual Simplex and Duality. Level 2 Understanding
9. Identify the Advantages of duality. Level 3 Applying
10. What do you think about Infeasible solution? Level 4 Analysing
11. How will you solve LPP graphically? Level 5 Evaluating
12.
Conclude your understanding on the mathematical
formulation of LPP.
Level 6 Creating
13. Define basic variables and artificial variables. Level 1 Remembering
14. Compare Slack variable & Surplus Variable. Level 2 Understanding
15.
Give some example for the role of Surplus variable & Slack
Variable in the simplex method
Level 3 Applying
16. How would you apply Artificial variable? Level 4 Analysing
17. What is Big M Method? Level 1 Remembering
18. Distinguish simplex and Big M method Level 2 Understanding
19.
What do you mean by Duality? List the Rules for primal and
dual.
Level 1 Remembering
20. What is Shadow price? Level 1 Remembering
PART- B
S.NO
QUESTIONS
BT
LEVEL
COMPETENCE
1.
(i)
Maximise Z=3x+4y subject to
2x+5y ?60,
4x+2y ?40.
x, y >0. Solve by Graphical Method
Plot the graph
(8)
Level 1 Remembering
(ii) Which one is the best solution? (5)
2.
(i)
Min Z= 20x
1
+10 x
2
subject to
x
1
+2x
2
? 40,
3x
1
+x
2
? 30,
4x
1
+3x
2
? 60,
x
1
,x
2
? 0.
Solve by Graphical Method,
Plot the graph
(8)
Level 2 Understanding
(ii) Predict the value of x & y. (5)
3 Max Z= 5x1+4x2 subject to
x
1
-2x
2
? 1,
x
1
+2x
2
?3,
x
1
,x
2
? 0. Solve Graphically. Which one is the best
solution?
Level 3 Applying
4.
(i)
A Plant Manufacturer 2 Product A & B. The Profit Contribution
of each product has been estimated as Rs.300 for product A
and Rs.400 for Product B. Each Product passes through 3
departments of the plant. The time required for each product
and total time available in each department is as follows.
Department Hours
Required
Hours
Required
Available
Hours
during
month
Product
A
Product
B
I 2 3 1600
II 3 2 1500
III 1 1 700
The company has a contract to supply atleast 300 units of
Product B per month.
Formulate the LPP
(5)
Level 4
Analysing
(ii) Solve through Graphical Method
(8)
5. Solve the following LPP by graphical method.
Maximize Z= 3x
1
+2x
2
Subject t o
- 2x
1
+x
2
?1,
x
1
? 2,
x
1
+ x
2
? 3
and x
1
,x
2
? 0
Level 5 Evaluating
6. (i) Max Z= 1000x
1
+4000x
2
+5000x
3
Subject to 3x1+3x
3
?22,
x1+2x2+3x
3
? 14,
3x1+2x2 ? 14
& x1,x2 ? 0
Develop a Simplex Table
(5)
Level 6 Creating
(ii) Analyse and find the value of x
1
, x
2
? (8)
7. Analyze the following LPP by Simplex Method:
Min Z = -10y
1
-15y
2
-20y
3
Subject to 2y
1
+4y
2
+6y
3
? 24,
3y
1
+9y
2
+6y
3
? 30,
& y
1
, y
2
, y
3
? 0.
Level 1 Remembering
(i)
Develop a Simplex Table (5)
(ii) Solve and find the value of y1 ,y2 and y3
(8)
8.
Solve By Graphical Method
Minimize Z= 40x
1
+24x
2
Subject to, 20x
1
+50 x
2
> 4,800
80 x
1
+50x
2
> 7,200
x
1
,x
2
>0
Level 2 Understanding
9. Solve the following LPP by simplex method:
Minimize Z= 8x
1
-2x
2
Subject to -4x
1
+2x
2
?1,
5x
1
-4x
2
?3,
and x
1
,x
2
? 0
Level 3 Applying
10. Solve the following LPP by simplex method:
Maximize Z= 3x1+2x
2
Subject to
2x
1
+x
2
?2,
3x
1
+4x
2
?12,
x
1
,x
2
? 0
Level 4 Analyzing
11. Review the LPP and solve by simplex method
Max Z= 25x+10y
Subject to the constraints
x+0.5y? 20
x+y? 50
x,y ? 0
Level 1 Remembering
12. A firm produces three products. These products are
processors on 3 different machines. The time required for
manufacturing one unit of cost of the products and the daily
capacity of the three machines is given in the table below.
Analyse and find the optimum solution.
Mac
hine
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Machine
Capacity
Min /Day
Product1 Product 2 Product 3
M1 2 8 2 940
M2 4 - 8 970
M3 2 5 - 430
It is required to determine the daily no. of units to be
manufactured for each product. The profit for unit for
Level 2 Understanding
product 1,2,3 is Rs.4,Rs.8,Rs.6 respectively. It is assumed
that all the amount produced are consumed in the market
13. Using dual simplex method , solve and find the optimum
solution for the given LPP.
Maximize Z=6x
1
+4x
2
+4x
3
Subject to 3x
1
,x
2
+2x
3
? 2
2x
1
+x
2
-x
3
? 1
-x
1
+x
2
+2x
3
? 1 &
x
1
,x
2
,x
3
? 0
Level 4 Analysing
14.
(i)
Evaluate by using dual simplex method and solve the LPP.
Minimize Z=2x
1
+x
2
Subject to 3x
1
+2x
2
? 3
4x
1
+3x
2
? 6
x
1
+x
2
? 5 & x
1
,x
2
?
Determine the dual simplex table
(5)
Level 1 Remembering
(ii)
Find the value of x
1
, x
2
(8)
PART - C
S.No Questions BT
LEVEL
COMPETENCE
1.
Max Z=300x+400y subject to
2x+3y ? 1600,
3x+2y ? 1500,
x+y ? 700,
y ? 300, x,y ? 0 Solve by Graphical Method, choose the
value of x & y which maximizes profit.
Level 1 Remembering
2. Solve the following LPP by graphical method.
Minimize Z= 6000x1+4000x
2
Subject t o
3x+x
2
? 40,
x
1
+2.5 x
2
? 22
3x
1
+3 x
2
? 40
and x
1
,x
2
? 0
Level 2 Understanding
3. Develop a Simplex Table and Solve
Max Z = 3 x1+2 x2,
Subject to
x1+ x2 ?4,
x1- x2 ? 2;
x1, x2 ?0.
Level 3 Applying
4. Solve by using Simplex Method.
Maximize Z= 3x+5y
Subject to the constraints
x+y? 60
x? 40
y ? 30
x,y ? 0
Level 1 Remembering
UNIT - II LINEAR PROGRAMMING EXTENSIONS
SYLLABUS: Transportation Models (Minimizing and Maximizing Problems) ? Balanced and unbalanced
Problems ? Initial Basic feasible solution by N-W Corner Rule, Least cost and Vogel?s approximation methods.
Check for optimality. Solution by MODI /. Case of Degeneracy. Trans-shipment Models. Assignment Models
(Minimising and Maximising Problems) ? Balanced and Unbalanced Problems. Solution by Hungarian and
Branch and Bound Algorithms. Travelling Salesman problem.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define Transportation & Transhipment. Level 1 Remembering
2. Differentiate balanced transportation problem & Unbalanced
Transportation Problem.
Level 2 Understanding
3. How would you show your understanding on unbalanced
transportation problem?
Level 3 Applying
4. Categorize the Phases of transportation model. Level 4 Analysing
5. Construct the basic feasible solution for the following
transportation problem.
1 2 3 4 SUPPLY
1 2 3 11 7 6
2 1 0 6 1 1
3 5 8 15 9 10
DEMAN D 7 5 3 2
Level 5 Evaluating
6 Interpret the need for Optimum solution in transportation. Level 6 Creating
7. What do you mean by Least cost method (LCM)? Level 1 Remembering
8. Compare Vogel approximation method (VAM) & Least Cost
Method.
Level 2 Understanding
9. How do you represent a travelling salesman problem
through mathematical formulation?
Level 3 Applying
10. Analyse the rules of travelling salesman Problem. Level 4 Analysing
11. Discuss the meaning of Assignment Level 5 Evaluating
12. Compare Balanced assignment problem & Unbalanced
Assignment Problem.
Level 6 Creating
13. What example can you give for Unbalanced assignment
problem?
Level 1 Remembering
14. How will you resolve degeneracy in Transportation Problem? Level 2 Understanding
15. Classify transportation problem. Level 3 Applying
16. Examine the Steps in Hungarian algorithm. Level 4 Analysing
17. What is Branch and bound algorithm in Assignment? Level 1 Remembering
18. Compare Assignment and transportation Problem. Level 2 Understanding
19. What do you mean by Travelling Salesman Problem? Level 1 Remembering
20. What is Restricted Assignment? Level 1 Remembering
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Solve and find the Transportation Problem and Which method will
you select if you want toMinimize Cost?
Destination Supply
1 2 3 4
I 21 16 25 13 11
II 17 18 14 23 13
III 32 27 18 41 19
Demand 6 10 12 15
Level 1 Remembering
2. Find the Initial Basic Feasible solution for following TP. Using NW
Rule, LCM, and VAM. Which method will you select if you want to
Minimize Cost?
D1 D2 D3 Supply
S1 7 3 2 2
S2 2 1 3 3
S3 3 4 6 5
Demand 4 1 5 10
Level 2 Understanding
3.
(i)
Analyze the transportation problem with unit transportation
costs,demand, and supply as given below:
Destination
Supply
Source
D1 D2 D3 D4
S1
6 1 9 3
70
11 5 2 8
S2 55
10 12 4 7
S3
70
Demand 85 35 50 45
Apply VAM for Initial solution.
(5)
Level 3 Applying
(ii)
Construct the final Solution by using MODIMethod.
(8)
4.
(i)
Analyze & solve the following transportation problem to maximize
profit.
A B C D Supply
1
Source 2
3
Demand
15 51 42 33 23
80 42 26 81 44
90 40 66 60 33
23
31
16
30
100
Examine Initial solution using VAM.
(5)
Level 4 Analysing
(ii)
Analyze and find out the final Solution by using MODI Method.
(8)
5. Solve the following transportation problem using Vogel?s
method
Factory? Warehouse ?Available
A B C D E F
1 9 12 9 6 9 10 5
2 7 3 7 7 5 5 6
3 6 5 9 11 3 11 2
4 6 8 11 2 2 10 9
4 4 6 2 4 2
Requirement?
(5)
Level 5 Evaluating
6. (i) Solve the transportation problem and decide using VAM for initial
solution.
(5) Level 6 Creating
(ii) Evaluate using NWC and Least Cost method for initial solution?
Destination Supply
I 2 1 25 13 11
II 1 1 14 23 13
III 3 2 18 41 19
Demand 6 1 22 15
(8)
7.
Maximize profit from the following transportationproblem.
A B C D Supply
I 40 25 22 33 100
SourceII 44 35 30 30 30
III 38 38 28 30 70
Demand 40 20 60 30
Level 1 Remembering
(i) How will you convert maximization problem to minimization.
Find the maximum profit
(8)
(ii) Explain stepping stone method for checking the
solution for optimality transportation problems.
(5)
8. A company has one surplus truck in each of the cities A, B, C, D, &
E and one deficit trucks in each of the cities 1,2,3,4,5,6. The
distance between the cities in kms is shown in the matrix below.
Can you select the assignment of trucks from cities in surplus to
cities in deficiency .so that total distance covered by the vehicles is
minimum?
1 2 3 4 5 6
A 12 10 15 22 18 8
B 10 18 25 15 16 12
C 11 10 3 8 5 9
D 6 4 10 13 13 12
E 8 12 11 7 13 10
Level 2 Understanding
9.
Consider the problem of assigning five jobs to five persons. The
assignment costs are given as follows:
PERSONS?JOBS ?
1 2 3 4 5
A 8 4 2 6 1
B 0 9 5 5 4
C 3 8 9 2 6
D 4 3 1 0 3
Level 3 Applying
E 9 5 8 9 5
Determine the optimum assignment schedule.
10. The assignment cost of assigning any one operator to any one
machine is given in the following table.
MACHINE?OPERATORS ?
I II III IV
A 10 5 13 15
B 3 9 18 3
C 10 7 3 2
D 5 11 9 7
Find the optimal assignment by Hungarian method.
Level 4 Analysing
11. A machine shop purchased a drilling machine and two lathes of
different capacities. The Positioning of the machines among 4
possible locations on the shop floor is important forms the
standard of materials handling. Given the cost estimate per unit
time of materials below, find the optimum location of the
machines.
LOCATIONS
1 2 3 4
Lathe 1 12 9 12 9
Drill 15 Not
suitable
13 20
Lathe 2 4 8 10 6
Level 1 Remembering
12.
Solve the assignment problem for maximization given profit
matrix(profit in rupees).
Machines
P Q R S
JOB
51 53 54 50
47 50 48 50
49 50 60 61
63 64 60 60
Level 2 Understanding
PART - C
S.No Questions Marks BT
Level
Competence
1.
a
Assume that you are an OR specialist. Identify the procedure
for each of the following Method to the employees in order to
help them achieve solution to Transportation Problems.
Northwest Corner Cell Method
(3)
Level 1 Remembering
b Least Cost cell Method (4)
c Vogel?s Approximation Method (4)
d U V Method. (4)
13. The processing time in hours for the jobs when allocated to the
different machines is indicated below. Select the best assignment
of the machines for the jobs so that the total processing time is
Minimum.
Machines
M1 M2 M3 M4 M5
J1 9 22 58 11 19
JOB J2 43 78 72 50 63
J3 41 28 91 37 45
J4 74 42 27 49 39
J5 36 11 57 22 25
Level 4 Analysing
14. For the given travelling salesman problem, Minimize the total cost.
To
1 2 3 4
From A - 46 16 40
B 41 - 50 40
C 82 32 - 60
D 40 40 36 -
Level 1 Remembering
(i) Observe the above travelling salesman
problem and find out minimize the cost per
cycle.
(8)
(ii) Find whether path is satisfied. (5)
2.
Solve the following transportation problem, in which a
i
is the
availability at Origin
O
i
and b
j
is the requirement at the destination D
j
and cell entries
are unit costs of transportation from any origin to any
destination:
D1 D2 D3 D4 D5 a
j
O1 4 7 3 8 2 4
O2 1 4 7 3 8 7
O3 7 2 4 7 7 9
O4 4 8 2 4 7 2
b
j
8 3 7 2 2
Predict the allocation to minimize the cost.
Level 2 Understanding
3. A company has a team of 4 Salesman and the company wants to
do in 4 districts. Considering the capabilities of salesmen
and nature of the district, the company has estimated the profit per
day in Rs. For each salesmen in each district as follows.
District
s
Salesmen 1 2 3 4
A 16 10 14 11
B 14 11 15 15
C 15 15 13 12
D 13 12 14 15
Develop the best assignment schedule and analyze the total cost.
Level 3 Applying
4. Five operators have to be assigned to Five Machines. The
assignment costs are given in thetablebelow.
Analyse using Hungarian algorithm & find out the assignment to
minimize the cost.
Machine
I II III IV V
Operator
A 5 5 - 2 6
B 7 4 2 3 4
C 9 3 5 - 3
D 7 2 6 7 2
E 6 5 7 9 1
Level 4 Analyzing
UNIT ? III ? INTEGER PROGRAMMING AND GAME THEORY
SYLLABUS: Integer Programming ? Introduction and types - Game Theory-Two-person Zero sum
games-Saddle point, Dominance Rule, graphical and LP solutions, Nash Equilibrium
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. What do you mean by integer programming problem?
Level 1 Remembering
2. In what respect a mixed IPP differs from pure IPP?
Level 2 Understanding
3. What is Nash Equilibrium?
Level 3 Applying
4. Classify the different types of strategy.
Level 4 Analysing
5. Compile the Characteristics of game.
Level 5 Evaluating
6. Can you assess the applications of integer
programming?
Level 6 Creating
7. Define Game.
Level 1 Remembering
8. Compare Mixed Strategy and Pure Strategy.
Level 2 Understanding
9. How would you make use of the concept of Game theory
in Managerial Decision Making?
Level 3 Applying
10. Conclude your understanding about Payoff Matrix.
Level 4 Analysing
11. How will you find the optimal strategies and value of the
following game?
Player B
Player
A
H T
H 2 -1
T -1 0
Level 5 Evaluating
12. Interpret the concept of two person zero sum game.
Level 6 Creating
13. What is Saddle point?
Level 1 Remembering
14. Compare Dominance Principle of Rows and Columns.
Level 2 Understanding
15. Identify the basic assumptions of the Game.
Level 3 Applying
16. Conclude the advantages of Game theory.
Level 4 Analysing
17. What are the Methods of Matrices?
Level 1 Remembering
18. Summarize how graphs and LP solution are used in
Game theory.
Level 2 Understanding
19. What is a Decision Tree?
Level 1 Remembering
20. Define Dominance principle.
Level 1 Remembering
S.N
O
PART - B QUESTIONS MA
RK
S
BT
LEVEL
COMPETENCE
1. (i) What do you mean by Pure IPP? (3) Level 1 Remembering
(ii) What do you mean by Mixed IPP? (5)
(iii)
List out the difference between Pure and Mixed IPP.
(5)
2. (i) For what value of ?,the game with the following
matrix is strictly determined
B
1
B
2
B
3
A
1
? 6 2
A
2
-1 ? -7
A
3
-2 4 ?
(8) Level 2 Understanding
(ii) Write down the assumptions of game theory. (5)
3. (i) Solve the game whose pay-off matrix is given by
B
1
B
2
B
3
A
1
1 3 1
A
2
0 -4 -3
A
3
1 5 -1
(8)
Level 3 Applying
(ii) Explain the concept of Nash Equilibrium. (5)
4.
Analyze the Value of the game graphically
B1 B2
A1 4 4
A2 2 7
A3 5 3
A4 6 2
Level 4 Analysing
5.
What inference can be made using Dominance
Principle to reduce the following game and estimate
the game value?
B1 B2 B3 B4
A1 3 2 4 0
A2 3 4 2 4
A3 4 2 2 0
A4 2 1 6 3
Level 5 Evaluating
6.
How would you evaluate the following game whose
Pay-Off matrix is Given Below?
9 3 1 8 0
6 5 4 6 7
2 4 3 3 8
5 6 2 2 1
Level 6 Creating
7.
(i)
Two players A&B match coins. If the coins match
then A wins one unit value, if the coins do not
match then B wins one unit of value.
Determine pay-off matrix which strategy is to be
chosen
(5)
Level 1 Remembering
(ii)
Find the value of game. (8)
8.
Predict the Value of the Game given above Pay
OffMatrix.
Player B
B1 B2 B3
A1 -2 5 -3
Player A A2 1 3 5
A3 -3 -7 11
Level 2 Understanding
9.
Apply graphical analysis to Solve the game.
A/
B
B1 B2 B3 B4
A1 3 3 4 0
A2 5 4 3 7
Level 3 Applying
10. Solve the following game by graphical method.
Player B
1 2 3
1 6 4 3
Player A 2 2 4 8
Level 4 Analysing
11.
(i)
A and B play a Match(Game) in which each has 3
coins 5 paise, 10 paise and 20 paise. Each player
selects a coin without the knowledge of others
choice. IF the sum is even, B wins A?s Coin. If sum
is Odd, A wins B?s coin.
How will you find the pay-off matrix ?
(5)
Level 1
Remembering
(ii)
Find the Best Strategy & value of the Game. (8)
12.
Consider the Pay Off Matrix of player A as shown in
the table below and solve it optimally using the
graphical method .
Player A
Player
B
1 2 3 4 5
1 3 6 8 4 4
2 -7 4 2 10 2
Level 2 Understanding
13.
(i)
Analyze the Game Graphically:
Player A
Player
A
B1 B2
A1 -3 1
A2 5 3
A3 6 -1
A4 1 4
A5 2 2
A6 0 -5
Plot the graph
(5)
Level 4 Analysing
(ii)
Analyse and find the value of the game.
(8)
14.
Which one is the best strategy using Dominance
Principle?
B1 B2 B3 B4 B5 B6
A1
4 2 0 2 1 1
A2
4 3 1 3 2 2
A3
4 3 7 -5 1 2
A4
4 3 4 -1 2 2
A5
4 3 3 -2 2 2
Level 1 Remembering
PART-C
S.No Questions BT
Level
Competence
1.
Using Dominance property Solve.
B
A
I II IIIIV
1 -5 3 1 20
2 5 5 4 6
3 -4 -2 0 -5
Level 1 Remembering
2. Examine the 2 * n Game by the Method of Sub Game:
B1 B2 B3
A1 1 3 11
A2 8 5 2
Level 2 Understanding
3. In a game of matching coins with 2 players, A wins 1 unit value
when there are 2 heads, wins nothing when there are 2 tails
and looses ? unit value when there are one head and one tail.
Develop Pay Off matrix and value of the game.
Level 3 Applying
4.
i
ii
iii
Assume you have to choice of 3 strategies for advertising
and you have one major
Analyse the theory on Two-person sum games competitor
with 3 strategies.
(5)
Level 4 Analysing
What are the assumptions of Game? (5)
Find value of game.
B1 B2 B3
A1 80 70 60
A2 90 80 100
A3 40 30 40
(5)
UNIT - IV INVENTORY MODELS, SIMULATION AND DECISION THEORY
SYLLABUS: Inventory Models ? EOQ and EBQ Models (With and without shortages), Quantity Discount
Models. Decision making under risk ? Decision trees ? Decision making under uncertainty. Monte-carlo
simulation.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define inventory. Level 1 Remembering
2.
Classify the Forms of inventory.
Level 2 Understanding
3.
Identify the Objectives/significance of inventory model.
Level 3 Applying
4.
Highlight the importance of Reorder level.
Level 4 Analysing
5.
Discuss the concept of Lead time.
Level 5 Evaluate
6.
Interpret the Types of stock replenishment.
Level 1 Remembering
7.
List the Basic inventory models.
Level 2 Understanding
8.
Compare Ordering Cost and Carrying Cost.
Level 3 Appyling
9.
Identify when shortage cost and stock out cost arises?
Level 5 Evaluating
10.
Analyze why safety stock is maintained.
Level 1 Remembering
11.
Discuss the concept of Quantity Discount Model.
Level 2 Understanding
12.
Interpret the meaning of EOQ & EBQ.
Level 3 Applying
13.
What are random and pseudo random numbers?
Level 4 Analysing
14.
Explain Monte Carlo Method.
Level 5 Evaluating
15.
Summarize the concept of EMV.
Level 1 Remembering
16.
What inference can you make about holding cost ?
Level 2 Understanding
17.
What is Shortage Cost?
Level 3 Applying
18. Classify and explain the various conditions under which
decisions are made.
Level 1 Remembering
19. What is meant by the following terms in inventory
management: i)Carrying cost ii) shortage costs
Level 2 Understanding
20. What is Decision theory? List the problems that can be solved
by Simulation.
Level 3 Applying
S.NO PART - B QUESTIONS Marks BT
LEVEL
COMPETENCE
1.
(i)
Alpha industry needs 5400 units per year of a bought out
component which will be
used in its main product. The ordering cost is Rs.250
per order and the carrying cost per unit per year is
Rs.30.
Which is the best order quantity?
(8)
Level 1 Remembering
(ii)
Find the number of order per year and Frequency of
orders?
(5)
2.
(i)
A stockiest has to supply 12000 units of a product per
year to his customer. Demand is
fixed and known. Shortage cost is assumed to be
infinite. Inventory holding cost is 20 paise per unit per
month. Ordering Cost is Rs. 250 and purchase price
is Rs.10 per unit.
Estimate the EOQ
(8)
Level 2 Understanding
(ii)
Find the Frequency of orders and total inventory cost. (5)
3.
ABC manufacturing company purchases 9000 parts of a
machine for its annual requirement. Each part costs
Rs.20. The ordering cost per order is Rs.15 and the
carrying charges are 15% of the average inventory per
year. Apply EOQ formulae and find out EOQ, No of
orders ,Total Inventory Cost and total cost.
Level 3 Applying
4.
(i)
Demand for an item in a company is 18,000 units per
year. The company can produce the items at a rate of
3000 units per month. The Cost of one setup is Rs.500
and the holding cost of one unit per month is 15 paise.
Shortage cost of one unit is Rs.20 per year.
Analyze and find the optimum manufacturing quantity.
(8)
Level 4 Analysing
(ii)
Find the number of shortages and frequency of
Production run.
(5)
5. A company has a demand of 12000 units/year for an
item and it can produce 2000 units per month. The
cost of one setup is Rs.400 and the holding
cost/unit/month is 15 paise. Select the optimum lot
size and total cost per year assuming the cost of 1 unit
as Rs.4. Find EBQ, the number of set ups & total cost.
Level 5 Evaluating
6.
(i)
Find the optimal order quantity for a product when the
annual demand for the product is 500 units. The Cost of
storage per unit per year is 10% of the unit cost. Ordering
cost per order is Rs. 180.
Determine EOQ
(8)
Level 6 Creating
(ii)
Evaluate the Total Cost
(5)
The unit cost are given below:
Quantity Unit Cost(Rs.)
O
1500<=Q3<3000 24.60
3000<=Q4 24.40
7. (i)
Formulate the Optimal order quantity for a product for
which the price breaks are as follows
(8)
Level 1 Remembering
(ii)
Also find the Total cost.
Quantity Unit Cost(Rs.)
O
750<=Q 875
(5)
8.
Compute the EOQ and the total variable cost for the
following:
Annual demand: 25 units
Unit price: Rs.2.50
Order cost: Rs.4.00
Storage rate: 1% per year
Level 2 Understand
9.
(i)
Identify the profit under three states of nature & three
decision alternative.
State of
Nature
State of
Nature
State of
Nature
N1 N2 N3
Decision
Naking
D1 150 250 300
Decision
Naking
D2 450 250 200
Decision
Naking
D3 100 180 290
Hurwitz criterion for alpha=0.5
(3)
Level 3 Applying
(ii)
Laplace condition
(5)
(iii)
Minimax Condition
(5)
10.
A Bakery keeps a stock of particular brand of cake. Daily
demand of past experience.
Daily
demand
0 15 25 35 45 50
Probability 0.01 0.15 0.20 0.50 0.12 0.02
Consider the following sequence of random numbers.
48 78 9 51 56 77 15 14 68 9
Using this sequence simulate the demand for next 10
days.
Find the stock situation if the owner makes 35 cakes
every day. Examine the daily average demand.
Level 1 Remembering
11.
Given above is the following pay off matrix.
Using EMV criterion . Decide which of the act can be
chosen at the best. FindEVPI & EOL.
Nature
Probability
Don?t
Expand
Expand
200
Expand
400
High
Demand
0.4 2500 3500 5000
Medium
Demand
0.4 2500 3500 2500
Low
Demand
0.2 2500 1500 1000
Level 2 Understanding
12.
A sample of 100 arrivals of customers at a retail sales
depot is according to the following distribution.
Time between arrivals(mins) Frequency
0.5 2
1.0 6
1.5 10
2.0 25
2.5 20
3.0 14
3.5 4
4.0 7
4.5 4
5.0 2
Use random numbers and predict the average time
between arrivals.
48 78 9 51 56 77 15 14 68 9
Level 3 Applying
13.
(i)
A departmental store purchases sprays which can be
ordered only in lots of 10. Each spray cost Rs.75 and
sells at Rs.90 each. Used sprays, however have \no
salvage value.
Demand 10 20 30 40 50
Probability 0.2 0.35 0.25 0.15 0.05
The probability distribution obtained from analysis of past
sales data is given below.
Analyse the payoff table.
(5)
Level 4 Analysing
(ii) How much quantity should the departmental store buy to
maximize its profit?
(8)
14. (i)
A company uses annually 50,000 units of an item each
costing Rs.1.20. Each order costs Rs.45 and inventory
carrying costs are 15% of the annual average inventory
value.
Find EOQ.
(3)
Level 2 Understanding
(ii) If the company operates 250 days a year and the
procurement time is 10 days and safety stock is 500
units, find reorder level, maximum, minimum and
average inventory
(10)
PART - C
S.No Questions BT
Level
Competence
1.
A contractor has to supply 10000 bearings per day to an
automobile manufacturer. He finds that when he starts a
production run he can produce 25000 bearings per day. The
cost of holding a bearing in stock for one year is 2 paise and
the set up cost of the production run is Rs.18. How frequently
should production run be made and which is the Best
Economic Batch Quantity? How much would be the No. of
Setup and Total Inventory Cost.
Level 1 Remembering
2.
A stockist has to supply 400 units of a product every
Monday to his customer.
He gets the product at Rs.50 per unit from the
manufacturer. The cost of ordering and transportation
from the manufacturer is Rs.75 per order. The cost of
carrying inventory is 7.5% per year of the cost of product.
Predict EOQ, Frequency of orders and Number of Orders,
Total Incremental cost and Total Cost.
Level 2 Understanding
3. (i) Identify the profit under three states of nature & three
decision alternative.
State of
Nature
N1 N2 N3
Decision
Making
D1 100 200 300
D2 400 200 200
D3 200 160 390
Hurwitz criterion for alpha=0.5
(5) Level 3 Applying
(ii)
Laplace Condition
(5)
(iii) Mininmax Condition (5)
4.
An automobile production line turns out about 100 cars a
day, but deviation occur owing to many causes. The
production is more accurately described by the
probability distribution given below;
Production/
Day
Probability
95 0.03
96 0.05
97 0.07
98 0.10
Level 4 Analysing
FirstRanker.com - FirstRanker's Choice
(An
?
DEPARTMENT OF MANAGEMENT STUDIES
QUESTION BANK
II SEMESTER
1915201? APPLIED OPERATIONS RESEACH
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Dr. Radha Ganesh Kumar ? Asst. Professor (Sel.G) and HOD
Mr.B. Sam Paul ? Asst. Professor (OG)
(An
? .
DEPARTMENT OFMANAGEMENT STUDIES
QUESTION BANK
SUBJECT :1915201 ?APPLIED OPERATIONS RESEACH
SEM / YEAR : IISemester / IYear
UNIT ? I ?INTRODUCTION TO LINEAR PROGRAMMING (LP)
SYLLABUS: Introduction to applications of operations research in functional areas of management.
Linear Programming-formulation, solution by graphical and simplex methods, Special cases. Dual
simplex method. Principles of Duality. Sensitivity Analysis.
PART- A
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Define Operations Research (OR). Level 1 Remembering
2. Differentiate between Simplex and Big M Method Level 2 Understanding
3. How do you show your understanding unbounded solution? Level 3 Applying
4. Categorize the forms of LPP. Level 4 Analysing
5.
Discuss why is two phase method is better than Big M
method?
Level 5 Evaluating
6. Interpret the usage of Sensitivity Analysis in LPP. Level 6 Creating
7. What are the assumptions and requirements of LPP? Level 1 Remembering
8. Compare Dual Simplex and Duality. Level 2 Understanding
9. Identify the Advantages of duality. Level 3 Applying
10. What do you think about Infeasible solution? Level 4 Analysing
11. How will you solve LPP graphically? Level 5 Evaluating
12.
Conclude your understanding on the mathematical
formulation of LPP.
Level 6 Creating
13. Define basic variables and artificial variables. Level 1 Remembering
14. Compare Slack variable & Surplus Variable. Level 2 Understanding
15.
Give some example for the role of Surplus variable & Slack
Variable in the simplex method
Level 3 Applying
16. How would you apply Artificial variable? Level 4 Analysing
17. What is Big M Method? Level 1 Remembering
18. Distinguish simplex and Big M method Level 2 Understanding
19.
What do you mean by Duality? List the Rules for primal and
dual.
Level 1 Remembering
20. What is Shadow price? Level 1 Remembering
PART- B
S.NO
QUESTIONS
BT
LEVEL
COMPETENCE
1.
(i)
Maximise Z=3x+4y subject to
2x+5y ?60,
4x+2y ?40.
x, y >0. Solve by Graphical Method
Plot the graph
(8)
Level 1 Remembering
(ii) Which one is the best solution? (5)
2.
(i)
Min Z= 20x
1
+10 x
2
subject to
x
1
+2x
2
? 40,
3x
1
+x
2
? 30,
4x
1
+3x
2
? 60,
x
1
,x
2
? 0.
Solve by Graphical Method,
Plot the graph
(8)
Level 2 Understanding
(ii) Predict the value of x & y. (5)
3 Max Z= 5x1+4x2 subject to
x
1
-2x
2
? 1,
x
1
+2x
2
?3,
x
1
,x
2
? 0. Solve Graphically. Which one is the best
solution?
Level 3 Applying
4.
(i)
A Plant Manufacturer 2 Product A & B. The Profit Contribution
of each product has been estimated as Rs.300 for product A
and Rs.400 for Product B. Each Product passes through 3
departments of the plant. The time required for each product
and total time available in each department is as follows.
Department Hours
Required
Hours
Required
Available
Hours
during
month
Product
A
Product
B
I 2 3 1600
II 3 2 1500
III 1 1 700
The company has a contract to supply atleast 300 units of
Product B per month.
Formulate the LPP
(5)
Level 4
Analysing
(ii) Solve through Graphical Method
(8)
5. Solve the following LPP by graphical method.
Maximize Z= 3x
1
+2x
2
Subject t o
- 2x
1
+x
2
?1,
x
1
? 2,
x
1
+ x
2
? 3
and x
1
,x
2
? 0
Level 5 Evaluating
6. (i) Max Z= 1000x
1
+4000x
2
+5000x
3
Subject to 3x1+3x
3
?22,
x1+2x2+3x
3
? 14,
3x1+2x2 ? 14
& x1,x2 ? 0
Develop a Simplex Table
(5)
Level 6 Creating
(ii) Analyse and find the value of x
1
, x
2
? (8)
7. Analyze the following LPP by Simplex Method:
Min Z = -10y
1
-15y
2
-20y
3
Subject to 2y
1
+4y
2
+6y
3
? 24,
3y
1
+9y
2
+6y
3
? 30,
& y
1
, y
2
, y
3
? 0.
Level 1 Remembering
(i)
Develop a Simplex Table (5)
(ii) Solve and find the value of y1 ,y2 and y3
(8)
8.
Solve By Graphical Method
Minimize Z= 40x
1
+24x
2
Subject to, 20x
1
+50 x
2
> 4,800
80 x
1
+50x
2
> 7,200
x
1
,x
2
>0
Level 2 Understanding
9. Solve the following LPP by simplex method:
Minimize Z= 8x
1
-2x
2
Subject to -4x
1
+2x
2
?1,
5x
1
-4x
2
?3,
and x
1
,x
2
? 0
Level 3 Applying
10. Solve the following LPP by simplex method:
Maximize Z= 3x1+2x
2
Subject to
2x
1
+x
2
?2,
3x
1
+4x
2
?12,
x
1
,x
2
? 0
Level 4 Analyzing
11. Review the LPP and solve by simplex method
Max Z= 25x+10y
Subject to the constraints
x+0.5y? 20
x+y? 50
x,y ? 0
Level 1 Remembering
12. A firm produces three products. These products are
processors on 3 different machines. The time required for
manufacturing one unit of cost of the products and the daily
capacity of the three machines is given in the table below.
Analyse and find the optimum solution.
Mac
hine
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Machine
Capacity
Min /Day
Product1 Product 2 Product 3
M1 2 8 2 940
M2 4 - 8 970
M3 2 5 - 430
It is required to determine the daily no. of units to be
manufactured for each product. The profit for unit for
Level 2 Understanding
product 1,2,3 is Rs.4,Rs.8,Rs.6 respectively. It is assumed
that all the amount produced are consumed in the market
13. Using dual simplex method , solve and find the optimum
solution for the given LPP.
Maximize Z=6x
1
+4x
2
+4x
3
Subject to 3x
1
,x
2
+2x
3
? 2
2x
1
+x
2
-x
3
? 1
-x
1
+x
2
+2x
3
? 1 &
x
1
,x
2
,x
3
? 0
Level 4 Analysing
14.
(i)
Evaluate by using dual simplex method and solve the LPP.
Minimize Z=2x
1
+x
2
Subject to 3x
1
+2x
2
? 3
4x
1
+3x
2
? 6
x
1
+x
2
? 5 & x
1
,x
2
?
Determine the dual simplex table
(5)
Level 1 Remembering
(ii)
Find the value of x
1
, x
2
(8)
PART - C
S.No Questions BT
LEVEL
COMPETENCE
1.
Max Z=300x+400y subject to
2x+3y ? 1600,
3x+2y ? 1500,
x+y ? 700,
y ? 300, x,y ? 0 Solve by Graphical Method, choose the
value of x & y which maximizes profit.
Level 1 Remembering
2. Solve the following LPP by graphical method.
Minimize Z= 6000x1+4000x
2
Subject t o
3x+x
2
? 40,
x
1
+2.5 x
2
? 22
3x
1
+3 x
2
? 40
and x
1
,x
2
? 0
Level 2 Understanding
3. Develop a Simplex Table and Solve
Max Z = 3 x1+2 x2,
Subject to
x1+ x2 ?4,
x1- x2 ? 2;
x1, x2 ?0.
Level 3 Applying
4. Solve by using Simplex Method.
Maximize Z= 3x+5y
Subject to the constraints
x+y? 60
x? 40
y ? 30
x,y ? 0
Level 1 Remembering
UNIT - II LINEAR PROGRAMMING EXTENSIONS
SYLLABUS: Transportation Models (Minimizing and Maximizing Problems) ? Balanced and unbalanced
Problems ? Initial Basic feasible solution by N-W Corner Rule, Least cost and Vogel?s approximation methods.
Check for optimality. Solution by MODI /. Case of Degeneracy. Trans-shipment Models. Assignment Models
(Minimising and Maximising Problems) ? Balanced and Unbalanced Problems. Solution by Hungarian and
Branch and Bound Algorithms. Travelling Salesman problem.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define Transportation & Transhipment. Level 1 Remembering
2. Differentiate balanced transportation problem & Unbalanced
Transportation Problem.
Level 2 Understanding
3. How would you show your understanding on unbalanced
transportation problem?
Level 3 Applying
4. Categorize the Phases of transportation model. Level 4 Analysing
5. Construct the basic feasible solution for the following
transportation problem.
1 2 3 4 SUPPLY
1 2 3 11 7 6
2 1 0 6 1 1
3 5 8 15 9 10
DEMAN D 7 5 3 2
Level 5 Evaluating
6 Interpret the need for Optimum solution in transportation. Level 6 Creating
7. What do you mean by Least cost method (LCM)? Level 1 Remembering
8. Compare Vogel approximation method (VAM) & Least Cost
Method.
Level 2 Understanding
9. How do you represent a travelling salesman problem
through mathematical formulation?
Level 3 Applying
10. Analyse the rules of travelling salesman Problem. Level 4 Analysing
11. Discuss the meaning of Assignment Level 5 Evaluating
12. Compare Balanced assignment problem & Unbalanced
Assignment Problem.
Level 6 Creating
13. What example can you give for Unbalanced assignment
problem?
Level 1 Remembering
14. How will you resolve degeneracy in Transportation Problem? Level 2 Understanding
15. Classify transportation problem. Level 3 Applying
16. Examine the Steps in Hungarian algorithm. Level 4 Analysing
17. What is Branch and bound algorithm in Assignment? Level 1 Remembering
18. Compare Assignment and transportation Problem. Level 2 Understanding
19. What do you mean by Travelling Salesman Problem? Level 1 Remembering
20. What is Restricted Assignment? Level 1 Remembering
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Solve and find the Transportation Problem and Which method will
you select if you want toMinimize Cost?
Destination Supply
1 2 3 4
I 21 16 25 13 11
II 17 18 14 23 13
III 32 27 18 41 19
Demand 6 10 12 15
Level 1 Remembering
2. Find the Initial Basic Feasible solution for following TP. Using NW
Rule, LCM, and VAM. Which method will you select if you want to
Minimize Cost?
D1 D2 D3 Supply
S1 7 3 2 2
S2 2 1 3 3
S3 3 4 6 5
Demand 4 1 5 10
Level 2 Understanding
3.
(i)
Analyze the transportation problem with unit transportation
costs,demand, and supply as given below:
Destination
Supply
Source
D1 D2 D3 D4
S1
6 1 9 3
70
11 5 2 8
S2 55
10 12 4 7
S3
70
Demand 85 35 50 45
Apply VAM for Initial solution.
(5)
Level 3 Applying
(ii)
Construct the final Solution by using MODIMethod.
(8)
4.
(i)
Analyze & solve the following transportation problem to maximize
profit.
A B C D Supply
1
Source 2
3
Demand
15 51 42 33 23
80 42 26 81 44
90 40 66 60 33
23
31
16
30
100
Examine Initial solution using VAM.
(5)
Level 4 Analysing
(ii)
Analyze and find out the final Solution by using MODI Method.
(8)
5. Solve the following transportation problem using Vogel?s
method
Factory? Warehouse ?Available
A B C D E F
1 9 12 9 6 9 10 5
2 7 3 7 7 5 5 6
3 6 5 9 11 3 11 2
4 6 8 11 2 2 10 9
4 4 6 2 4 2
Requirement?
(5)
Level 5 Evaluating
6. (i) Solve the transportation problem and decide using VAM for initial
solution.
(5) Level 6 Creating
(ii) Evaluate using NWC and Least Cost method for initial solution?
Destination Supply
I 2 1 25 13 11
II 1 1 14 23 13
III 3 2 18 41 19
Demand 6 1 22 15
(8)
7.
Maximize profit from the following transportationproblem.
A B C D Supply
I 40 25 22 33 100
SourceII 44 35 30 30 30
III 38 38 28 30 70
Demand 40 20 60 30
Level 1 Remembering
(i) How will you convert maximization problem to minimization.
Find the maximum profit
(8)
(ii) Explain stepping stone method for checking the
solution for optimality transportation problems.
(5)
8. A company has one surplus truck in each of the cities A, B, C, D, &
E and one deficit trucks in each of the cities 1,2,3,4,5,6. The
distance between the cities in kms is shown in the matrix below.
Can you select the assignment of trucks from cities in surplus to
cities in deficiency .so that total distance covered by the vehicles is
minimum?
1 2 3 4 5 6
A 12 10 15 22 18 8
B 10 18 25 15 16 12
C 11 10 3 8 5 9
D 6 4 10 13 13 12
E 8 12 11 7 13 10
Level 2 Understanding
9.
Consider the problem of assigning five jobs to five persons. The
assignment costs are given as follows:
PERSONS?JOBS ?
1 2 3 4 5
A 8 4 2 6 1
B 0 9 5 5 4
C 3 8 9 2 6
D 4 3 1 0 3
Level 3 Applying
E 9 5 8 9 5
Determine the optimum assignment schedule.
10. The assignment cost of assigning any one operator to any one
machine is given in the following table.
MACHINE?OPERATORS ?
I II III IV
A 10 5 13 15
B 3 9 18 3
C 10 7 3 2
D 5 11 9 7
Find the optimal assignment by Hungarian method.
Level 4 Analysing
11. A machine shop purchased a drilling machine and two lathes of
different capacities. The Positioning of the machines among 4
possible locations on the shop floor is important forms the
standard of materials handling. Given the cost estimate per unit
time of materials below, find the optimum location of the
machines.
LOCATIONS
1 2 3 4
Lathe 1 12 9 12 9
Drill 15 Not
suitable
13 20
Lathe 2 4 8 10 6
Level 1 Remembering
12.
Solve the assignment problem for maximization given profit
matrix(profit in rupees).
Machines
P Q R S
JOB
51 53 54 50
47 50 48 50
49 50 60 61
63 64 60 60
Level 2 Understanding
PART - C
S.No Questions Marks BT
Level
Competence
1.
a
Assume that you are an OR specialist. Identify the procedure
for each of the following Method to the employees in order to
help them achieve solution to Transportation Problems.
Northwest Corner Cell Method
(3)
Level 1 Remembering
b Least Cost cell Method (4)
c Vogel?s Approximation Method (4)
d U V Method. (4)
13. The processing time in hours for the jobs when allocated to the
different machines is indicated below. Select the best assignment
of the machines for the jobs so that the total processing time is
Minimum.
Machines
M1 M2 M3 M4 M5
J1 9 22 58 11 19
JOB J2 43 78 72 50 63
J3 41 28 91 37 45
J4 74 42 27 49 39
J5 36 11 57 22 25
Level 4 Analysing
14. For the given travelling salesman problem, Minimize the total cost.
To
1 2 3 4
From A - 46 16 40
B 41 - 50 40
C 82 32 - 60
D 40 40 36 -
Level 1 Remembering
(i) Observe the above travelling salesman
problem and find out minimize the cost per
cycle.
(8)
(ii) Find whether path is satisfied. (5)
2.
Solve the following transportation problem, in which a
i
is the
availability at Origin
O
i
and b
j
is the requirement at the destination D
j
and cell entries
are unit costs of transportation from any origin to any
destination:
D1 D2 D3 D4 D5 a
j
O1 4 7 3 8 2 4
O2 1 4 7 3 8 7
O3 7 2 4 7 7 9
O4 4 8 2 4 7 2
b
j
8 3 7 2 2
Predict the allocation to minimize the cost.
Level 2 Understanding
3. A company has a team of 4 Salesman and the company wants to
do in 4 districts. Considering the capabilities of salesmen
and nature of the district, the company has estimated the profit per
day in Rs. For each salesmen in each district as follows.
District
s
Salesmen 1 2 3 4
A 16 10 14 11
B 14 11 15 15
C 15 15 13 12
D 13 12 14 15
Develop the best assignment schedule and analyze the total cost.
Level 3 Applying
4. Five operators have to be assigned to Five Machines. The
assignment costs are given in thetablebelow.
Analyse using Hungarian algorithm & find out the assignment to
minimize the cost.
Machine
I II III IV V
Operator
A 5 5 - 2 6
B 7 4 2 3 4
C 9 3 5 - 3
D 7 2 6 7 2
E 6 5 7 9 1
Level 4 Analyzing
UNIT ? III ? INTEGER PROGRAMMING AND GAME THEORY
SYLLABUS: Integer Programming ? Introduction and types - Game Theory-Two-person Zero sum
games-Saddle point, Dominance Rule, graphical and LP solutions, Nash Equilibrium
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. What do you mean by integer programming problem?
Level 1 Remembering
2. In what respect a mixed IPP differs from pure IPP?
Level 2 Understanding
3. What is Nash Equilibrium?
Level 3 Applying
4. Classify the different types of strategy.
Level 4 Analysing
5. Compile the Characteristics of game.
Level 5 Evaluating
6. Can you assess the applications of integer
programming?
Level 6 Creating
7. Define Game.
Level 1 Remembering
8. Compare Mixed Strategy and Pure Strategy.
Level 2 Understanding
9. How would you make use of the concept of Game theory
in Managerial Decision Making?
Level 3 Applying
10. Conclude your understanding about Payoff Matrix.
Level 4 Analysing
11. How will you find the optimal strategies and value of the
following game?
Player B
Player
A
H T
H 2 -1
T -1 0
Level 5 Evaluating
12. Interpret the concept of two person zero sum game.
Level 6 Creating
13. What is Saddle point?
Level 1 Remembering
14. Compare Dominance Principle of Rows and Columns.
Level 2 Understanding
15. Identify the basic assumptions of the Game.
Level 3 Applying
16. Conclude the advantages of Game theory.
Level 4 Analysing
17. What are the Methods of Matrices?
Level 1 Remembering
18. Summarize how graphs and LP solution are used in
Game theory.
Level 2 Understanding
19. What is a Decision Tree?
Level 1 Remembering
20. Define Dominance principle.
Level 1 Remembering
S.N
O
PART - B QUESTIONS MA
RK
S
BT
LEVEL
COMPETENCE
1. (i) What do you mean by Pure IPP? (3) Level 1 Remembering
(ii) What do you mean by Mixed IPP? (5)
(iii)
List out the difference between Pure and Mixed IPP.
(5)
2. (i) For what value of ?,the game with the following
matrix is strictly determined
B
1
B
2
B
3
A
1
? 6 2
A
2
-1 ? -7
A
3
-2 4 ?
(8) Level 2 Understanding
(ii) Write down the assumptions of game theory. (5)
3. (i) Solve the game whose pay-off matrix is given by
B
1
B
2
B
3
A
1
1 3 1
A
2
0 -4 -3
A
3
1 5 -1
(8)
Level 3 Applying
(ii) Explain the concept of Nash Equilibrium. (5)
4.
Analyze the Value of the game graphically
B1 B2
A1 4 4
A2 2 7
A3 5 3
A4 6 2
Level 4 Analysing
5.
What inference can be made using Dominance
Principle to reduce the following game and estimate
the game value?
B1 B2 B3 B4
A1 3 2 4 0
A2 3 4 2 4
A3 4 2 2 0
A4 2 1 6 3
Level 5 Evaluating
6.
How would you evaluate the following game whose
Pay-Off matrix is Given Below?
9 3 1 8 0
6 5 4 6 7
2 4 3 3 8
5 6 2 2 1
Level 6 Creating
7.
(i)
Two players A&B match coins. If the coins match
then A wins one unit value, if the coins do not
match then B wins one unit of value.
Determine pay-off matrix which strategy is to be
chosen
(5)
Level 1 Remembering
(ii)
Find the value of game. (8)
8.
Predict the Value of the Game given above Pay
OffMatrix.
Player B
B1 B2 B3
A1 -2 5 -3
Player A A2 1 3 5
A3 -3 -7 11
Level 2 Understanding
9.
Apply graphical analysis to Solve the game.
A/
B
B1 B2 B3 B4
A1 3 3 4 0
A2 5 4 3 7
Level 3 Applying
10. Solve the following game by graphical method.
Player B
1 2 3
1 6 4 3
Player A 2 2 4 8
Level 4 Analysing
11.
(i)
A and B play a Match(Game) in which each has 3
coins 5 paise, 10 paise and 20 paise. Each player
selects a coin without the knowledge of others
choice. IF the sum is even, B wins A?s Coin. If sum
is Odd, A wins B?s coin.
How will you find the pay-off matrix ?
(5)
Level 1
Remembering
(ii)
Find the Best Strategy & value of the Game. (8)
12.
Consider the Pay Off Matrix of player A as shown in
the table below and solve it optimally using the
graphical method .
Player A
Player
B
1 2 3 4 5
1 3 6 8 4 4
2 -7 4 2 10 2
Level 2 Understanding
13.
(i)
Analyze the Game Graphically:
Player A
Player
A
B1 B2
A1 -3 1
A2 5 3
A3 6 -1
A4 1 4
A5 2 2
A6 0 -5
Plot the graph
(5)
Level 4 Analysing
(ii)
Analyse and find the value of the game.
(8)
14.
Which one is the best strategy using Dominance
Principle?
B1 B2 B3 B4 B5 B6
A1
4 2 0 2 1 1
A2
4 3 1 3 2 2
A3
4 3 7 -5 1 2
A4
4 3 4 -1 2 2
A5
4 3 3 -2 2 2
Level 1 Remembering
PART-C
S.No Questions BT
Level
Competence
1.
Using Dominance property Solve.
B
A
I II IIIIV
1 -5 3 1 20
2 5 5 4 6
3 -4 -2 0 -5
Level 1 Remembering
2. Examine the 2 * n Game by the Method of Sub Game:
B1 B2 B3
A1 1 3 11
A2 8 5 2
Level 2 Understanding
3. In a game of matching coins with 2 players, A wins 1 unit value
when there are 2 heads, wins nothing when there are 2 tails
and looses ? unit value when there are one head and one tail.
Develop Pay Off matrix and value of the game.
Level 3 Applying
4.
i
ii
iii
Assume you have to choice of 3 strategies for advertising
and you have one major
Analyse the theory on Two-person sum games competitor
with 3 strategies.
(5)
Level 4 Analysing
What are the assumptions of Game? (5)
Find value of game.
B1 B2 B3
A1 80 70 60
A2 90 80 100
A3 40 30 40
(5)
UNIT - IV INVENTORY MODELS, SIMULATION AND DECISION THEORY
SYLLABUS: Inventory Models ? EOQ and EBQ Models (With and without shortages), Quantity Discount
Models. Decision making under risk ? Decision trees ? Decision making under uncertainty. Monte-carlo
simulation.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define inventory. Level 1 Remembering
2.
Classify the Forms of inventory.
Level 2 Understanding
3.
Identify the Objectives/significance of inventory model.
Level 3 Applying
4.
Highlight the importance of Reorder level.
Level 4 Analysing
5.
Discuss the concept of Lead time.
Level 5 Evaluate
6.
Interpret the Types of stock replenishment.
Level 1 Remembering
7.
List the Basic inventory models.
Level 2 Understanding
8.
Compare Ordering Cost and Carrying Cost.
Level 3 Appyling
9.
Identify when shortage cost and stock out cost arises?
Level 5 Evaluating
10.
Analyze why safety stock is maintained.
Level 1 Remembering
11.
Discuss the concept of Quantity Discount Model.
Level 2 Understanding
12.
Interpret the meaning of EOQ & EBQ.
Level 3 Applying
13.
What are random and pseudo random numbers?
Level 4 Analysing
14.
Explain Monte Carlo Method.
Level 5 Evaluating
15.
Summarize the concept of EMV.
Level 1 Remembering
16.
What inference can you make about holding cost ?
Level 2 Understanding
17.
What is Shortage Cost?
Level 3 Applying
18. Classify and explain the various conditions under which
decisions are made.
Level 1 Remembering
19. What is meant by the following terms in inventory
management: i)Carrying cost ii) shortage costs
Level 2 Understanding
20. What is Decision theory? List the problems that can be solved
by Simulation.
Level 3 Applying
S.NO PART - B QUESTIONS Marks BT
LEVEL
COMPETENCE
1.
(i)
Alpha industry needs 5400 units per year of a bought out
component which will be
used in its main product. The ordering cost is Rs.250
per order and the carrying cost per unit per year is
Rs.30.
Which is the best order quantity?
(8)
Level 1 Remembering
(ii)
Find the number of order per year and Frequency of
orders?
(5)
2.
(i)
A stockiest has to supply 12000 units of a product per
year to his customer. Demand is
fixed and known. Shortage cost is assumed to be
infinite. Inventory holding cost is 20 paise per unit per
month. Ordering Cost is Rs. 250 and purchase price
is Rs.10 per unit.
Estimate the EOQ
(8)
Level 2 Understanding
(ii)
Find the Frequency of orders and total inventory cost. (5)
3.
ABC manufacturing company purchases 9000 parts of a
machine for its annual requirement. Each part costs
Rs.20. The ordering cost per order is Rs.15 and the
carrying charges are 15% of the average inventory per
year. Apply EOQ formulae and find out EOQ, No of
orders ,Total Inventory Cost and total cost.
Level 3 Applying
4.
(i)
Demand for an item in a company is 18,000 units per
year. The company can produce the items at a rate of
3000 units per month. The Cost of one setup is Rs.500
and the holding cost of one unit per month is 15 paise.
Shortage cost of one unit is Rs.20 per year.
Analyze and find the optimum manufacturing quantity.
(8)
Level 4 Analysing
(ii)
Find the number of shortages and frequency of
Production run.
(5)
5. A company has a demand of 12000 units/year for an
item and it can produce 2000 units per month. The
cost of one setup is Rs.400 and the holding
cost/unit/month is 15 paise. Select the optimum lot
size and total cost per year assuming the cost of 1 unit
as Rs.4. Find EBQ, the number of set ups & total cost.
Level 5 Evaluating
6.
(i)
Find the optimal order quantity for a product when the
annual demand for the product is 500 units. The Cost of
storage per unit per year is 10% of the unit cost. Ordering
cost per order is Rs. 180.
Determine EOQ
(8)
Level 6 Creating
(ii)
Evaluate the Total Cost
(5)
The unit cost are given below:
Quantity Unit Cost(Rs.)
O
1500<=Q3<3000 24.60
3000<=Q4 24.40
7. (i)
Formulate the Optimal order quantity for a product for
which the price breaks are as follows
(8)
Level 1 Remembering
(ii)
Also find the Total cost.
Quantity Unit Cost(Rs.)
O
750<=Q 875
(5)
8.
Compute the EOQ and the total variable cost for the
following:
Annual demand: 25 units
Unit price: Rs.2.50
Order cost: Rs.4.00
Storage rate: 1% per year
Level 2 Understand
9.
(i)
Identify the profit under three states of nature & three
decision alternative.
State of
Nature
State of
Nature
State of
Nature
N1 N2 N3
Decision
Naking
D1 150 250 300
Decision
Naking
D2 450 250 200
Decision
Naking
D3 100 180 290
Hurwitz criterion for alpha=0.5
(3)
Level 3 Applying
(ii)
Laplace condition
(5)
(iii)
Minimax Condition
(5)
10.
A Bakery keeps a stock of particular brand of cake. Daily
demand of past experience.
Daily
demand
0 15 25 35 45 50
Probability 0.01 0.15 0.20 0.50 0.12 0.02
Consider the following sequence of random numbers.
48 78 9 51 56 77 15 14 68 9
Using this sequence simulate the demand for next 10
days.
Find the stock situation if the owner makes 35 cakes
every day. Examine the daily average demand.
Level 1 Remembering
11.
Given above is the following pay off matrix.
Using EMV criterion . Decide which of the act can be
chosen at the best. FindEVPI & EOL.
Nature
Probability
Don?t
Expand
Expand
200
Expand
400
High
Demand
0.4 2500 3500 5000
Medium
Demand
0.4 2500 3500 2500
Low
Demand
0.2 2500 1500 1000
Level 2 Understanding
12.
A sample of 100 arrivals of customers at a retail sales
depot is according to the following distribution.
Time between arrivals(mins) Frequency
0.5 2
1.0 6
1.5 10
2.0 25
2.5 20
3.0 14
3.5 4
4.0 7
4.5 4
5.0 2
Use random numbers and predict the average time
between arrivals.
48 78 9 51 56 77 15 14 68 9
Level 3 Applying
13.
(i)
A departmental store purchases sprays which can be
ordered only in lots of 10. Each spray cost Rs.75 and
sells at Rs.90 each. Used sprays, however have \no
salvage value.
Demand 10 20 30 40 50
Probability 0.2 0.35 0.25 0.15 0.05
The probability distribution obtained from analysis of past
sales data is given below.
Analyse the payoff table.
(5)
Level 4 Analysing
(ii) How much quantity should the departmental store buy to
maximize its profit?
(8)
14. (i)
A company uses annually 50,000 units of an item each
costing Rs.1.20. Each order costs Rs.45 and inventory
carrying costs are 15% of the annual average inventory
value.
Find EOQ.
(3)
Level 2 Understanding
(ii) If the company operates 250 days a year and the
procurement time is 10 days and safety stock is 500
units, find reorder level, maximum, minimum and
average inventory
(10)
PART - C
S.No Questions BT
Level
Competence
1.
A contractor has to supply 10000 bearings per day to an
automobile manufacturer. He finds that when he starts a
production run he can produce 25000 bearings per day. The
cost of holding a bearing in stock for one year is 2 paise and
the set up cost of the production run is Rs.18. How frequently
should production run be made and which is the Best
Economic Batch Quantity? How much would be the No. of
Setup and Total Inventory Cost.
Level 1 Remembering
2.
A stockist has to supply 400 units of a product every
Monday to his customer.
He gets the product at Rs.50 per unit from the
manufacturer. The cost of ordering and transportation
from the manufacturer is Rs.75 per order. The cost of
carrying inventory is 7.5% per year of the cost of product.
Predict EOQ, Frequency of orders and Number of Orders,
Total Incremental cost and Total Cost.
Level 2 Understanding
3. (i) Identify the profit under three states of nature & three
decision alternative.
State of
Nature
N1 N2 N3
Decision
Making
D1 100 200 300
D2 400 200 200
D3 200 160 390
Hurwitz criterion for alpha=0.5
(5) Level 3 Applying
(ii)
Laplace Condition
(5)
(iii) Mininmax Condition (5)
4.
An automobile production line turns out about 100 cars a
day, but deviation occur owing to many causes. The
production is more accurately described by the
probability distribution given below;
Production/
Day
Probability
95 0.03
96 0.05
97 0.07
98 0.10
Level 4 Analysing
99 0.15
100 0.20
101 0.15
102 0.10
103 0.07
104 0.05
105 0.03
Use the random numbers &find the average demand
48 78 9 51 56 77 15 14 68 9
UNIT - V QUEUING THEORYAND REPLACEMENT MODELS
SYLLABUS:Queuing Theory ?Single and Multi-Channel models-infinite number of customers and
infinite calling resource Replacement Models-Individuals replacement Models (With and without time
value of money) ? Group Replacement Models.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define Queue.
Level 1 Remembering
2. How do you show your understanding on replacement theory?
Level 2 Understanding
3. In a bank, 20 customers on an average are served by a
cashier in an hour. If the service time has exponential
distribution, what is the probability that it will take more than
10 minutes to serve a customer?
Level 3 Applying
4. Classify the types of Queue.
Level 4 Analysing
5. How waiting time cost is related to queuing system?
Level 5 Evaluating
6. Interpret the Characteristics Of Queuing Models.
Level 4 Evaluating
7. How would you explain consumer behavior in queues?
Level 1 Remembering
8. Compare Serial and parallel Queue with Examples. Level 2 Understanding
9. Classify the types of Replacement model.
Level 3 Applying
10. Describe Kendall?s Notation for identifying a Queue Model with
single channel, Poisson arrivals, exponential service unlimited
queue and infinite calling population.
Level 4 Analysing
11. GRP includes IRP .Do You Agree?
Level 5 Evaluating
12. What is GRP &IRP?
Level 6 Creating
FirstRanker.com - FirstRanker's Choice
(An
?
DEPARTMENT OF MANAGEMENT STUDIES
QUESTION BANK
II SEMESTER
1915201? APPLIED OPERATIONS RESEACH
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Dr. Radha Ganesh Kumar ? Asst. Professor (Sel.G) and HOD
Mr.B. Sam Paul ? Asst. Professor (OG)
(An
? .
DEPARTMENT OFMANAGEMENT STUDIES
QUESTION BANK
SUBJECT :1915201 ?APPLIED OPERATIONS RESEACH
SEM / YEAR : IISemester / IYear
UNIT ? I ?INTRODUCTION TO LINEAR PROGRAMMING (LP)
SYLLABUS: Introduction to applications of operations research in functional areas of management.
Linear Programming-formulation, solution by graphical and simplex methods, Special cases. Dual
simplex method. Principles of Duality. Sensitivity Analysis.
PART- A
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Define Operations Research (OR). Level 1 Remembering
2. Differentiate between Simplex and Big M Method Level 2 Understanding
3. How do you show your understanding unbounded solution? Level 3 Applying
4. Categorize the forms of LPP. Level 4 Analysing
5.
Discuss why is two phase method is better than Big M
method?
Level 5 Evaluating
6. Interpret the usage of Sensitivity Analysis in LPP. Level 6 Creating
7. What are the assumptions and requirements of LPP? Level 1 Remembering
8. Compare Dual Simplex and Duality. Level 2 Understanding
9. Identify the Advantages of duality. Level 3 Applying
10. What do you think about Infeasible solution? Level 4 Analysing
11. How will you solve LPP graphically? Level 5 Evaluating
12.
Conclude your understanding on the mathematical
formulation of LPP.
Level 6 Creating
13. Define basic variables and artificial variables. Level 1 Remembering
14. Compare Slack variable & Surplus Variable. Level 2 Understanding
15.
Give some example for the role of Surplus variable & Slack
Variable in the simplex method
Level 3 Applying
16. How would you apply Artificial variable? Level 4 Analysing
17. What is Big M Method? Level 1 Remembering
18. Distinguish simplex and Big M method Level 2 Understanding
19.
What do you mean by Duality? List the Rules for primal and
dual.
Level 1 Remembering
20. What is Shadow price? Level 1 Remembering
PART- B
S.NO
QUESTIONS
BT
LEVEL
COMPETENCE
1.
(i)
Maximise Z=3x+4y subject to
2x+5y ?60,
4x+2y ?40.
x, y >0. Solve by Graphical Method
Plot the graph
(8)
Level 1 Remembering
(ii) Which one is the best solution? (5)
2.
(i)
Min Z= 20x
1
+10 x
2
subject to
x
1
+2x
2
? 40,
3x
1
+x
2
? 30,
4x
1
+3x
2
? 60,
x
1
,x
2
? 0.
Solve by Graphical Method,
Plot the graph
(8)
Level 2 Understanding
(ii) Predict the value of x & y. (5)
3 Max Z= 5x1+4x2 subject to
x
1
-2x
2
? 1,
x
1
+2x
2
?3,
x
1
,x
2
? 0. Solve Graphically. Which one is the best
solution?
Level 3 Applying
4.
(i)
A Plant Manufacturer 2 Product A & B. The Profit Contribution
of each product has been estimated as Rs.300 for product A
and Rs.400 for Product B. Each Product passes through 3
departments of the plant. The time required for each product
and total time available in each department is as follows.
Department Hours
Required
Hours
Required
Available
Hours
during
month
Product
A
Product
B
I 2 3 1600
II 3 2 1500
III 1 1 700
The company has a contract to supply atleast 300 units of
Product B per month.
Formulate the LPP
(5)
Level 4
Analysing
(ii) Solve through Graphical Method
(8)
5. Solve the following LPP by graphical method.
Maximize Z= 3x
1
+2x
2
Subject t o
- 2x
1
+x
2
?1,
x
1
? 2,
x
1
+ x
2
? 3
and x
1
,x
2
? 0
Level 5 Evaluating
6. (i) Max Z= 1000x
1
+4000x
2
+5000x
3
Subject to 3x1+3x
3
?22,
x1+2x2+3x
3
? 14,
3x1+2x2 ? 14
& x1,x2 ? 0
Develop a Simplex Table
(5)
Level 6 Creating
(ii) Analyse and find the value of x
1
, x
2
? (8)
7. Analyze the following LPP by Simplex Method:
Min Z = -10y
1
-15y
2
-20y
3
Subject to 2y
1
+4y
2
+6y
3
? 24,
3y
1
+9y
2
+6y
3
? 30,
& y
1
, y
2
, y
3
? 0.
Level 1 Remembering
(i)
Develop a Simplex Table (5)
(ii) Solve and find the value of y1 ,y2 and y3
(8)
8.
Solve By Graphical Method
Minimize Z= 40x
1
+24x
2
Subject to, 20x
1
+50 x
2
> 4,800
80 x
1
+50x
2
> 7,200
x
1
,x
2
>0
Level 2 Understanding
9. Solve the following LPP by simplex method:
Minimize Z= 8x
1
-2x
2
Subject to -4x
1
+2x
2
?1,
5x
1
-4x
2
?3,
and x
1
,x
2
? 0
Level 3 Applying
10. Solve the following LPP by simplex method:
Maximize Z= 3x1+2x
2
Subject to
2x
1
+x
2
?2,
3x
1
+4x
2
?12,
x
1
,x
2
? 0
Level 4 Analyzing
11. Review the LPP and solve by simplex method
Max Z= 25x+10y
Subject to the constraints
x+0.5y? 20
x+y? 50
x,y ? 0
Level 1 Remembering
12. A firm produces three products. These products are
processors on 3 different machines. The time required for
manufacturing one unit of cost of the products and the daily
capacity of the three machines is given in the table below.
Analyse and find the optimum solution.
Mac
hine
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Machine
Capacity
Min /Day
Product1 Product 2 Product 3
M1 2 8 2 940
M2 4 - 8 970
M3 2 5 - 430
It is required to determine the daily no. of units to be
manufactured for each product. The profit for unit for
Level 2 Understanding
product 1,2,3 is Rs.4,Rs.8,Rs.6 respectively. It is assumed
that all the amount produced are consumed in the market
13. Using dual simplex method , solve and find the optimum
solution for the given LPP.
Maximize Z=6x
1
+4x
2
+4x
3
Subject to 3x
1
,x
2
+2x
3
? 2
2x
1
+x
2
-x
3
? 1
-x
1
+x
2
+2x
3
? 1 &
x
1
,x
2
,x
3
? 0
Level 4 Analysing
14.
(i)
Evaluate by using dual simplex method and solve the LPP.
Minimize Z=2x
1
+x
2
Subject to 3x
1
+2x
2
? 3
4x
1
+3x
2
? 6
x
1
+x
2
? 5 & x
1
,x
2
?
Determine the dual simplex table
(5)
Level 1 Remembering
(ii)
Find the value of x
1
, x
2
(8)
PART - C
S.No Questions BT
LEVEL
COMPETENCE
1.
Max Z=300x+400y subject to
2x+3y ? 1600,
3x+2y ? 1500,
x+y ? 700,
y ? 300, x,y ? 0 Solve by Graphical Method, choose the
value of x & y which maximizes profit.
Level 1 Remembering
2. Solve the following LPP by graphical method.
Minimize Z= 6000x1+4000x
2
Subject t o
3x+x
2
? 40,
x
1
+2.5 x
2
? 22
3x
1
+3 x
2
? 40
and x
1
,x
2
? 0
Level 2 Understanding
3. Develop a Simplex Table and Solve
Max Z = 3 x1+2 x2,
Subject to
x1+ x2 ?4,
x1- x2 ? 2;
x1, x2 ?0.
Level 3 Applying
4. Solve by using Simplex Method.
Maximize Z= 3x+5y
Subject to the constraints
x+y? 60
x? 40
y ? 30
x,y ? 0
Level 1 Remembering
UNIT - II LINEAR PROGRAMMING EXTENSIONS
SYLLABUS: Transportation Models (Minimizing and Maximizing Problems) ? Balanced and unbalanced
Problems ? Initial Basic feasible solution by N-W Corner Rule, Least cost and Vogel?s approximation methods.
Check for optimality. Solution by MODI /. Case of Degeneracy. Trans-shipment Models. Assignment Models
(Minimising and Maximising Problems) ? Balanced and Unbalanced Problems. Solution by Hungarian and
Branch and Bound Algorithms. Travelling Salesman problem.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define Transportation & Transhipment. Level 1 Remembering
2. Differentiate balanced transportation problem & Unbalanced
Transportation Problem.
Level 2 Understanding
3. How would you show your understanding on unbalanced
transportation problem?
Level 3 Applying
4. Categorize the Phases of transportation model. Level 4 Analysing
5. Construct the basic feasible solution for the following
transportation problem.
1 2 3 4 SUPPLY
1 2 3 11 7 6
2 1 0 6 1 1
3 5 8 15 9 10
DEMAN D 7 5 3 2
Level 5 Evaluating
6 Interpret the need for Optimum solution in transportation. Level 6 Creating
7. What do you mean by Least cost method (LCM)? Level 1 Remembering
8. Compare Vogel approximation method (VAM) & Least Cost
Method.
Level 2 Understanding
9. How do you represent a travelling salesman problem
through mathematical formulation?
Level 3 Applying
10. Analyse the rules of travelling salesman Problem. Level 4 Analysing
11. Discuss the meaning of Assignment Level 5 Evaluating
12. Compare Balanced assignment problem & Unbalanced
Assignment Problem.
Level 6 Creating
13. What example can you give for Unbalanced assignment
problem?
Level 1 Remembering
14. How will you resolve degeneracy in Transportation Problem? Level 2 Understanding
15. Classify transportation problem. Level 3 Applying
16. Examine the Steps in Hungarian algorithm. Level 4 Analysing
17. What is Branch and bound algorithm in Assignment? Level 1 Remembering
18. Compare Assignment and transportation Problem. Level 2 Understanding
19. What do you mean by Travelling Salesman Problem? Level 1 Remembering
20. What is Restricted Assignment? Level 1 Remembering
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Solve and find the Transportation Problem and Which method will
you select if you want toMinimize Cost?
Destination Supply
1 2 3 4
I 21 16 25 13 11
II 17 18 14 23 13
III 32 27 18 41 19
Demand 6 10 12 15
Level 1 Remembering
2. Find the Initial Basic Feasible solution for following TP. Using NW
Rule, LCM, and VAM. Which method will you select if you want to
Minimize Cost?
D1 D2 D3 Supply
S1 7 3 2 2
S2 2 1 3 3
S3 3 4 6 5
Demand 4 1 5 10
Level 2 Understanding
3.
(i)
Analyze the transportation problem with unit transportation
costs,demand, and supply as given below:
Destination
Supply
Source
D1 D2 D3 D4
S1
6 1 9 3
70
11 5 2 8
S2 55
10 12 4 7
S3
70
Demand 85 35 50 45
Apply VAM for Initial solution.
(5)
Level 3 Applying
(ii)
Construct the final Solution by using MODIMethod.
(8)
4.
(i)
Analyze & solve the following transportation problem to maximize
profit.
A B C D Supply
1
Source 2
3
Demand
15 51 42 33 23
80 42 26 81 44
90 40 66 60 33
23
31
16
30
100
Examine Initial solution using VAM.
(5)
Level 4 Analysing
(ii)
Analyze and find out the final Solution by using MODI Method.
(8)
5. Solve the following transportation problem using Vogel?s
method
Factory? Warehouse ?Available
A B C D E F
1 9 12 9 6 9 10 5
2 7 3 7 7 5 5 6
3 6 5 9 11 3 11 2
4 6 8 11 2 2 10 9
4 4 6 2 4 2
Requirement?
(5)
Level 5 Evaluating
6. (i) Solve the transportation problem and decide using VAM for initial
solution.
(5) Level 6 Creating
(ii) Evaluate using NWC and Least Cost method for initial solution?
Destination Supply
I 2 1 25 13 11
II 1 1 14 23 13
III 3 2 18 41 19
Demand 6 1 22 15
(8)
7.
Maximize profit from the following transportationproblem.
A B C D Supply
I 40 25 22 33 100
SourceII 44 35 30 30 30
III 38 38 28 30 70
Demand 40 20 60 30
Level 1 Remembering
(i) How will you convert maximization problem to minimization.
Find the maximum profit
(8)
(ii) Explain stepping stone method for checking the
solution for optimality transportation problems.
(5)
8. A company has one surplus truck in each of the cities A, B, C, D, &
E and one deficit trucks in each of the cities 1,2,3,4,5,6. The
distance between the cities in kms is shown in the matrix below.
Can you select the assignment of trucks from cities in surplus to
cities in deficiency .so that total distance covered by the vehicles is
minimum?
1 2 3 4 5 6
A 12 10 15 22 18 8
B 10 18 25 15 16 12
C 11 10 3 8 5 9
D 6 4 10 13 13 12
E 8 12 11 7 13 10
Level 2 Understanding
9.
Consider the problem of assigning five jobs to five persons. The
assignment costs are given as follows:
PERSONS?JOBS ?
1 2 3 4 5
A 8 4 2 6 1
B 0 9 5 5 4
C 3 8 9 2 6
D 4 3 1 0 3
Level 3 Applying
E 9 5 8 9 5
Determine the optimum assignment schedule.
10. The assignment cost of assigning any one operator to any one
machine is given in the following table.
MACHINE?OPERATORS ?
I II III IV
A 10 5 13 15
B 3 9 18 3
C 10 7 3 2
D 5 11 9 7
Find the optimal assignment by Hungarian method.
Level 4 Analysing
11. A machine shop purchased a drilling machine and two lathes of
different capacities. The Positioning of the machines among 4
possible locations on the shop floor is important forms the
standard of materials handling. Given the cost estimate per unit
time of materials below, find the optimum location of the
machines.
LOCATIONS
1 2 3 4
Lathe 1 12 9 12 9
Drill 15 Not
suitable
13 20
Lathe 2 4 8 10 6
Level 1 Remembering
12.
Solve the assignment problem for maximization given profit
matrix(profit in rupees).
Machines
P Q R S
JOB
51 53 54 50
47 50 48 50
49 50 60 61
63 64 60 60
Level 2 Understanding
PART - C
S.No Questions Marks BT
Level
Competence
1.
a
Assume that you are an OR specialist. Identify the procedure
for each of the following Method to the employees in order to
help them achieve solution to Transportation Problems.
Northwest Corner Cell Method
(3)
Level 1 Remembering
b Least Cost cell Method (4)
c Vogel?s Approximation Method (4)
d U V Method. (4)
13. The processing time in hours for the jobs when allocated to the
different machines is indicated below. Select the best assignment
of the machines for the jobs so that the total processing time is
Minimum.
Machines
M1 M2 M3 M4 M5
J1 9 22 58 11 19
JOB J2 43 78 72 50 63
J3 41 28 91 37 45
J4 74 42 27 49 39
J5 36 11 57 22 25
Level 4 Analysing
14. For the given travelling salesman problem, Minimize the total cost.
To
1 2 3 4
From A - 46 16 40
B 41 - 50 40
C 82 32 - 60
D 40 40 36 -
Level 1 Remembering
(i) Observe the above travelling salesman
problem and find out minimize the cost per
cycle.
(8)
(ii) Find whether path is satisfied. (5)
2.
Solve the following transportation problem, in which a
i
is the
availability at Origin
O
i
and b
j
is the requirement at the destination D
j
and cell entries
are unit costs of transportation from any origin to any
destination:
D1 D2 D3 D4 D5 a
j
O1 4 7 3 8 2 4
O2 1 4 7 3 8 7
O3 7 2 4 7 7 9
O4 4 8 2 4 7 2
b
j
8 3 7 2 2
Predict the allocation to minimize the cost.
Level 2 Understanding
3. A company has a team of 4 Salesman and the company wants to
do in 4 districts. Considering the capabilities of salesmen
and nature of the district, the company has estimated the profit per
day in Rs. For each salesmen in each district as follows.
District
s
Salesmen 1 2 3 4
A 16 10 14 11
B 14 11 15 15
C 15 15 13 12
D 13 12 14 15
Develop the best assignment schedule and analyze the total cost.
Level 3 Applying
4. Five operators have to be assigned to Five Machines. The
assignment costs are given in thetablebelow.
Analyse using Hungarian algorithm & find out the assignment to
minimize the cost.
Machine
I II III IV V
Operator
A 5 5 - 2 6
B 7 4 2 3 4
C 9 3 5 - 3
D 7 2 6 7 2
E 6 5 7 9 1
Level 4 Analyzing
UNIT ? III ? INTEGER PROGRAMMING AND GAME THEORY
SYLLABUS: Integer Programming ? Introduction and types - Game Theory-Two-person Zero sum
games-Saddle point, Dominance Rule, graphical and LP solutions, Nash Equilibrium
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. What do you mean by integer programming problem?
Level 1 Remembering
2. In what respect a mixed IPP differs from pure IPP?
Level 2 Understanding
3. What is Nash Equilibrium?
Level 3 Applying
4. Classify the different types of strategy.
Level 4 Analysing
5. Compile the Characteristics of game.
Level 5 Evaluating
6. Can you assess the applications of integer
programming?
Level 6 Creating
7. Define Game.
Level 1 Remembering
8. Compare Mixed Strategy and Pure Strategy.
Level 2 Understanding
9. How would you make use of the concept of Game theory
in Managerial Decision Making?
Level 3 Applying
10. Conclude your understanding about Payoff Matrix.
Level 4 Analysing
11. How will you find the optimal strategies and value of the
following game?
Player B
Player
A
H T
H 2 -1
T -1 0
Level 5 Evaluating
12. Interpret the concept of two person zero sum game.
Level 6 Creating
13. What is Saddle point?
Level 1 Remembering
14. Compare Dominance Principle of Rows and Columns.
Level 2 Understanding
15. Identify the basic assumptions of the Game.
Level 3 Applying
16. Conclude the advantages of Game theory.
Level 4 Analysing
17. What are the Methods of Matrices?
Level 1 Remembering
18. Summarize how graphs and LP solution are used in
Game theory.
Level 2 Understanding
19. What is a Decision Tree?
Level 1 Remembering
20. Define Dominance principle.
Level 1 Remembering
S.N
O
PART - B QUESTIONS MA
RK
S
BT
LEVEL
COMPETENCE
1. (i) What do you mean by Pure IPP? (3) Level 1 Remembering
(ii) What do you mean by Mixed IPP? (5)
(iii)
List out the difference between Pure and Mixed IPP.
(5)
2. (i) For what value of ?,the game with the following
matrix is strictly determined
B
1
B
2
B
3
A
1
? 6 2
A
2
-1 ? -7
A
3
-2 4 ?
(8) Level 2 Understanding
(ii) Write down the assumptions of game theory. (5)
3. (i) Solve the game whose pay-off matrix is given by
B
1
B
2
B
3
A
1
1 3 1
A
2
0 -4 -3
A
3
1 5 -1
(8)
Level 3 Applying
(ii) Explain the concept of Nash Equilibrium. (5)
4.
Analyze the Value of the game graphically
B1 B2
A1 4 4
A2 2 7
A3 5 3
A4 6 2
Level 4 Analysing
5.
What inference can be made using Dominance
Principle to reduce the following game and estimate
the game value?
B1 B2 B3 B4
A1 3 2 4 0
A2 3 4 2 4
A3 4 2 2 0
A4 2 1 6 3
Level 5 Evaluating
6.
How would you evaluate the following game whose
Pay-Off matrix is Given Below?
9 3 1 8 0
6 5 4 6 7
2 4 3 3 8
5 6 2 2 1
Level 6 Creating
7.
(i)
Two players A&B match coins. If the coins match
then A wins one unit value, if the coins do not
match then B wins one unit of value.
Determine pay-off matrix which strategy is to be
chosen
(5)
Level 1 Remembering
(ii)
Find the value of game. (8)
8.
Predict the Value of the Game given above Pay
OffMatrix.
Player B
B1 B2 B3
A1 -2 5 -3
Player A A2 1 3 5
A3 -3 -7 11
Level 2 Understanding
9.
Apply graphical analysis to Solve the game.
A/
B
B1 B2 B3 B4
A1 3 3 4 0
A2 5 4 3 7
Level 3 Applying
10. Solve the following game by graphical method.
Player B
1 2 3
1 6 4 3
Player A 2 2 4 8
Level 4 Analysing
11.
(i)
A and B play a Match(Game) in which each has 3
coins 5 paise, 10 paise and 20 paise. Each player
selects a coin without the knowledge of others
choice. IF the sum is even, B wins A?s Coin. If sum
is Odd, A wins B?s coin.
How will you find the pay-off matrix ?
(5)
Level 1
Remembering
(ii)
Find the Best Strategy & value of the Game. (8)
12.
Consider the Pay Off Matrix of player A as shown in
the table below and solve it optimally using the
graphical method .
Player A
Player
B
1 2 3 4 5
1 3 6 8 4 4
2 -7 4 2 10 2
Level 2 Understanding
13.
(i)
Analyze the Game Graphically:
Player A
Player
A
B1 B2
A1 -3 1
A2 5 3
A3 6 -1
A4 1 4
A5 2 2
A6 0 -5
Plot the graph
(5)
Level 4 Analysing
(ii)
Analyse and find the value of the game.
(8)
14.
Which one is the best strategy using Dominance
Principle?
B1 B2 B3 B4 B5 B6
A1
4 2 0 2 1 1
A2
4 3 1 3 2 2
A3
4 3 7 -5 1 2
A4
4 3 4 -1 2 2
A5
4 3 3 -2 2 2
Level 1 Remembering
PART-C
S.No Questions BT
Level
Competence
1.
Using Dominance property Solve.
B
A
I II IIIIV
1 -5 3 1 20
2 5 5 4 6
3 -4 -2 0 -5
Level 1 Remembering
2. Examine the 2 * n Game by the Method of Sub Game:
B1 B2 B3
A1 1 3 11
A2 8 5 2
Level 2 Understanding
3. In a game of matching coins with 2 players, A wins 1 unit value
when there are 2 heads, wins nothing when there are 2 tails
and looses ? unit value when there are one head and one tail.
Develop Pay Off matrix and value of the game.
Level 3 Applying
4.
i
ii
iii
Assume you have to choice of 3 strategies for advertising
and you have one major
Analyse the theory on Two-person sum games competitor
with 3 strategies.
(5)
Level 4 Analysing
What are the assumptions of Game? (5)
Find value of game.
B1 B2 B3
A1 80 70 60
A2 90 80 100
A3 40 30 40
(5)
UNIT - IV INVENTORY MODELS, SIMULATION AND DECISION THEORY
SYLLABUS: Inventory Models ? EOQ and EBQ Models (With and without shortages), Quantity Discount
Models. Decision making under risk ? Decision trees ? Decision making under uncertainty. Monte-carlo
simulation.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define inventory. Level 1 Remembering
2.
Classify the Forms of inventory.
Level 2 Understanding
3.
Identify the Objectives/significance of inventory model.
Level 3 Applying
4.
Highlight the importance of Reorder level.
Level 4 Analysing
5.
Discuss the concept of Lead time.
Level 5 Evaluate
6.
Interpret the Types of stock replenishment.
Level 1 Remembering
7.
List the Basic inventory models.
Level 2 Understanding
8.
Compare Ordering Cost and Carrying Cost.
Level 3 Appyling
9.
Identify when shortage cost and stock out cost arises?
Level 5 Evaluating
10.
Analyze why safety stock is maintained.
Level 1 Remembering
11.
Discuss the concept of Quantity Discount Model.
Level 2 Understanding
12.
Interpret the meaning of EOQ & EBQ.
Level 3 Applying
13.
What are random and pseudo random numbers?
Level 4 Analysing
14.
Explain Monte Carlo Method.
Level 5 Evaluating
15.
Summarize the concept of EMV.
Level 1 Remembering
16.
What inference can you make about holding cost ?
Level 2 Understanding
17.
What is Shortage Cost?
Level 3 Applying
18. Classify and explain the various conditions under which
decisions are made.
Level 1 Remembering
19. What is meant by the following terms in inventory
management: i)Carrying cost ii) shortage costs
Level 2 Understanding
20. What is Decision theory? List the problems that can be solved
by Simulation.
Level 3 Applying
S.NO PART - B QUESTIONS Marks BT
LEVEL
COMPETENCE
1.
(i)
Alpha industry needs 5400 units per year of a bought out
component which will be
used in its main product. The ordering cost is Rs.250
per order and the carrying cost per unit per year is
Rs.30.
Which is the best order quantity?
(8)
Level 1 Remembering
(ii)
Find the number of order per year and Frequency of
orders?
(5)
2.
(i)
A stockiest has to supply 12000 units of a product per
year to his customer. Demand is
fixed and known. Shortage cost is assumed to be
infinite. Inventory holding cost is 20 paise per unit per
month. Ordering Cost is Rs. 250 and purchase price
is Rs.10 per unit.
Estimate the EOQ
(8)
Level 2 Understanding
(ii)
Find the Frequency of orders and total inventory cost. (5)
3.
ABC manufacturing company purchases 9000 parts of a
machine for its annual requirement. Each part costs
Rs.20. The ordering cost per order is Rs.15 and the
carrying charges are 15% of the average inventory per
year. Apply EOQ formulae and find out EOQ, No of
orders ,Total Inventory Cost and total cost.
Level 3 Applying
4.
(i)
Demand for an item in a company is 18,000 units per
year. The company can produce the items at a rate of
3000 units per month. The Cost of one setup is Rs.500
and the holding cost of one unit per month is 15 paise.
Shortage cost of one unit is Rs.20 per year.
Analyze and find the optimum manufacturing quantity.
(8)
Level 4 Analysing
(ii)
Find the number of shortages and frequency of
Production run.
(5)
5. A company has a demand of 12000 units/year for an
item and it can produce 2000 units per month. The
cost of one setup is Rs.400 and the holding
cost/unit/month is 15 paise. Select the optimum lot
size and total cost per year assuming the cost of 1 unit
as Rs.4. Find EBQ, the number of set ups & total cost.
Level 5 Evaluating
6.
(i)
Find the optimal order quantity for a product when the
annual demand for the product is 500 units. The Cost of
storage per unit per year is 10% of the unit cost. Ordering
cost per order is Rs. 180.
Determine EOQ
(8)
Level 6 Creating
(ii)
Evaluate the Total Cost
(5)
The unit cost are given below:
Quantity Unit Cost(Rs.)
O
1500<=Q3<3000 24.60
3000<=Q4 24.40
7. (i)
Formulate the Optimal order quantity for a product for
which the price breaks are as follows
(8)
Level 1 Remembering
(ii)
Also find the Total cost.
Quantity Unit Cost(Rs.)
O
750<=Q 875
(5)
8.
Compute the EOQ and the total variable cost for the
following:
Annual demand: 25 units
Unit price: Rs.2.50
Order cost: Rs.4.00
Storage rate: 1% per year
Level 2 Understand
9.
(i)
Identify the profit under three states of nature & three
decision alternative.
State of
Nature
State of
Nature
State of
Nature
N1 N2 N3
Decision
Naking
D1 150 250 300
Decision
Naking
D2 450 250 200
Decision
Naking
D3 100 180 290
Hurwitz criterion for alpha=0.5
(3)
Level 3 Applying
(ii)
Laplace condition
(5)
(iii)
Minimax Condition
(5)
10.
A Bakery keeps a stock of particular brand of cake. Daily
demand of past experience.
Daily
demand
0 15 25 35 45 50
Probability 0.01 0.15 0.20 0.50 0.12 0.02
Consider the following sequence of random numbers.
48 78 9 51 56 77 15 14 68 9
Using this sequence simulate the demand for next 10
days.
Find the stock situation if the owner makes 35 cakes
every day. Examine the daily average demand.
Level 1 Remembering
11.
Given above is the following pay off matrix.
Using EMV criterion . Decide which of the act can be
chosen at the best. FindEVPI & EOL.
Nature
Probability
Don?t
Expand
Expand
200
Expand
400
High
Demand
0.4 2500 3500 5000
Medium
Demand
0.4 2500 3500 2500
Low
Demand
0.2 2500 1500 1000
Level 2 Understanding
12.
A sample of 100 arrivals of customers at a retail sales
depot is according to the following distribution.
Time between arrivals(mins) Frequency
0.5 2
1.0 6
1.5 10
2.0 25
2.5 20
3.0 14
3.5 4
4.0 7
4.5 4
5.0 2
Use random numbers and predict the average time
between arrivals.
48 78 9 51 56 77 15 14 68 9
Level 3 Applying
13.
(i)
A departmental store purchases sprays which can be
ordered only in lots of 10. Each spray cost Rs.75 and
sells at Rs.90 each. Used sprays, however have \no
salvage value.
Demand 10 20 30 40 50
Probability 0.2 0.35 0.25 0.15 0.05
The probability distribution obtained from analysis of past
sales data is given below.
Analyse the payoff table.
(5)
Level 4 Analysing
(ii) How much quantity should the departmental store buy to
maximize its profit?
(8)
14. (i)
A company uses annually 50,000 units of an item each
costing Rs.1.20. Each order costs Rs.45 and inventory
carrying costs are 15% of the annual average inventory
value.
Find EOQ.
(3)
Level 2 Understanding
(ii) If the company operates 250 days a year and the
procurement time is 10 days and safety stock is 500
units, find reorder level, maximum, minimum and
average inventory
(10)
PART - C
S.No Questions BT
Level
Competence
1.
A contractor has to supply 10000 bearings per day to an
automobile manufacturer. He finds that when he starts a
production run he can produce 25000 bearings per day. The
cost of holding a bearing in stock for one year is 2 paise and
the set up cost of the production run is Rs.18. How frequently
should production run be made and which is the Best
Economic Batch Quantity? How much would be the No. of
Setup and Total Inventory Cost.
Level 1 Remembering
2.
A stockist has to supply 400 units of a product every
Monday to his customer.
He gets the product at Rs.50 per unit from the
manufacturer. The cost of ordering and transportation
from the manufacturer is Rs.75 per order. The cost of
carrying inventory is 7.5% per year of the cost of product.
Predict EOQ, Frequency of orders and Number of Orders,
Total Incremental cost and Total Cost.
Level 2 Understanding
3. (i) Identify the profit under three states of nature & three
decision alternative.
State of
Nature
N1 N2 N3
Decision
Making
D1 100 200 300
D2 400 200 200
D3 200 160 390
Hurwitz criterion for alpha=0.5
(5) Level 3 Applying
(ii)
Laplace Condition
(5)
(iii) Mininmax Condition (5)
4.
An automobile production line turns out about 100 cars a
day, but deviation occur owing to many causes. The
production is more accurately described by the
probability distribution given below;
Production/
Day
Probability
95 0.03
96 0.05
97 0.07
98 0.10
Level 4 Analysing
99 0.15
100 0.20
101 0.15
102 0.10
103 0.07
104 0.05
105 0.03
Use the random numbers &find the average demand
48 78 9 51 56 77 15 14 68 9
UNIT - V QUEUING THEORYAND REPLACEMENT MODELS
SYLLABUS:Queuing Theory ?Single and Multi-Channel models-infinite number of customers and
infinite calling resource Replacement Models-Individuals replacement Models (With and without time
value of money) ? Group Replacement Models.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define Queue.
Level 1 Remembering
2. How do you show your understanding on replacement theory?
Level 2 Understanding
3. In a bank, 20 customers on an average are served by a
cashier in an hour. If the service time has exponential
distribution, what is the probability that it will take more than
10 minutes to serve a customer?
Level 3 Applying
4. Classify the types of Queue.
Level 4 Analysing
5. How waiting time cost is related to queuing system?
Level 5 Evaluating
6. Interpret the Characteristics Of Queuing Models.
Level 4 Evaluating
7. How would you explain consumer behavior in queues?
Level 1 Remembering
8. Compare Serial and parallel Queue with Examples. Level 2 Understanding
9. Classify the types of Replacement model.
Level 3 Applying
10. Describe Kendall?s Notation for identifying a Queue Model with
single channel, Poisson arrivals, exponential service unlimited
queue and infinite calling population.
Level 4 Analysing
11. GRP includes IRP .Do You Agree?
Level 5 Evaluating
12. What is GRP &IRP?
Level 6 Creating
13. Distinguish between breakdown maintenance and preventive
maintenance.
Level 1 Remembering
14. How do you show your understanding on Little?s formula in
queuing theory?
Level 2 Understanding
15. Categorize Queue Discipline.
Level 3 Applying
16. Develop Kendall?s Notation of a Queue.
Level 4 Analysing
17. What is ?Collusion? in Queue Discipline?
Level 1 Remembering
18. Compare the Queue Length and No. of Customers in the System.
Level 2 Understanding
19. Distinguish between individual replacement and group
replacement?
Level 3 Applying
20. Describe Kendall?s Notation for identifying a Queue Model with
two channels, Poisson arrivals, exponential service Unlimited
Queue and infinite calling population.
Level 1 Remembering
S.No
PART - B QUESTIONS Marks
BT
LEVEL
COMPETENCE
1. The cost of machine is Rs.16, 00 and scrap value is
Rs.1,100. Maintenance Cost form for machine are as
follows:
Year 1 2 3 4 5 6 7 8
Maintenance
cost
300 459 600 800 100 1200 1500 2000
When should the machine be the replaced?
Level 1 Remembering
2.
The following table gives to cost of spares per year,
overhead cost of maintenance per year and resale value of
certain equipment whose purchase price is Rs. 50,000:
Illustrate when the machine can be replaced.
Year 1 2 3 4 5
Cost of Spares 10000 12000 14000 15000 17000
Overhead
Maintenance
Cost
5000 5000 6000 6000 8000
Resale Value 40000 32000 28000 25000 22000
Level 2 Understanding
3.
A Taxi owner estimates from his past records that the cost
per year for operating a taxi whose purchase price when
new is Rs.60,000 are as follows.
Age 1 2 3 4 5
Operating cost 10000 12000 15000 18000 20000
After 5 years the operating cost is Rs.6000 x K, Where ?k?
is 6,7,8,9,10(age). If the resale value decreases by 10% of
Level 3 Applying
FirstRanker.com - FirstRanker's Choice
(An
?
DEPARTMENT OF MANAGEMENT STUDIES
QUESTION BANK
II SEMESTER
1915201? APPLIED OPERATIONS RESEACH
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Dr. Radha Ganesh Kumar ? Asst. Professor (Sel.G) and HOD
Mr.B. Sam Paul ? Asst. Professor (OG)
(An
? .
DEPARTMENT OFMANAGEMENT STUDIES
QUESTION BANK
SUBJECT :1915201 ?APPLIED OPERATIONS RESEACH
SEM / YEAR : IISemester / IYear
UNIT ? I ?INTRODUCTION TO LINEAR PROGRAMMING (LP)
SYLLABUS: Introduction to applications of operations research in functional areas of management.
Linear Programming-formulation, solution by graphical and simplex methods, Special cases. Dual
simplex method. Principles of Duality. Sensitivity Analysis.
PART- A
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Define Operations Research (OR). Level 1 Remembering
2. Differentiate between Simplex and Big M Method Level 2 Understanding
3. How do you show your understanding unbounded solution? Level 3 Applying
4. Categorize the forms of LPP. Level 4 Analysing
5.
Discuss why is two phase method is better than Big M
method?
Level 5 Evaluating
6. Interpret the usage of Sensitivity Analysis in LPP. Level 6 Creating
7. What are the assumptions and requirements of LPP? Level 1 Remembering
8. Compare Dual Simplex and Duality. Level 2 Understanding
9. Identify the Advantages of duality. Level 3 Applying
10. What do you think about Infeasible solution? Level 4 Analysing
11. How will you solve LPP graphically? Level 5 Evaluating
12.
Conclude your understanding on the mathematical
formulation of LPP.
Level 6 Creating
13. Define basic variables and artificial variables. Level 1 Remembering
14. Compare Slack variable & Surplus Variable. Level 2 Understanding
15.
Give some example for the role of Surplus variable & Slack
Variable in the simplex method
Level 3 Applying
16. How would you apply Artificial variable? Level 4 Analysing
17. What is Big M Method? Level 1 Remembering
18. Distinguish simplex and Big M method Level 2 Understanding
19.
What do you mean by Duality? List the Rules for primal and
dual.
Level 1 Remembering
20. What is Shadow price? Level 1 Remembering
PART- B
S.NO
QUESTIONS
BT
LEVEL
COMPETENCE
1.
(i)
Maximise Z=3x+4y subject to
2x+5y ?60,
4x+2y ?40.
x, y >0. Solve by Graphical Method
Plot the graph
(8)
Level 1 Remembering
(ii) Which one is the best solution? (5)
2.
(i)
Min Z= 20x
1
+10 x
2
subject to
x
1
+2x
2
? 40,
3x
1
+x
2
? 30,
4x
1
+3x
2
? 60,
x
1
,x
2
? 0.
Solve by Graphical Method,
Plot the graph
(8)
Level 2 Understanding
(ii) Predict the value of x & y. (5)
3 Max Z= 5x1+4x2 subject to
x
1
-2x
2
? 1,
x
1
+2x
2
?3,
x
1
,x
2
? 0. Solve Graphically. Which one is the best
solution?
Level 3 Applying
4.
(i)
A Plant Manufacturer 2 Product A & B. The Profit Contribution
of each product has been estimated as Rs.300 for product A
and Rs.400 for Product B. Each Product passes through 3
departments of the plant. The time required for each product
and total time available in each department is as follows.
Department Hours
Required
Hours
Required
Available
Hours
during
month
Product
A
Product
B
I 2 3 1600
II 3 2 1500
III 1 1 700
The company has a contract to supply atleast 300 units of
Product B per month.
Formulate the LPP
(5)
Level 4
Analysing
(ii) Solve through Graphical Method
(8)
5. Solve the following LPP by graphical method.
Maximize Z= 3x
1
+2x
2
Subject t o
- 2x
1
+x
2
?1,
x
1
? 2,
x
1
+ x
2
? 3
and x
1
,x
2
? 0
Level 5 Evaluating
6. (i) Max Z= 1000x
1
+4000x
2
+5000x
3
Subject to 3x1+3x
3
?22,
x1+2x2+3x
3
? 14,
3x1+2x2 ? 14
& x1,x2 ? 0
Develop a Simplex Table
(5)
Level 6 Creating
(ii) Analyse and find the value of x
1
, x
2
? (8)
7. Analyze the following LPP by Simplex Method:
Min Z = -10y
1
-15y
2
-20y
3
Subject to 2y
1
+4y
2
+6y
3
? 24,
3y
1
+9y
2
+6y
3
? 30,
& y
1
, y
2
, y
3
? 0.
Level 1 Remembering
(i)
Develop a Simplex Table (5)
(ii) Solve and find the value of y1 ,y2 and y3
(8)
8.
Solve By Graphical Method
Minimize Z= 40x
1
+24x
2
Subject to, 20x
1
+50 x
2
> 4,800
80 x
1
+50x
2
> 7,200
x
1
,x
2
>0
Level 2 Understanding
9. Solve the following LPP by simplex method:
Minimize Z= 8x
1
-2x
2
Subject to -4x
1
+2x
2
?1,
5x
1
-4x
2
?3,
and x
1
,x
2
? 0
Level 3 Applying
10. Solve the following LPP by simplex method:
Maximize Z= 3x1+2x
2
Subject to
2x
1
+x
2
?2,
3x
1
+4x
2
?12,
x
1
,x
2
? 0
Level 4 Analyzing
11. Review the LPP and solve by simplex method
Max Z= 25x+10y
Subject to the constraints
x+0.5y? 20
x+y? 50
x,y ? 0
Level 1 Remembering
12. A firm produces three products. These products are
processors on 3 different machines. The time required for
manufacturing one unit of cost of the products and the daily
capacity of the three machines is given in the table below.
Analyse and find the optimum solution.
Mac
hine
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Machine
Capacity
Min /Day
Product1 Product 2 Product 3
M1 2 8 2 940
M2 4 - 8 970
M3 2 5 - 430
It is required to determine the daily no. of units to be
manufactured for each product. The profit for unit for
Level 2 Understanding
product 1,2,3 is Rs.4,Rs.8,Rs.6 respectively. It is assumed
that all the amount produced are consumed in the market
13. Using dual simplex method , solve and find the optimum
solution for the given LPP.
Maximize Z=6x
1
+4x
2
+4x
3
Subject to 3x
1
,x
2
+2x
3
? 2
2x
1
+x
2
-x
3
? 1
-x
1
+x
2
+2x
3
? 1 &
x
1
,x
2
,x
3
? 0
Level 4 Analysing
14.
(i)
Evaluate by using dual simplex method and solve the LPP.
Minimize Z=2x
1
+x
2
Subject to 3x
1
+2x
2
? 3
4x
1
+3x
2
? 6
x
1
+x
2
? 5 & x
1
,x
2
?
Determine the dual simplex table
(5)
Level 1 Remembering
(ii)
Find the value of x
1
, x
2
(8)
PART - C
S.No Questions BT
LEVEL
COMPETENCE
1.
Max Z=300x+400y subject to
2x+3y ? 1600,
3x+2y ? 1500,
x+y ? 700,
y ? 300, x,y ? 0 Solve by Graphical Method, choose the
value of x & y which maximizes profit.
Level 1 Remembering
2. Solve the following LPP by graphical method.
Minimize Z= 6000x1+4000x
2
Subject t o
3x+x
2
? 40,
x
1
+2.5 x
2
? 22
3x
1
+3 x
2
? 40
and x
1
,x
2
? 0
Level 2 Understanding
3. Develop a Simplex Table and Solve
Max Z = 3 x1+2 x2,
Subject to
x1+ x2 ?4,
x1- x2 ? 2;
x1, x2 ?0.
Level 3 Applying
4. Solve by using Simplex Method.
Maximize Z= 3x+5y
Subject to the constraints
x+y? 60
x? 40
y ? 30
x,y ? 0
Level 1 Remembering
UNIT - II LINEAR PROGRAMMING EXTENSIONS
SYLLABUS: Transportation Models (Minimizing and Maximizing Problems) ? Balanced and unbalanced
Problems ? Initial Basic feasible solution by N-W Corner Rule, Least cost and Vogel?s approximation methods.
Check for optimality. Solution by MODI /. Case of Degeneracy. Trans-shipment Models. Assignment Models
(Minimising and Maximising Problems) ? Balanced and Unbalanced Problems. Solution by Hungarian and
Branch and Bound Algorithms. Travelling Salesman problem.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define Transportation & Transhipment. Level 1 Remembering
2. Differentiate balanced transportation problem & Unbalanced
Transportation Problem.
Level 2 Understanding
3. How would you show your understanding on unbalanced
transportation problem?
Level 3 Applying
4. Categorize the Phases of transportation model. Level 4 Analysing
5. Construct the basic feasible solution for the following
transportation problem.
1 2 3 4 SUPPLY
1 2 3 11 7 6
2 1 0 6 1 1
3 5 8 15 9 10
DEMAN D 7 5 3 2
Level 5 Evaluating
6 Interpret the need for Optimum solution in transportation. Level 6 Creating
7. What do you mean by Least cost method (LCM)? Level 1 Remembering
8. Compare Vogel approximation method (VAM) & Least Cost
Method.
Level 2 Understanding
9. How do you represent a travelling salesman problem
through mathematical formulation?
Level 3 Applying
10. Analyse the rules of travelling salesman Problem. Level 4 Analysing
11. Discuss the meaning of Assignment Level 5 Evaluating
12. Compare Balanced assignment problem & Unbalanced
Assignment Problem.
Level 6 Creating
13. What example can you give for Unbalanced assignment
problem?
Level 1 Remembering
14. How will you resolve degeneracy in Transportation Problem? Level 2 Understanding
15. Classify transportation problem. Level 3 Applying
16. Examine the Steps in Hungarian algorithm. Level 4 Analysing
17. What is Branch and bound algorithm in Assignment? Level 1 Remembering
18. Compare Assignment and transportation Problem. Level 2 Understanding
19. What do you mean by Travelling Salesman Problem? Level 1 Remembering
20. What is Restricted Assignment? Level 1 Remembering
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Solve and find the Transportation Problem and Which method will
you select if you want toMinimize Cost?
Destination Supply
1 2 3 4
I 21 16 25 13 11
II 17 18 14 23 13
III 32 27 18 41 19
Demand 6 10 12 15
Level 1 Remembering
2. Find the Initial Basic Feasible solution for following TP. Using NW
Rule, LCM, and VAM. Which method will you select if you want to
Minimize Cost?
D1 D2 D3 Supply
S1 7 3 2 2
S2 2 1 3 3
S3 3 4 6 5
Demand 4 1 5 10
Level 2 Understanding
3.
(i)
Analyze the transportation problem with unit transportation
costs,demand, and supply as given below:
Destination
Supply
Source
D1 D2 D3 D4
S1
6 1 9 3
70
11 5 2 8
S2 55
10 12 4 7
S3
70
Demand 85 35 50 45
Apply VAM for Initial solution.
(5)
Level 3 Applying
(ii)
Construct the final Solution by using MODIMethod.
(8)
4.
(i)
Analyze & solve the following transportation problem to maximize
profit.
A B C D Supply
1
Source 2
3
Demand
15 51 42 33 23
80 42 26 81 44
90 40 66 60 33
23
31
16
30
100
Examine Initial solution using VAM.
(5)
Level 4 Analysing
(ii)
Analyze and find out the final Solution by using MODI Method.
(8)
5. Solve the following transportation problem using Vogel?s
method
Factory? Warehouse ?Available
A B C D E F
1 9 12 9 6 9 10 5
2 7 3 7 7 5 5 6
3 6 5 9 11 3 11 2
4 6 8 11 2 2 10 9
4 4 6 2 4 2
Requirement?
(5)
Level 5 Evaluating
6. (i) Solve the transportation problem and decide using VAM for initial
solution.
(5) Level 6 Creating
(ii) Evaluate using NWC and Least Cost method for initial solution?
Destination Supply
I 2 1 25 13 11
II 1 1 14 23 13
III 3 2 18 41 19
Demand 6 1 22 15
(8)
7.
Maximize profit from the following transportationproblem.
A B C D Supply
I 40 25 22 33 100
SourceII 44 35 30 30 30
III 38 38 28 30 70
Demand 40 20 60 30
Level 1 Remembering
(i) How will you convert maximization problem to minimization.
Find the maximum profit
(8)
(ii) Explain stepping stone method for checking the
solution for optimality transportation problems.
(5)
8. A company has one surplus truck in each of the cities A, B, C, D, &
E and one deficit trucks in each of the cities 1,2,3,4,5,6. The
distance between the cities in kms is shown in the matrix below.
Can you select the assignment of trucks from cities in surplus to
cities in deficiency .so that total distance covered by the vehicles is
minimum?
1 2 3 4 5 6
A 12 10 15 22 18 8
B 10 18 25 15 16 12
C 11 10 3 8 5 9
D 6 4 10 13 13 12
E 8 12 11 7 13 10
Level 2 Understanding
9.
Consider the problem of assigning five jobs to five persons. The
assignment costs are given as follows:
PERSONS?JOBS ?
1 2 3 4 5
A 8 4 2 6 1
B 0 9 5 5 4
C 3 8 9 2 6
D 4 3 1 0 3
Level 3 Applying
E 9 5 8 9 5
Determine the optimum assignment schedule.
10. The assignment cost of assigning any one operator to any one
machine is given in the following table.
MACHINE?OPERATORS ?
I II III IV
A 10 5 13 15
B 3 9 18 3
C 10 7 3 2
D 5 11 9 7
Find the optimal assignment by Hungarian method.
Level 4 Analysing
11. A machine shop purchased a drilling machine and two lathes of
different capacities. The Positioning of the machines among 4
possible locations on the shop floor is important forms the
standard of materials handling. Given the cost estimate per unit
time of materials below, find the optimum location of the
machines.
LOCATIONS
1 2 3 4
Lathe 1 12 9 12 9
Drill 15 Not
suitable
13 20
Lathe 2 4 8 10 6
Level 1 Remembering
12.
Solve the assignment problem for maximization given profit
matrix(profit in rupees).
Machines
P Q R S
JOB
51 53 54 50
47 50 48 50
49 50 60 61
63 64 60 60
Level 2 Understanding
PART - C
S.No Questions Marks BT
Level
Competence
1.
a
Assume that you are an OR specialist. Identify the procedure
for each of the following Method to the employees in order to
help them achieve solution to Transportation Problems.
Northwest Corner Cell Method
(3)
Level 1 Remembering
b Least Cost cell Method (4)
c Vogel?s Approximation Method (4)
d U V Method. (4)
13. The processing time in hours for the jobs when allocated to the
different machines is indicated below. Select the best assignment
of the machines for the jobs so that the total processing time is
Minimum.
Machines
M1 M2 M3 M4 M5
J1 9 22 58 11 19
JOB J2 43 78 72 50 63
J3 41 28 91 37 45
J4 74 42 27 49 39
J5 36 11 57 22 25
Level 4 Analysing
14. For the given travelling salesman problem, Minimize the total cost.
To
1 2 3 4
From A - 46 16 40
B 41 - 50 40
C 82 32 - 60
D 40 40 36 -
Level 1 Remembering
(i) Observe the above travelling salesman
problem and find out minimize the cost per
cycle.
(8)
(ii) Find whether path is satisfied. (5)
2.
Solve the following transportation problem, in which a
i
is the
availability at Origin
O
i
and b
j
is the requirement at the destination D
j
and cell entries
are unit costs of transportation from any origin to any
destination:
D1 D2 D3 D4 D5 a
j
O1 4 7 3 8 2 4
O2 1 4 7 3 8 7
O3 7 2 4 7 7 9
O4 4 8 2 4 7 2
b
j
8 3 7 2 2
Predict the allocation to minimize the cost.
Level 2 Understanding
3. A company has a team of 4 Salesman and the company wants to
do in 4 districts. Considering the capabilities of salesmen
and nature of the district, the company has estimated the profit per
day in Rs. For each salesmen in each district as follows.
District
s
Salesmen 1 2 3 4
A 16 10 14 11
B 14 11 15 15
C 15 15 13 12
D 13 12 14 15
Develop the best assignment schedule and analyze the total cost.
Level 3 Applying
4. Five operators have to be assigned to Five Machines. The
assignment costs are given in thetablebelow.
Analyse using Hungarian algorithm & find out the assignment to
minimize the cost.
Machine
I II III IV V
Operator
A 5 5 - 2 6
B 7 4 2 3 4
C 9 3 5 - 3
D 7 2 6 7 2
E 6 5 7 9 1
Level 4 Analyzing
UNIT ? III ? INTEGER PROGRAMMING AND GAME THEORY
SYLLABUS: Integer Programming ? Introduction and types - Game Theory-Two-person Zero sum
games-Saddle point, Dominance Rule, graphical and LP solutions, Nash Equilibrium
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. What do you mean by integer programming problem?
Level 1 Remembering
2. In what respect a mixed IPP differs from pure IPP?
Level 2 Understanding
3. What is Nash Equilibrium?
Level 3 Applying
4. Classify the different types of strategy.
Level 4 Analysing
5. Compile the Characteristics of game.
Level 5 Evaluating
6. Can you assess the applications of integer
programming?
Level 6 Creating
7. Define Game.
Level 1 Remembering
8. Compare Mixed Strategy and Pure Strategy.
Level 2 Understanding
9. How would you make use of the concept of Game theory
in Managerial Decision Making?
Level 3 Applying
10. Conclude your understanding about Payoff Matrix.
Level 4 Analysing
11. How will you find the optimal strategies and value of the
following game?
Player B
Player
A
H T
H 2 -1
T -1 0
Level 5 Evaluating
12. Interpret the concept of two person zero sum game.
Level 6 Creating
13. What is Saddle point?
Level 1 Remembering
14. Compare Dominance Principle of Rows and Columns.
Level 2 Understanding
15. Identify the basic assumptions of the Game.
Level 3 Applying
16. Conclude the advantages of Game theory.
Level 4 Analysing
17. What are the Methods of Matrices?
Level 1 Remembering
18. Summarize how graphs and LP solution are used in
Game theory.
Level 2 Understanding
19. What is a Decision Tree?
Level 1 Remembering
20. Define Dominance principle.
Level 1 Remembering
S.N
O
PART - B QUESTIONS MA
RK
S
BT
LEVEL
COMPETENCE
1. (i) What do you mean by Pure IPP? (3) Level 1 Remembering
(ii) What do you mean by Mixed IPP? (5)
(iii)
List out the difference between Pure and Mixed IPP.
(5)
2. (i) For what value of ?,the game with the following
matrix is strictly determined
B
1
B
2
B
3
A
1
? 6 2
A
2
-1 ? -7
A
3
-2 4 ?
(8) Level 2 Understanding
(ii) Write down the assumptions of game theory. (5)
3. (i) Solve the game whose pay-off matrix is given by
B
1
B
2
B
3
A
1
1 3 1
A
2
0 -4 -3
A
3
1 5 -1
(8)
Level 3 Applying
(ii) Explain the concept of Nash Equilibrium. (5)
4.
Analyze the Value of the game graphically
B1 B2
A1 4 4
A2 2 7
A3 5 3
A4 6 2
Level 4 Analysing
5.
What inference can be made using Dominance
Principle to reduce the following game and estimate
the game value?
B1 B2 B3 B4
A1 3 2 4 0
A2 3 4 2 4
A3 4 2 2 0
A4 2 1 6 3
Level 5 Evaluating
6.
How would you evaluate the following game whose
Pay-Off matrix is Given Below?
9 3 1 8 0
6 5 4 6 7
2 4 3 3 8
5 6 2 2 1
Level 6 Creating
7.
(i)
Two players A&B match coins. If the coins match
then A wins one unit value, if the coins do not
match then B wins one unit of value.
Determine pay-off matrix which strategy is to be
chosen
(5)
Level 1 Remembering
(ii)
Find the value of game. (8)
8.
Predict the Value of the Game given above Pay
OffMatrix.
Player B
B1 B2 B3
A1 -2 5 -3
Player A A2 1 3 5
A3 -3 -7 11
Level 2 Understanding
9.
Apply graphical analysis to Solve the game.
A/
B
B1 B2 B3 B4
A1 3 3 4 0
A2 5 4 3 7
Level 3 Applying
10. Solve the following game by graphical method.
Player B
1 2 3
1 6 4 3
Player A 2 2 4 8
Level 4 Analysing
11.
(i)
A and B play a Match(Game) in which each has 3
coins 5 paise, 10 paise and 20 paise. Each player
selects a coin without the knowledge of others
choice. IF the sum is even, B wins A?s Coin. If sum
is Odd, A wins B?s coin.
How will you find the pay-off matrix ?
(5)
Level 1
Remembering
(ii)
Find the Best Strategy & value of the Game. (8)
12.
Consider the Pay Off Matrix of player A as shown in
the table below and solve it optimally using the
graphical method .
Player A
Player
B
1 2 3 4 5
1 3 6 8 4 4
2 -7 4 2 10 2
Level 2 Understanding
13.
(i)
Analyze the Game Graphically:
Player A
Player
A
B1 B2
A1 -3 1
A2 5 3
A3 6 -1
A4 1 4
A5 2 2
A6 0 -5
Plot the graph
(5)
Level 4 Analysing
(ii)
Analyse and find the value of the game.
(8)
14.
Which one is the best strategy using Dominance
Principle?
B1 B2 B3 B4 B5 B6
A1
4 2 0 2 1 1
A2
4 3 1 3 2 2
A3
4 3 7 -5 1 2
A4
4 3 4 -1 2 2
A5
4 3 3 -2 2 2
Level 1 Remembering
PART-C
S.No Questions BT
Level
Competence
1.
Using Dominance property Solve.
B
A
I II IIIIV
1 -5 3 1 20
2 5 5 4 6
3 -4 -2 0 -5
Level 1 Remembering
2. Examine the 2 * n Game by the Method of Sub Game:
B1 B2 B3
A1 1 3 11
A2 8 5 2
Level 2 Understanding
3. In a game of matching coins with 2 players, A wins 1 unit value
when there are 2 heads, wins nothing when there are 2 tails
and looses ? unit value when there are one head and one tail.
Develop Pay Off matrix and value of the game.
Level 3 Applying
4.
i
ii
iii
Assume you have to choice of 3 strategies for advertising
and you have one major
Analyse the theory on Two-person sum games competitor
with 3 strategies.
(5)
Level 4 Analysing
What are the assumptions of Game? (5)
Find value of game.
B1 B2 B3
A1 80 70 60
A2 90 80 100
A3 40 30 40
(5)
UNIT - IV INVENTORY MODELS, SIMULATION AND DECISION THEORY
SYLLABUS: Inventory Models ? EOQ and EBQ Models (With and without shortages), Quantity Discount
Models. Decision making under risk ? Decision trees ? Decision making under uncertainty. Monte-carlo
simulation.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define inventory. Level 1 Remembering
2.
Classify the Forms of inventory.
Level 2 Understanding
3.
Identify the Objectives/significance of inventory model.
Level 3 Applying
4.
Highlight the importance of Reorder level.
Level 4 Analysing
5.
Discuss the concept of Lead time.
Level 5 Evaluate
6.
Interpret the Types of stock replenishment.
Level 1 Remembering
7.
List the Basic inventory models.
Level 2 Understanding
8.
Compare Ordering Cost and Carrying Cost.
Level 3 Appyling
9.
Identify when shortage cost and stock out cost arises?
Level 5 Evaluating
10.
Analyze why safety stock is maintained.
Level 1 Remembering
11.
Discuss the concept of Quantity Discount Model.
Level 2 Understanding
12.
Interpret the meaning of EOQ & EBQ.
Level 3 Applying
13.
What are random and pseudo random numbers?
Level 4 Analysing
14.
Explain Monte Carlo Method.
Level 5 Evaluating
15.
Summarize the concept of EMV.
Level 1 Remembering
16.
What inference can you make about holding cost ?
Level 2 Understanding
17.
What is Shortage Cost?
Level 3 Applying
18. Classify and explain the various conditions under which
decisions are made.
Level 1 Remembering
19. What is meant by the following terms in inventory
management: i)Carrying cost ii) shortage costs
Level 2 Understanding
20. What is Decision theory? List the problems that can be solved
by Simulation.
Level 3 Applying
S.NO PART - B QUESTIONS Marks BT
LEVEL
COMPETENCE
1.
(i)
Alpha industry needs 5400 units per year of a bought out
component which will be
used in its main product. The ordering cost is Rs.250
per order and the carrying cost per unit per year is
Rs.30.
Which is the best order quantity?
(8)
Level 1 Remembering
(ii)
Find the number of order per year and Frequency of
orders?
(5)
2.
(i)
A stockiest has to supply 12000 units of a product per
year to his customer. Demand is
fixed and known. Shortage cost is assumed to be
infinite. Inventory holding cost is 20 paise per unit per
month. Ordering Cost is Rs. 250 and purchase price
is Rs.10 per unit.
Estimate the EOQ
(8)
Level 2 Understanding
(ii)
Find the Frequency of orders and total inventory cost. (5)
3.
ABC manufacturing company purchases 9000 parts of a
machine for its annual requirement. Each part costs
Rs.20. The ordering cost per order is Rs.15 and the
carrying charges are 15% of the average inventory per
year. Apply EOQ formulae and find out EOQ, No of
orders ,Total Inventory Cost and total cost.
Level 3 Applying
4.
(i)
Demand for an item in a company is 18,000 units per
year. The company can produce the items at a rate of
3000 units per month. The Cost of one setup is Rs.500
and the holding cost of one unit per month is 15 paise.
Shortage cost of one unit is Rs.20 per year.
Analyze and find the optimum manufacturing quantity.
(8)
Level 4 Analysing
(ii)
Find the number of shortages and frequency of
Production run.
(5)
5. A company has a demand of 12000 units/year for an
item and it can produce 2000 units per month. The
cost of one setup is Rs.400 and the holding
cost/unit/month is 15 paise. Select the optimum lot
size and total cost per year assuming the cost of 1 unit
as Rs.4. Find EBQ, the number of set ups & total cost.
Level 5 Evaluating
6.
(i)
Find the optimal order quantity for a product when the
annual demand for the product is 500 units. The Cost of
storage per unit per year is 10% of the unit cost. Ordering
cost per order is Rs. 180.
Determine EOQ
(8)
Level 6 Creating
(ii)
Evaluate the Total Cost
(5)
The unit cost are given below:
Quantity Unit Cost(Rs.)
O
1500<=Q3<3000 24.60
3000<=Q4 24.40
7. (i)
Formulate the Optimal order quantity for a product for
which the price breaks are as follows
(8)
Level 1 Remembering
(ii)
Also find the Total cost.
Quantity Unit Cost(Rs.)
O
750<=Q 875
(5)
8.
Compute the EOQ and the total variable cost for the
following:
Annual demand: 25 units
Unit price: Rs.2.50
Order cost: Rs.4.00
Storage rate: 1% per year
Level 2 Understand
9.
(i)
Identify the profit under three states of nature & three
decision alternative.
State of
Nature
State of
Nature
State of
Nature
N1 N2 N3
Decision
Naking
D1 150 250 300
Decision
Naking
D2 450 250 200
Decision
Naking
D3 100 180 290
Hurwitz criterion for alpha=0.5
(3)
Level 3 Applying
(ii)
Laplace condition
(5)
(iii)
Minimax Condition
(5)
10.
A Bakery keeps a stock of particular brand of cake. Daily
demand of past experience.
Daily
demand
0 15 25 35 45 50
Probability 0.01 0.15 0.20 0.50 0.12 0.02
Consider the following sequence of random numbers.
48 78 9 51 56 77 15 14 68 9
Using this sequence simulate the demand for next 10
days.
Find the stock situation if the owner makes 35 cakes
every day. Examine the daily average demand.
Level 1 Remembering
11.
Given above is the following pay off matrix.
Using EMV criterion . Decide which of the act can be
chosen at the best. FindEVPI & EOL.
Nature
Probability
Don?t
Expand
Expand
200
Expand
400
High
Demand
0.4 2500 3500 5000
Medium
Demand
0.4 2500 3500 2500
Low
Demand
0.2 2500 1500 1000
Level 2 Understanding
12.
A sample of 100 arrivals of customers at a retail sales
depot is according to the following distribution.
Time between arrivals(mins) Frequency
0.5 2
1.0 6
1.5 10
2.0 25
2.5 20
3.0 14
3.5 4
4.0 7
4.5 4
5.0 2
Use random numbers and predict the average time
between arrivals.
48 78 9 51 56 77 15 14 68 9
Level 3 Applying
13.
(i)
A departmental store purchases sprays which can be
ordered only in lots of 10. Each spray cost Rs.75 and
sells at Rs.90 each. Used sprays, however have \no
salvage value.
Demand 10 20 30 40 50
Probability 0.2 0.35 0.25 0.15 0.05
The probability distribution obtained from analysis of past
sales data is given below.
Analyse the payoff table.
(5)
Level 4 Analysing
(ii) How much quantity should the departmental store buy to
maximize its profit?
(8)
14. (i)
A company uses annually 50,000 units of an item each
costing Rs.1.20. Each order costs Rs.45 and inventory
carrying costs are 15% of the annual average inventory
value.
Find EOQ.
(3)
Level 2 Understanding
(ii) If the company operates 250 days a year and the
procurement time is 10 days and safety stock is 500
units, find reorder level, maximum, minimum and
average inventory
(10)
PART - C
S.No Questions BT
Level
Competence
1.
A contractor has to supply 10000 bearings per day to an
automobile manufacturer. He finds that when he starts a
production run he can produce 25000 bearings per day. The
cost of holding a bearing in stock for one year is 2 paise and
the set up cost of the production run is Rs.18. How frequently
should production run be made and which is the Best
Economic Batch Quantity? How much would be the No. of
Setup and Total Inventory Cost.
Level 1 Remembering
2.
A stockist has to supply 400 units of a product every
Monday to his customer.
He gets the product at Rs.50 per unit from the
manufacturer. The cost of ordering and transportation
from the manufacturer is Rs.75 per order. The cost of
carrying inventory is 7.5% per year of the cost of product.
Predict EOQ, Frequency of orders and Number of Orders,
Total Incremental cost and Total Cost.
Level 2 Understanding
3. (i) Identify the profit under three states of nature & three
decision alternative.
State of
Nature
N1 N2 N3
Decision
Making
D1 100 200 300
D2 400 200 200
D3 200 160 390
Hurwitz criterion for alpha=0.5
(5) Level 3 Applying
(ii)
Laplace Condition
(5)
(iii) Mininmax Condition (5)
4.
An automobile production line turns out about 100 cars a
day, but deviation occur owing to many causes. The
production is more accurately described by the
probability distribution given below;
Production/
Day
Probability
95 0.03
96 0.05
97 0.07
98 0.10
Level 4 Analysing
99 0.15
100 0.20
101 0.15
102 0.10
103 0.07
104 0.05
105 0.03
Use the random numbers &find the average demand
48 78 9 51 56 77 15 14 68 9
UNIT - V QUEUING THEORYAND REPLACEMENT MODELS
SYLLABUS:Queuing Theory ?Single and Multi-Channel models-infinite number of customers and
infinite calling resource Replacement Models-Individuals replacement Models (With and without time
value of money) ? Group Replacement Models.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define Queue.
Level 1 Remembering
2. How do you show your understanding on replacement theory?
Level 2 Understanding
3. In a bank, 20 customers on an average are served by a
cashier in an hour. If the service time has exponential
distribution, what is the probability that it will take more than
10 minutes to serve a customer?
Level 3 Applying
4. Classify the types of Queue.
Level 4 Analysing
5. How waiting time cost is related to queuing system?
Level 5 Evaluating
6. Interpret the Characteristics Of Queuing Models.
Level 4 Evaluating
7. How would you explain consumer behavior in queues?
Level 1 Remembering
8. Compare Serial and parallel Queue with Examples. Level 2 Understanding
9. Classify the types of Replacement model.
Level 3 Applying
10. Describe Kendall?s Notation for identifying a Queue Model with
single channel, Poisson arrivals, exponential service unlimited
queue and infinite calling population.
Level 4 Analysing
11. GRP includes IRP .Do You Agree?
Level 5 Evaluating
12. What is GRP &IRP?
Level 6 Creating
13. Distinguish between breakdown maintenance and preventive
maintenance.
Level 1 Remembering
14. How do you show your understanding on Little?s formula in
queuing theory?
Level 2 Understanding
15. Categorize Queue Discipline.
Level 3 Applying
16. Develop Kendall?s Notation of a Queue.
Level 4 Analysing
17. What is ?Collusion? in Queue Discipline?
Level 1 Remembering
18. Compare the Queue Length and No. of Customers in the System.
Level 2 Understanding
19. Distinguish between individual replacement and group
replacement?
Level 3 Applying
20. Describe Kendall?s Notation for identifying a Queue Model with
two channels, Poisson arrivals, exponential service Unlimited
Queue and infinite calling population.
Level 1 Remembering
S.No
PART - B QUESTIONS Marks
BT
LEVEL
COMPETENCE
1. The cost of machine is Rs.16, 00 and scrap value is
Rs.1,100. Maintenance Cost form for machine are as
follows:
Year 1 2 3 4 5 6 7 8
Maintenance
cost
300 459 600 800 100 1200 1500 2000
When should the machine be the replaced?
Level 1 Remembering
2.
The following table gives to cost of spares per year,
overhead cost of maintenance per year and resale value of
certain equipment whose purchase price is Rs. 50,000:
Illustrate when the machine can be replaced.
Year 1 2 3 4 5
Cost of Spares 10000 12000 14000 15000 17000
Overhead
Maintenance
Cost
5000 5000 6000 6000 8000
Resale Value 40000 32000 28000 25000 22000
Level 2 Understanding
3.
A Taxi owner estimates from his past records that the cost
per year for operating a taxi whose purchase price when
new is Rs.60,000 are as follows.
Age 1 2 3 4 5
Operating cost 10000 12000 15000 18000 20000
After 5 years the operating cost is Rs.6000 x K, Where ?k?
is 6,7,8,9,10(age). If the resale value decreases by 10% of
Level 3 Applying
purchase price each year, calculate the best time of
replacement if time value is not implemented?
4.
(i)
A cost of a machine is 6100 and its scrap value is Rs.
100. The maintenance Cost from the experience are as
follows:
Year 1 2 3 4 5 6 7 8
Maintenance
cost
100 250 400 600 900 1200 1600 2000
Examine the average cost of replacement
(8)
Level 4 Analysing
(ii) Analyze when the asset can be replaced (5)
5.
(i)
Week 1 2 3 4 5 6 7
Conditional
Probability
0.07 0.15 0.25 0.45 0.75 0.9 1
IRP
Co
st
is Rs.1.25 per item
GRP Cost is Rs.60 Paise Per item.
Estimate the IRP Cost
(5)
Level 5 Evaluating
(ii)
Predict GRP cost and Determine whether GRP or IRP is the
Best Policy
(8)
6.
Machine A Costs Rs.9000. Annual Operating Cost is
Rs.200 for the 1
st
year and then increases by 2000 every
year. Determine the best age at which to replace the
machine. Assume the machine has no resale value.
Machine B Costs Rs.10,000 . Annual operating cost is
Rs.400 for the 1
st
year and then increases by 800 every
year. No resale value. You have now a machine of type A
which is one year old. Conclude if M/c A can be replaced
by M/c B. Is so, When?
Level 6 Creating
7.
A manufacturer is offered two machines A and B. A has
cost price of Rs.2,500, its running cost is Rs. 400 for each
of first years and increased by Rs. 100 every subsequent
year, Taking money?s value as 10% per year, when
machine should be replaced?
Level 1 Remembering
8.
The maintenance cost and resale value per year of a
machine whose purchase price is Rs.7000 is given below :
Year Operating Cost Resale Value
1 900 400
2 1200 2000
3 1600 1200
4 2100 600
5 2800 500
6 3700 400
7 4700 400
8 5900 400
When should the machine be replaced ?
Level 2 Understanding
FirstRanker.com - FirstRanker's Choice
(An
?
DEPARTMENT OF MANAGEMENT STUDIES
QUESTION BANK
II SEMESTER
1915201? APPLIED OPERATIONS RESEACH
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Dr. Radha Ganesh Kumar ? Asst. Professor (Sel.G) and HOD
Mr.B. Sam Paul ? Asst. Professor (OG)
(An
? .
DEPARTMENT OFMANAGEMENT STUDIES
QUESTION BANK
SUBJECT :1915201 ?APPLIED OPERATIONS RESEACH
SEM / YEAR : IISemester / IYear
UNIT ? I ?INTRODUCTION TO LINEAR PROGRAMMING (LP)
SYLLABUS: Introduction to applications of operations research in functional areas of management.
Linear Programming-formulation, solution by graphical and simplex methods, Special cases. Dual
simplex method. Principles of Duality. Sensitivity Analysis.
PART- A
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Define Operations Research (OR). Level 1 Remembering
2. Differentiate between Simplex and Big M Method Level 2 Understanding
3. How do you show your understanding unbounded solution? Level 3 Applying
4. Categorize the forms of LPP. Level 4 Analysing
5.
Discuss why is two phase method is better than Big M
method?
Level 5 Evaluating
6. Interpret the usage of Sensitivity Analysis in LPP. Level 6 Creating
7. What are the assumptions and requirements of LPP? Level 1 Remembering
8. Compare Dual Simplex and Duality. Level 2 Understanding
9. Identify the Advantages of duality. Level 3 Applying
10. What do you think about Infeasible solution? Level 4 Analysing
11. How will you solve LPP graphically? Level 5 Evaluating
12.
Conclude your understanding on the mathematical
formulation of LPP.
Level 6 Creating
13. Define basic variables and artificial variables. Level 1 Remembering
14. Compare Slack variable & Surplus Variable. Level 2 Understanding
15.
Give some example for the role of Surplus variable & Slack
Variable in the simplex method
Level 3 Applying
16. How would you apply Artificial variable? Level 4 Analysing
17. What is Big M Method? Level 1 Remembering
18. Distinguish simplex and Big M method Level 2 Understanding
19.
What do you mean by Duality? List the Rules for primal and
dual.
Level 1 Remembering
20. What is Shadow price? Level 1 Remembering
PART- B
S.NO
QUESTIONS
BT
LEVEL
COMPETENCE
1.
(i)
Maximise Z=3x+4y subject to
2x+5y ?60,
4x+2y ?40.
x, y >0. Solve by Graphical Method
Plot the graph
(8)
Level 1 Remembering
(ii) Which one is the best solution? (5)
2.
(i)
Min Z= 20x
1
+10 x
2
subject to
x
1
+2x
2
? 40,
3x
1
+x
2
? 30,
4x
1
+3x
2
? 60,
x
1
,x
2
? 0.
Solve by Graphical Method,
Plot the graph
(8)
Level 2 Understanding
(ii) Predict the value of x & y. (5)
3 Max Z= 5x1+4x2 subject to
x
1
-2x
2
? 1,
x
1
+2x
2
?3,
x
1
,x
2
? 0. Solve Graphically. Which one is the best
solution?
Level 3 Applying
4.
(i)
A Plant Manufacturer 2 Product A & B. The Profit Contribution
of each product has been estimated as Rs.300 for product A
and Rs.400 for Product B. Each Product passes through 3
departments of the plant. The time required for each product
and total time available in each department is as follows.
Department Hours
Required
Hours
Required
Available
Hours
during
month
Product
A
Product
B
I 2 3 1600
II 3 2 1500
III 1 1 700
The company has a contract to supply atleast 300 units of
Product B per month.
Formulate the LPP
(5)
Level 4
Analysing
(ii) Solve through Graphical Method
(8)
5. Solve the following LPP by graphical method.
Maximize Z= 3x
1
+2x
2
Subject t o
- 2x
1
+x
2
?1,
x
1
? 2,
x
1
+ x
2
? 3
and x
1
,x
2
? 0
Level 5 Evaluating
6. (i) Max Z= 1000x
1
+4000x
2
+5000x
3
Subject to 3x1+3x
3
?22,
x1+2x2+3x
3
? 14,
3x1+2x2 ? 14
& x1,x2 ? 0
Develop a Simplex Table
(5)
Level 6 Creating
(ii) Analyse and find the value of x
1
, x
2
? (8)
7. Analyze the following LPP by Simplex Method:
Min Z = -10y
1
-15y
2
-20y
3
Subject to 2y
1
+4y
2
+6y
3
? 24,
3y
1
+9y
2
+6y
3
? 30,
& y
1
, y
2
, y
3
? 0.
Level 1 Remembering
(i)
Develop a Simplex Table (5)
(ii) Solve and find the value of y1 ,y2 and y3
(8)
8.
Solve By Graphical Method
Minimize Z= 40x
1
+24x
2
Subject to, 20x
1
+50 x
2
> 4,800
80 x
1
+50x
2
> 7,200
x
1
,x
2
>0
Level 2 Understanding
9. Solve the following LPP by simplex method:
Minimize Z= 8x
1
-2x
2
Subject to -4x
1
+2x
2
?1,
5x
1
-4x
2
?3,
and x
1
,x
2
? 0
Level 3 Applying
10. Solve the following LPP by simplex method:
Maximize Z= 3x1+2x
2
Subject to
2x
1
+x
2
?2,
3x
1
+4x
2
?12,
x
1
,x
2
? 0
Level 4 Analyzing
11. Review the LPP and solve by simplex method
Max Z= 25x+10y
Subject to the constraints
x+0.5y? 20
x+y? 50
x,y ? 0
Level 1 Remembering
12. A firm produces three products. These products are
processors on 3 different machines. The time required for
manufacturing one unit of cost of the products and the daily
capacity of the three machines is given in the table below.
Analyse and find the optimum solution.
Mac
hine
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Machine
Capacity
Min /Day
Product1 Product 2 Product 3
M1 2 8 2 940
M2 4 - 8 970
M3 2 5 - 430
It is required to determine the daily no. of units to be
manufactured for each product. The profit for unit for
Level 2 Understanding
product 1,2,3 is Rs.4,Rs.8,Rs.6 respectively. It is assumed
that all the amount produced are consumed in the market
13. Using dual simplex method , solve and find the optimum
solution for the given LPP.
Maximize Z=6x
1
+4x
2
+4x
3
Subject to 3x
1
,x
2
+2x
3
? 2
2x
1
+x
2
-x
3
? 1
-x
1
+x
2
+2x
3
? 1 &
x
1
,x
2
,x
3
? 0
Level 4 Analysing
14.
(i)
Evaluate by using dual simplex method and solve the LPP.
Minimize Z=2x
1
+x
2
Subject to 3x
1
+2x
2
? 3
4x
1
+3x
2
? 6
x
1
+x
2
? 5 & x
1
,x
2
?
Determine the dual simplex table
(5)
Level 1 Remembering
(ii)
Find the value of x
1
, x
2
(8)
PART - C
S.No Questions BT
LEVEL
COMPETENCE
1.
Max Z=300x+400y subject to
2x+3y ? 1600,
3x+2y ? 1500,
x+y ? 700,
y ? 300, x,y ? 0 Solve by Graphical Method, choose the
value of x & y which maximizes profit.
Level 1 Remembering
2. Solve the following LPP by graphical method.
Minimize Z= 6000x1+4000x
2
Subject t o
3x+x
2
? 40,
x
1
+2.5 x
2
? 22
3x
1
+3 x
2
? 40
and x
1
,x
2
? 0
Level 2 Understanding
3. Develop a Simplex Table and Solve
Max Z = 3 x1+2 x2,
Subject to
x1+ x2 ?4,
x1- x2 ? 2;
x1, x2 ?0.
Level 3 Applying
4. Solve by using Simplex Method.
Maximize Z= 3x+5y
Subject to the constraints
x+y? 60
x? 40
y ? 30
x,y ? 0
Level 1 Remembering
UNIT - II LINEAR PROGRAMMING EXTENSIONS
SYLLABUS: Transportation Models (Minimizing and Maximizing Problems) ? Balanced and unbalanced
Problems ? Initial Basic feasible solution by N-W Corner Rule, Least cost and Vogel?s approximation methods.
Check for optimality. Solution by MODI /. Case of Degeneracy. Trans-shipment Models. Assignment Models
(Minimising and Maximising Problems) ? Balanced and Unbalanced Problems. Solution by Hungarian and
Branch and Bound Algorithms. Travelling Salesman problem.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define Transportation & Transhipment. Level 1 Remembering
2. Differentiate balanced transportation problem & Unbalanced
Transportation Problem.
Level 2 Understanding
3. How would you show your understanding on unbalanced
transportation problem?
Level 3 Applying
4. Categorize the Phases of transportation model. Level 4 Analysing
5. Construct the basic feasible solution for the following
transportation problem.
1 2 3 4 SUPPLY
1 2 3 11 7 6
2 1 0 6 1 1
3 5 8 15 9 10
DEMAN D 7 5 3 2
Level 5 Evaluating
6 Interpret the need for Optimum solution in transportation. Level 6 Creating
7. What do you mean by Least cost method (LCM)? Level 1 Remembering
8. Compare Vogel approximation method (VAM) & Least Cost
Method.
Level 2 Understanding
9. How do you represent a travelling salesman problem
through mathematical formulation?
Level 3 Applying
10. Analyse the rules of travelling salesman Problem. Level 4 Analysing
11. Discuss the meaning of Assignment Level 5 Evaluating
12. Compare Balanced assignment problem & Unbalanced
Assignment Problem.
Level 6 Creating
13. What example can you give for Unbalanced assignment
problem?
Level 1 Remembering
14. How will you resolve degeneracy in Transportation Problem? Level 2 Understanding
15. Classify transportation problem. Level 3 Applying
16. Examine the Steps in Hungarian algorithm. Level 4 Analysing
17. What is Branch and bound algorithm in Assignment? Level 1 Remembering
18. Compare Assignment and transportation Problem. Level 2 Understanding
19. What do you mean by Travelling Salesman Problem? Level 1 Remembering
20. What is Restricted Assignment? Level 1 Remembering
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Solve and find the Transportation Problem and Which method will
you select if you want toMinimize Cost?
Destination Supply
1 2 3 4
I 21 16 25 13 11
II 17 18 14 23 13
III 32 27 18 41 19
Demand 6 10 12 15
Level 1 Remembering
2. Find the Initial Basic Feasible solution for following TP. Using NW
Rule, LCM, and VAM. Which method will you select if you want to
Minimize Cost?
D1 D2 D3 Supply
S1 7 3 2 2
S2 2 1 3 3
S3 3 4 6 5
Demand 4 1 5 10
Level 2 Understanding
3.
(i)
Analyze the transportation problem with unit transportation
costs,demand, and supply as given below:
Destination
Supply
Source
D1 D2 D3 D4
S1
6 1 9 3
70
11 5 2 8
S2 55
10 12 4 7
S3
70
Demand 85 35 50 45
Apply VAM for Initial solution.
(5)
Level 3 Applying
(ii)
Construct the final Solution by using MODIMethod.
(8)
4.
(i)
Analyze & solve the following transportation problem to maximize
profit.
A B C D Supply
1
Source 2
3
Demand
15 51 42 33 23
80 42 26 81 44
90 40 66 60 33
23
31
16
30
100
Examine Initial solution using VAM.
(5)
Level 4 Analysing
(ii)
Analyze and find out the final Solution by using MODI Method.
(8)
5. Solve the following transportation problem using Vogel?s
method
Factory? Warehouse ?Available
A B C D E F
1 9 12 9 6 9 10 5
2 7 3 7 7 5 5 6
3 6 5 9 11 3 11 2
4 6 8 11 2 2 10 9
4 4 6 2 4 2
Requirement?
(5)
Level 5 Evaluating
6. (i) Solve the transportation problem and decide using VAM for initial
solution.
(5) Level 6 Creating
(ii) Evaluate using NWC and Least Cost method for initial solution?
Destination Supply
I 2 1 25 13 11
II 1 1 14 23 13
III 3 2 18 41 19
Demand 6 1 22 15
(8)
7.
Maximize profit from the following transportationproblem.
A B C D Supply
I 40 25 22 33 100
SourceII 44 35 30 30 30
III 38 38 28 30 70
Demand 40 20 60 30
Level 1 Remembering
(i) How will you convert maximization problem to minimization.
Find the maximum profit
(8)
(ii) Explain stepping stone method for checking the
solution for optimality transportation problems.
(5)
8. A company has one surplus truck in each of the cities A, B, C, D, &
E and one deficit trucks in each of the cities 1,2,3,4,5,6. The
distance between the cities in kms is shown in the matrix below.
Can you select the assignment of trucks from cities in surplus to
cities in deficiency .so that total distance covered by the vehicles is
minimum?
1 2 3 4 5 6
A 12 10 15 22 18 8
B 10 18 25 15 16 12
C 11 10 3 8 5 9
D 6 4 10 13 13 12
E 8 12 11 7 13 10
Level 2 Understanding
9.
Consider the problem of assigning five jobs to five persons. The
assignment costs are given as follows:
PERSONS?JOBS ?
1 2 3 4 5
A 8 4 2 6 1
B 0 9 5 5 4
C 3 8 9 2 6
D 4 3 1 0 3
Level 3 Applying
E 9 5 8 9 5
Determine the optimum assignment schedule.
10. The assignment cost of assigning any one operator to any one
machine is given in the following table.
MACHINE?OPERATORS ?
I II III IV
A 10 5 13 15
B 3 9 18 3
C 10 7 3 2
D 5 11 9 7
Find the optimal assignment by Hungarian method.
Level 4 Analysing
11. A machine shop purchased a drilling machine and two lathes of
different capacities. The Positioning of the machines among 4
possible locations on the shop floor is important forms the
standard of materials handling. Given the cost estimate per unit
time of materials below, find the optimum location of the
machines.
LOCATIONS
1 2 3 4
Lathe 1 12 9 12 9
Drill 15 Not
suitable
13 20
Lathe 2 4 8 10 6
Level 1 Remembering
12.
Solve the assignment problem for maximization given profit
matrix(profit in rupees).
Machines
P Q R S
JOB
51 53 54 50
47 50 48 50
49 50 60 61
63 64 60 60
Level 2 Understanding
PART - C
S.No Questions Marks BT
Level
Competence
1.
a
Assume that you are an OR specialist. Identify the procedure
for each of the following Method to the employees in order to
help them achieve solution to Transportation Problems.
Northwest Corner Cell Method
(3)
Level 1 Remembering
b Least Cost cell Method (4)
c Vogel?s Approximation Method (4)
d U V Method. (4)
13. The processing time in hours for the jobs when allocated to the
different machines is indicated below. Select the best assignment
of the machines for the jobs so that the total processing time is
Minimum.
Machines
M1 M2 M3 M4 M5
J1 9 22 58 11 19
JOB J2 43 78 72 50 63
J3 41 28 91 37 45
J4 74 42 27 49 39
J5 36 11 57 22 25
Level 4 Analysing
14. For the given travelling salesman problem, Minimize the total cost.
To
1 2 3 4
From A - 46 16 40
B 41 - 50 40
C 82 32 - 60
D 40 40 36 -
Level 1 Remembering
(i) Observe the above travelling salesman
problem and find out minimize the cost per
cycle.
(8)
(ii) Find whether path is satisfied. (5)
2.
Solve the following transportation problem, in which a
i
is the
availability at Origin
O
i
and b
j
is the requirement at the destination D
j
and cell entries
are unit costs of transportation from any origin to any
destination:
D1 D2 D3 D4 D5 a
j
O1 4 7 3 8 2 4
O2 1 4 7 3 8 7
O3 7 2 4 7 7 9
O4 4 8 2 4 7 2
b
j
8 3 7 2 2
Predict the allocation to minimize the cost.
Level 2 Understanding
3. A company has a team of 4 Salesman and the company wants to
do in 4 districts. Considering the capabilities of salesmen
and nature of the district, the company has estimated the profit per
day in Rs. For each salesmen in each district as follows.
District
s
Salesmen 1 2 3 4
A 16 10 14 11
B 14 11 15 15
C 15 15 13 12
D 13 12 14 15
Develop the best assignment schedule and analyze the total cost.
Level 3 Applying
4. Five operators have to be assigned to Five Machines. The
assignment costs are given in thetablebelow.
Analyse using Hungarian algorithm & find out the assignment to
minimize the cost.
Machine
I II III IV V
Operator
A 5 5 - 2 6
B 7 4 2 3 4
C 9 3 5 - 3
D 7 2 6 7 2
E 6 5 7 9 1
Level 4 Analyzing
UNIT ? III ? INTEGER PROGRAMMING AND GAME THEORY
SYLLABUS: Integer Programming ? Introduction and types - Game Theory-Two-person Zero sum
games-Saddle point, Dominance Rule, graphical and LP solutions, Nash Equilibrium
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. What do you mean by integer programming problem?
Level 1 Remembering
2. In what respect a mixed IPP differs from pure IPP?
Level 2 Understanding
3. What is Nash Equilibrium?
Level 3 Applying
4. Classify the different types of strategy.
Level 4 Analysing
5. Compile the Characteristics of game.
Level 5 Evaluating
6. Can you assess the applications of integer
programming?
Level 6 Creating
7. Define Game.
Level 1 Remembering
8. Compare Mixed Strategy and Pure Strategy.
Level 2 Understanding
9. How would you make use of the concept of Game theory
in Managerial Decision Making?
Level 3 Applying
10. Conclude your understanding about Payoff Matrix.
Level 4 Analysing
11. How will you find the optimal strategies and value of the
following game?
Player B
Player
A
H T
H 2 -1
T -1 0
Level 5 Evaluating
12. Interpret the concept of two person zero sum game.
Level 6 Creating
13. What is Saddle point?
Level 1 Remembering
14. Compare Dominance Principle of Rows and Columns.
Level 2 Understanding
15. Identify the basic assumptions of the Game.
Level 3 Applying
16. Conclude the advantages of Game theory.
Level 4 Analysing
17. What are the Methods of Matrices?
Level 1 Remembering
18. Summarize how graphs and LP solution are used in
Game theory.
Level 2 Understanding
19. What is a Decision Tree?
Level 1 Remembering
20. Define Dominance principle.
Level 1 Remembering
S.N
O
PART - B QUESTIONS MA
RK
S
BT
LEVEL
COMPETENCE
1. (i) What do you mean by Pure IPP? (3) Level 1 Remembering
(ii) What do you mean by Mixed IPP? (5)
(iii)
List out the difference between Pure and Mixed IPP.
(5)
2. (i) For what value of ?,the game with the following
matrix is strictly determined
B
1
B
2
B
3
A
1
? 6 2
A
2
-1 ? -7
A
3
-2 4 ?
(8) Level 2 Understanding
(ii) Write down the assumptions of game theory. (5)
3. (i) Solve the game whose pay-off matrix is given by
B
1
B
2
B
3
A
1
1 3 1
A
2
0 -4 -3
A
3
1 5 -1
(8)
Level 3 Applying
(ii) Explain the concept of Nash Equilibrium. (5)
4.
Analyze the Value of the game graphically
B1 B2
A1 4 4
A2 2 7
A3 5 3
A4 6 2
Level 4 Analysing
5.
What inference can be made using Dominance
Principle to reduce the following game and estimate
the game value?
B1 B2 B3 B4
A1 3 2 4 0
A2 3 4 2 4
A3 4 2 2 0
A4 2 1 6 3
Level 5 Evaluating
6.
How would you evaluate the following game whose
Pay-Off matrix is Given Below?
9 3 1 8 0
6 5 4 6 7
2 4 3 3 8
5 6 2 2 1
Level 6 Creating
7.
(i)
Two players A&B match coins. If the coins match
then A wins one unit value, if the coins do not
match then B wins one unit of value.
Determine pay-off matrix which strategy is to be
chosen
(5)
Level 1 Remembering
(ii)
Find the value of game. (8)
8.
Predict the Value of the Game given above Pay
OffMatrix.
Player B
B1 B2 B3
A1 -2 5 -3
Player A A2 1 3 5
A3 -3 -7 11
Level 2 Understanding
9.
Apply graphical analysis to Solve the game.
A/
B
B1 B2 B3 B4
A1 3 3 4 0
A2 5 4 3 7
Level 3 Applying
10. Solve the following game by graphical method.
Player B
1 2 3
1 6 4 3
Player A 2 2 4 8
Level 4 Analysing
11.
(i)
A and B play a Match(Game) in which each has 3
coins 5 paise, 10 paise and 20 paise. Each player
selects a coin without the knowledge of others
choice. IF the sum is even, B wins A?s Coin. If sum
is Odd, A wins B?s coin.
How will you find the pay-off matrix ?
(5)
Level 1
Remembering
(ii)
Find the Best Strategy & value of the Game. (8)
12.
Consider the Pay Off Matrix of player A as shown in
the table below and solve it optimally using the
graphical method .
Player A
Player
B
1 2 3 4 5
1 3 6 8 4 4
2 -7 4 2 10 2
Level 2 Understanding
13.
(i)
Analyze the Game Graphically:
Player A
Player
A
B1 B2
A1 -3 1
A2 5 3
A3 6 -1
A4 1 4
A5 2 2
A6 0 -5
Plot the graph
(5)
Level 4 Analysing
(ii)
Analyse and find the value of the game.
(8)
14.
Which one is the best strategy using Dominance
Principle?
B1 B2 B3 B4 B5 B6
A1
4 2 0 2 1 1
A2
4 3 1 3 2 2
A3
4 3 7 -5 1 2
A4
4 3 4 -1 2 2
A5
4 3 3 -2 2 2
Level 1 Remembering
PART-C
S.No Questions BT
Level
Competence
1.
Using Dominance property Solve.
B
A
I II IIIIV
1 -5 3 1 20
2 5 5 4 6
3 -4 -2 0 -5
Level 1 Remembering
2. Examine the 2 * n Game by the Method of Sub Game:
B1 B2 B3
A1 1 3 11
A2 8 5 2
Level 2 Understanding
3. In a game of matching coins with 2 players, A wins 1 unit value
when there are 2 heads, wins nothing when there are 2 tails
and looses ? unit value when there are one head and one tail.
Develop Pay Off matrix and value of the game.
Level 3 Applying
4.
i
ii
iii
Assume you have to choice of 3 strategies for advertising
and you have one major
Analyse the theory on Two-person sum games competitor
with 3 strategies.
(5)
Level 4 Analysing
What are the assumptions of Game? (5)
Find value of game.
B1 B2 B3
A1 80 70 60
A2 90 80 100
A3 40 30 40
(5)
UNIT - IV INVENTORY MODELS, SIMULATION AND DECISION THEORY
SYLLABUS: Inventory Models ? EOQ and EBQ Models (With and without shortages), Quantity Discount
Models. Decision making under risk ? Decision trees ? Decision making under uncertainty. Monte-carlo
simulation.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define inventory. Level 1 Remembering
2.
Classify the Forms of inventory.
Level 2 Understanding
3.
Identify the Objectives/significance of inventory model.
Level 3 Applying
4.
Highlight the importance of Reorder level.
Level 4 Analysing
5.
Discuss the concept of Lead time.
Level 5 Evaluate
6.
Interpret the Types of stock replenishment.
Level 1 Remembering
7.
List the Basic inventory models.
Level 2 Understanding
8.
Compare Ordering Cost and Carrying Cost.
Level 3 Appyling
9.
Identify when shortage cost and stock out cost arises?
Level 5 Evaluating
10.
Analyze why safety stock is maintained.
Level 1 Remembering
11.
Discuss the concept of Quantity Discount Model.
Level 2 Understanding
12.
Interpret the meaning of EOQ & EBQ.
Level 3 Applying
13.
What are random and pseudo random numbers?
Level 4 Analysing
14.
Explain Monte Carlo Method.
Level 5 Evaluating
15.
Summarize the concept of EMV.
Level 1 Remembering
16.
What inference can you make about holding cost ?
Level 2 Understanding
17.
What is Shortage Cost?
Level 3 Applying
18. Classify and explain the various conditions under which
decisions are made.
Level 1 Remembering
19. What is meant by the following terms in inventory
management: i)Carrying cost ii) shortage costs
Level 2 Understanding
20. What is Decision theory? List the problems that can be solved
by Simulation.
Level 3 Applying
S.NO PART - B QUESTIONS Marks BT
LEVEL
COMPETENCE
1.
(i)
Alpha industry needs 5400 units per year of a bought out
component which will be
used in its main product. The ordering cost is Rs.250
per order and the carrying cost per unit per year is
Rs.30.
Which is the best order quantity?
(8)
Level 1 Remembering
(ii)
Find the number of order per year and Frequency of
orders?
(5)
2.
(i)
A stockiest has to supply 12000 units of a product per
year to his customer. Demand is
fixed and known. Shortage cost is assumed to be
infinite. Inventory holding cost is 20 paise per unit per
month. Ordering Cost is Rs. 250 and purchase price
is Rs.10 per unit.
Estimate the EOQ
(8)
Level 2 Understanding
(ii)
Find the Frequency of orders and total inventory cost. (5)
3.
ABC manufacturing company purchases 9000 parts of a
machine for its annual requirement. Each part costs
Rs.20. The ordering cost per order is Rs.15 and the
carrying charges are 15% of the average inventory per
year. Apply EOQ formulae and find out EOQ, No of
orders ,Total Inventory Cost and total cost.
Level 3 Applying
4.
(i)
Demand for an item in a company is 18,000 units per
year. The company can produce the items at a rate of
3000 units per month. The Cost of one setup is Rs.500
and the holding cost of one unit per month is 15 paise.
Shortage cost of one unit is Rs.20 per year.
Analyze and find the optimum manufacturing quantity.
(8)
Level 4 Analysing
(ii)
Find the number of shortages and frequency of
Production run.
(5)
5. A company has a demand of 12000 units/year for an
item and it can produce 2000 units per month. The
cost of one setup is Rs.400 and the holding
cost/unit/month is 15 paise. Select the optimum lot
size and total cost per year assuming the cost of 1 unit
as Rs.4. Find EBQ, the number of set ups & total cost.
Level 5 Evaluating
6.
(i)
Find the optimal order quantity for a product when the
annual demand for the product is 500 units. The Cost of
storage per unit per year is 10% of the unit cost. Ordering
cost per order is Rs. 180.
Determine EOQ
(8)
Level 6 Creating
(ii)
Evaluate the Total Cost
(5)
The unit cost are given below:
Quantity Unit Cost(Rs.)
O
1500<=Q3<3000 24.60
3000<=Q4 24.40
7. (i)
Formulate the Optimal order quantity for a product for
which the price breaks are as follows
(8)
Level 1 Remembering
(ii)
Also find the Total cost.
Quantity Unit Cost(Rs.)
O
750<=Q 875
(5)
8.
Compute the EOQ and the total variable cost for the
following:
Annual demand: 25 units
Unit price: Rs.2.50
Order cost: Rs.4.00
Storage rate: 1% per year
Level 2 Understand
9.
(i)
Identify the profit under three states of nature & three
decision alternative.
State of
Nature
State of
Nature
State of
Nature
N1 N2 N3
Decision
Naking
D1 150 250 300
Decision
Naking
D2 450 250 200
Decision
Naking
D3 100 180 290
Hurwitz criterion for alpha=0.5
(3)
Level 3 Applying
(ii)
Laplace condition
(5)
(iii)
Minimax Condition
(5)
10.
A Bakery keeps a stock of particular brand of cake. Daily
demand of past experience.
Daily
demand
0 15 25 35 45 50
Probability 0.01 0.15 0.20 0.50 0.12 0.02
Consider the following sequence of random numbers.
48 78 9 51 56 77 15 14 68 9
Using this sequence simulate the demand for next 10
days.
Find the stock situation if the owner makes 35 cakes
every day. Examine the daily average demand.
Level 1 Remembering
11.
Given above is the following pay off matrix.
Using EMV criterion . Decide which of the act can be
chosen at the best. FindEVPI & EOL.
Nature
Probability
Don?t
Expand
Expand
200
Expand
400
High
Demand
0.4 2500 3500 5000
Medium
Demand
0.4 2500 3500 2500
Low
Demand
0.2 2500 1500 1000
Level 2 Understanding
12.
A sample of 100 arrivals of customers at a retail sales
depot is according to the following distribution.
Time between arrivals(mins) Frequency
0.5 2
1.0 6
1.5 10
2.0 25
2.5 20
3.0 14
3.5 4
4.0 7
4.5 4
5.0 2
Use random numbers and predict the average time
between arrivals.
48 78 9 51 56 77 15 14 68 9
Level 3 Applying
13.
(i)
A departmental store purchases sprays which can be
ordered only in lots of 10. Each spray cost Rs.75 and
sells at Rs.90 each. Used sprays, however have \no
salvage value.
Demand 10 20 30 40 50
Probability 0.2 0.35 0.25 0.15 0.05
The probability distribution obtained from analysis of past
sales data is given below.
Analyse the payoff table.
(5)
Level 4 Analysing
(ii) How much quantity should the departmental store buy to
maximize its profit?
(8)
14. (i)
A company uses annually 50,000 units of an item each
costing Rs.1.20. Each order costs Rs.45 and inventory
carrying costs are 15% of the annual average inventory
value.
Find EOQ.
(3)
Level 2 Understanding
(ii) If the company operates 250 days a year and the
procurement time is 10 days and safety stock is 500
units, find reorder level, maximum, minimum and
average inventory
(10)
PART - C
S.No Questions BT
Level
Competence
1.
A contractor has to supply 10000 bearings per day to an
automobile manufacturer. He finds that when he starts a
production run he can produce 25000 bearings per day. The
cost of holding a bearing in stock for one year is 2 paise and
the set up cost of the production run is Rs.18. How frequently
should production run be made and which is the Best
Economic Batch Quantity? How much would be the No. of
Setup and Total Inventory Cost.
Level 1 Remembering
2.
A stockist has to supply 400 units of a product every
Monday to his customer.
He gets the product at Rs.50 per unit from the
manufacturer. The cost of ordering and transportation
from the manufacturer is Rs.75 per order. The cost of
carrying inventory is 7.5% per year of the cost of product.
Predict EOQ, Frequency of orders and Number of Orders,
Total Incremental cost and Total Cost.
Level 2 Understanding
3. (i) Identify the profit under three states of nature & three
decision alternative.
State of
Nature
N1 N2 N3
Decision
Making
D1 100 200 300
D2 400 200 200
D3 200 160 390
Hurwitz criterion for alpha=0.5
(5) Level 3 Applying
(ii)
Laplace Condition
(5)
(iii) Mininmax Condition (5)
4.
An automobile production line turns out about 100 cars a
day, but deviation occur owing to many causes. The
production is more accurately described by the
probability distribution given below;
Production/
Day
Probability
95 0.03
96 0.05
97 0.07
98 0.10
Level 4 Analysing
99 0.15
100 0.20
101 0.15
102 0.10
103 0.07
104 0.05
105 0.03
Use the random numbers &find the average demand
48 78 9 51 56 77 15 14 68 9
UNIT - V QUEUING THEORYAND REPLACEMENT MODELS
SYLLABUS:Queuing Theory ?Single and Multi-Channel models-infinite number of customers and
infinite calling resource Replacement Models-Individuals replacement Models (With and without time
value of money) ? Group Replacement Models.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define Queue.
Level 1 Remembering
2. How do you show your understanding on replacement theory?
Level 2 Understanding
3. In a bank, 20 customers on an average are served by a
cashier in an hour. If the service time has exponential
distribution, what is the probability that it will take more than
10 minutes to serve a customer?
Level 3 Applying
4. Classify the types of Queue.
Level 4 Analysing
5. How waiting time cost is related to queuing system?
Level 5 Evaluating
6. Interpret the Characteristics Of Queuing Models.
Level 4 Evaluating
7. How would you explain consumer behavior in queues?
Level 1 Remembering
8. Compare Serial and parallel Queue with Examples. Level 2 Understanding
9. Classify the types of Replacement model.
Level 3 Applying
10. Describe Kendall?s Notation for identifying a Queue Model with
single channel, Poisson arrivals, exponential service unlimited
queue and infinite calling population.
Level 4 Analysing
11. GRP includes IRP .Do You Agree?
Level 5 Evaluating
12. What is GRP &IRP?
Level 6 Creating
13. Distinguish between breakdown maintenance and preventive
maintenance.
Level 1 Remembering
14. How do you show your understanding on Little?s formula in
queuing theory?
Level 2 Understanding
15. Categorize Queue Discipline.
Level 3 Applying
16. Develop Kendall?s Notation of a Queue.
Level 4 Analysing
17. What is ?Collusion? in Queue Discipline?
Level 1 Remembering
18. Compare the Queue Length and No. of Customers in the System.
Level 2 Understanding
19. Distinguish between individual replacement and group
replacement?
Level 3 Applying
20. Describe Kendall?s Notation for identifying a Queue Model with
two channels, Poisson arrivals, exponential service Unlimited
Queue and infinite calling population.
Level 1 Remembering
S.No
PART - B QUESTIONS Marks
BT
LEVEL
COMPETENCE
1. The cost of machine is Rs.16, 00 and scrap value is
Rs.1,100. Maintenance Cost form for machine are as
follows:
Year 1 2 3 4 5 6 7 8
Maintenance
cost
300 459 600 800 100 1200 1500 2000
When should the machine be the replaced?
Level 1 Remembering
2.
The following table gives to cost of spares per year,
overhead cost of maintenance per year and resale value of
certain equipment whose purchase price is Rs. 50,000:
Illustrate when the machine can be replaced.
Year 1 2 3 4 5
Cost of Spares 10000 12000 14000 15000 17000
Overhead
Maintenance
Cost
5000 5000 6000 6000 8000
Resale Value 40000 32000 28000 25000 22000
Level 2 Understanding
3.
A Taxi owner estimates from his past records that the cost
per year for operating a taxi whose purchase price when
new is Rs.60,000 are as follows.
Age 1 2 3 4 5
Operating cost 10000 12000 15000 18000 20000
After 5 years the operating cost is Rs.6000 x K, Where ?k?
is 6,7,8,9,10(age). If the resale value decreases by 10% of
Level 3 Applying
purchase price each year, calculate the best time of
replacement if time value is not implemented?
4.
(i)
A cost of a machine is 6100 and its scrap value is Rs.
100. The maintenance Cost from the experience are as
follows:
Year 1 2 3 4 5 6 7 8
Maintenance
cost
100 250 400 600 900 1200 1600 2000
Examine the average cost of replacement
(8)
Level 4 Analysing
(ii) Analyze when the asset can be replaced (5)
5.
(i)
Week 1 2 3 4 5 6 7
Conditional
Probability
0.07 0.15 0.25 0.45 0.75 0.9 1
IRP
Co
st
is Rs.1.25 per item
GRP Cost is Rs.60 Paise Per item.
Estimate the IRP Cost
(5)
Level 5 Evaluating
(ii)
Predict GRP cost and Determine whether GRP or IRP is the
Best Policy
(8)
6.
Machine A Costs Rs.9000. Annual Operating Cost is
Rs.200 for the 1
st
year and then increases by 2000 every
year. Determine the best age at which to replace the
machine. Assume the machine has no resale value.
Machine B Costs Rs.10,000 . Annual operating cost is
Rs.400 for the 1
st
year and then increases by 800 every
year. No resale value. You have now a machine of type A
which is one year old. Conclude if M/c A can be replaced
by M/c B. Is so, When?
Level 6 Creating
7.
A manufacturer is offered two machines A and B. A has
cost price of Rs.2,500, its running cost is Rs. 400 for each
of first years and increased by Rs. 100 every subsequent
year, Taking money?s value as 10% per year, when
machine should be replaced?
Level 1 Remembering
8.
The maintenance cost and resale value per year of a
machine whose purchase price is Rs.7000 is given below :
Year Operating Cost Resale Value
1 900 400
2 1200 2000
3 1600 1200
4 2100 600
5 2800 500
6 3700 400
7 4700 400
8 5900 400
When should the machine be replaced ?
Level 2 Understanding
10.
(i)
IRP cost Rs 4/item. GRP cost is
80paise/item.
Week 1 2 3 4 5 6
Probability
0.09
0.25
0.49
0.85
0.97
1
Find the IRP cost
5
Level 4 Analysing
(ii) Compare IRP or GRP and conclude which is best. 8
11. A machine owner finds from his past records that the
cost per year of maintaining a machine, whose purchase
price is Rs.6,000 are as given below.
Year 1 2 3 4 5 6 7 8
Maint
en
Ance
Cost
100 1200 140
0
180
0
230
0
280
0
340
0
400
0
Resal
e
Price
3000 150
0
750 375 200 200 200 200
Find at what age a replacement is due, assuming time
value is 10%
Level 1 Remembering
12.
(i)
(ii)
Cars arrive at a petrol pump, having one petrol
unit, in poisson fashion with an average of 10 cars
per hour. The service time is distributed
exponentially with a mean of 3 minutes.
(3)
Level 2 Understanding
PredictAverage number of cars in the system
Average waiting time in the queue
(3)
(iii)
Average queue length
(3)
(iv) The probability that the number of cars in the system is (4)
13.
(i)
In a public telephone booth, the arrivals are on the
average 15 per hour. A call on the average takes 3
minutes. If there is just one phone, Analyse and find:
The expected number of callers in the booth at any
time.
(6)
Level 4 Analysing
(ii) The proportion of the time the booth is expected tobe
idle
(7)
9.
A truck owner finds from his past experience that the
maintenance costs rs.200 for the first year and then
increases by rs.2000 every year, The cost of the truck type
A is rs.9000. Determine the best age at which to replace
the truck. Truck B type cost rs.10000.Annual Maintenance
costs are rs.400 and increased by Rs.800 every year. The
truck owner now has truck type A which is one year old
and should be replaced by Type B and if so when?
Level 3 Applying
FirstRanker.com - FirstRanker's Choice
(An
?
DEPARTMENT OF MANAGEMENT STUDIES
QUESTION BANK
II SEMESTER
1915201? APPLIED OPERATIONS RESEACH
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Dr. Radha Ganesh Kumar ? Asst. Professor (Sel.G) and HOD
Mr.B. Sam Paul ? Asst. Professor (OG)
(An
? .
DEPARTMENT OFMANAGEMENT STUDIES
QUESTION BANK
SUBJECT :1915201 ?APPLIED OPERATIONS RESEACH
SEM / YEAR : IISemester / IYear
UNIT ? I ?INTRODUCTION TO LINEAR PROGRAMMING (LP)
SYLLABUS: Introduction to applications of operations research in functional areas of management.
Linear Programming-formulation, solution by graphical and simplex methods, Special cases. Dual
simplex method. Principles of Duality. Sensitivity Analysis.
PART- A
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Define Operations Research (OR). Level 1 Remembering
2. Differentiate between Simplex and Big M Method Level 2 Understanding
3. How do you show your understanding unbounded solution? Level 3 Applying
4. Categorize the forms of LPP. Level 4 Analysing
5.
Discuss why is two phase method is better than Big M
method?
Level 5 Evaluating
6. Interpret the usage of Sensitivity Analysis in LPP. Level 6 Creating
7. What are the assumptions and requirements of LPP? Level 1 Remembering
8. Compare Dual Simplex and Duality. Level 2 Understanding
9. Identify the Advantages of duality. Level 3 Applying
10. What do you think about Infeasible solution? Level 4 Analysing
11. How will you solve LPP graphically? Level 5 Evaluating
12.
Conclude your understanding on the mathematical
formulation of LPP.
Level 6 Creating
13. Define basic variables and artificial variables. Level 1 Remembering
14. Compare Slack variable & Surplus Variable. Level 2 Understanding
15.
Give some example for the role of Surplus variable & Slack
Variable in the simplex method
Level 3 Applying
16. How would you apply Artificial variable? Level 4 Analysing
17. What is Big M Method? Level 1 Remembering
18. Distinguish simplex and Big M method Level 2 Understanding
19.
What do you mean by Duality? List the Rules for primal and
dual.
Level 1 Remembering
20. What is Shadow price? Level 1 Remembering
PART- B
S.NO
QUESTIONS
BT
LEVEL
COMPETENCE
1.
(i)
Maximise Z=3x+4y subject to
2x+5y ?60,
4x+2y ?40.
x, y >0. Solve by Graphical Method
Plot the graph
(8)
Level 1 Remembering
(ii) Which one is the best solution? (5)
2.
(i)
Min Z= 20x
1
+10 x
2
subject to
x
1
+2x
2
? 40,
3x
1
+x
2
? 30,
4x
1
+3x
2
? 60,
x
1
,x
2
? 0.
Solve by Graphical Method,
Plot the graph
(8)
Level 2 Understanding
(ii) Predict the value of x & y. (5)
3 Max Z= 5x1+4x2 subject to
x
1
-2x
2
? 1,
x
1
+2x
2
?3,
x
1
,x
2
? 0. Solve Graphically. Which one is the best
solution?
Level 3 Applying
4.
(i)
A Plant Manufacturer 2 Product A & B. The Profit Contribution
of each product has been estimated as Rs.300 for product A
and Rs.400 for Product B. Each Product passes through 3
departments of the plant. The time required for each product
and total time available in each department is as follows.
Department Hours
Required
Hours
Required
Available
Hours
during
month
Product
A
Product
B
I 2 3 1600
II 3 2 1500
III 1 1 700
The company has a contract to supply atleast 300 units of
Product B per month.
Formulate the LPP
(5)
Level 4
Analysing
(ii) Solve through Graphical Method
(8)
5. Solve the following LPP by graphical method.
Maximize Z= 3x
1
+2x
2
Subject t o
- 2x
1
+x
2
?1,
x
1
? 2,
x
1
+ x
2
? 3
and x
1
,x
2
? 0
Level 5 Evaluating
6. (i) Max Z= 1000x
1
+4000x
2
+5000x
3
Subject to 3x1+3x
3
?22,
x1+2x2+3x
3
? 14,
3x1+2x2 ? 14
& x1,x2 ? 0
Develop a Simplex Table
(5)
Level 6 Creating
(ii) Analyse and find the value of x
1
, x
2
? (8)
7. Analyze the following LPP by Simplex Method:
Min Z = -10y
1
-15y
2
-20y
3
Subject to 2y
1
+4y
2
+6y
3
? 24,
3y
1
+9y
2
+6y
3
? 30,
& y
1
, y
2
, y
3
? 0.
Level 1 Remembering
(i)
Develop a Simplex Table (5)
(ii) Solve and find the value of y1 ,y2 and y3
(8)
8.
Solve By Graphical Method
Minimize Z= 40x
1
+24x
2
Subject to, 20x
1
+50 x
2
> 4,800
80 x
1
+50x
2
> 7,200
x
1
,x
2
>0
Level 2 Understanding
9. Solve the following LPP by simplex method:
Minimize Z= 8x
1
-2x
2
Subject to -4x
1
+2x
2
?1,
5x
1
-4x
2
?3,
and x
1
,x
2
? 0
Level 3 Applying
10. Solve the following LPP by simplex method:
Maximize Z= 3x1+2x
2
Subject to
2x
1
+x
2
?2,
3x
1
+4x
2
?12,
x
1
,x
2
? 0
Level 4 Analyzing
11. Review the LPP and solve by simplex method
Max Z= 25x+10y
Subject to the constraints
x+0.5y? 20
x+y? 50
x,y ? 0
Level 1 Remembering
12. A firm produces three products. These products are
processors on 3 different machines. The time required for
manufacturing one unit of cost of the products and the daily
capacity of the three machines is given in the table below.
Analyse and find the optimum solution.
Mac
hine
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Machine
Capacity
Min /Day
Product1 Product 2 Product 3
M1 2 8 2 940
M2 4 - 8 970
M3 2 5 - 430
It is required to determine the daily no. of units to be
manufactured for each product. The profit for unit for
Level 2 Understanding
product 1,2,3 is Rs.4,Rs.8,Rs.6 respectively. It is assumed
that all the amount produced are consumed in the market
13. Using dual simplex method , solve and find the optimum
solution for the given LPP.
Maximize Z=6x
1
+4x
2
+4x
3
Subject to 3x
1
,x
2
+2x
3
? 2
2x
1
+x
2
-x
3
? 1
-x
1
+x
2
+2x
3
? 1 &
x
1
,x
2
,x
3
? 0
Level 4 Analysing
14.
(i)
Evaluate by using dual simplex method and solve the LPP.
Minimize Z=2x
1
+x
2
Subject to 3x
1
+2x
2
? 3
4x
1
+3x
2
? 6
x
1
+x
2
? 5 & x
1
,x
2
?
Determine the dual simplex table
(5)
Level 1 Remembering
(ii)
Find the value of x
1
, x
2
(8)
PART - C
S.No Questions BT
LEVEL
COMPETENCE
1.
Max Z=300x+400y subject to
2x+3y ? 1600,
3x+2y ? 1500,
x+y ? 700,
y ? 300, x,y ? 0 Solve by Graphical Method, choose the
value of x & y which maximizes profit.
Level 1 Remembering
2. Solve the following LPP by graphical method.
Minimize Z= 6000x1+4000x
2
Subject t o
3x+x
2
? 40,
x
1
+2.5 x
2
? 22
3x
1
+3 x
2
? 40
and x
1
,x
2
? 0
Level 2 Understanding
3. Develop a Simplex Table and Solve
Max Z = 3 x1+2 x2,
Subject to
x1+ x2 ?4,
x1- x2 ? 2;
x1, x2 ?0.
Level 3 Applying
4. Solve by using Simplex Method.
Maximize Z= 3x+5y
Subject to the constraints
x+y? 60
x? 40
y ? 30
x,y ? 0
Level 1 Remembering
UNIT - II LINEAR PROGRAMMING EXTENSIONS
SYLLABUS: Transportation Models (Minimizing and Maximizing Problems) ? Balanced and unbalanced
Problems ? Initial Basic feasible solution by N-W Corner Rule, Least cost and Vogel?s approximation methods.
Check for optimality. Solution by MODI /. Case of Degeneracy. Trans-shipment Models. Assignment Models
(Minimising and Maximising Problems) ? Balanced and Unbalanced Problems. Solution by Hungarian and
Branch and Bound Algorithms. Travelling Salesman problem.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define Transportation & Transhipment. Level 1 Remembering
2. Differentiate balanced transportation problem & Unbalanced
Transportation Problem.
Level 2 Understanding
3. How would you show your understanding on unbalanced
transportation problem?
Level 3 Applying
4. Categorize the Phases of transportation model. Level 4 Analysing
5. Construct the basic feasible solution for the following
transportation problem.
1 2 3 4 SUPPLY
1 2 3 11 7 6
2 1 0 6 1 1
3 5 8 15 9 10
DEMAN D 7 5 3 2
Level 5 Evaluating
6 Interpret the need for Optimum solution in transportation. Level 6 Creating
7. What do you mean by Least cost method (LCM)? Level 1 Remembering
8. Compare Vogel approximation method (VAM) & Least Cost
Method.
Level 2 Understanding
9. How do you represent a travelling salesman problem
through mathematical formulation?
Level 3 Applying
10. Analyse the rules of travelling salesman Problem. Level 4 Analysing
11. Discuss the meaning of Assignment Level 5 Evaluating
12. Compare Balanced assignment problem & Unbalanced
Assignment Problem.
Level 6 Creating
13. What example can you give for Unbalanced assignment
problem?
Level 1 Remembering
14. How will you resolve degeneracy in Transportation Problem? Level 2 Understanding
15. Classify transportation problem. Level 3 Applying
16. Examine the Steps in Hungarian algorithm. Level 4 Analysing
17. What is Branch and bound algorithm in Assignment? Level 1 Remembering
18. Compare Assignment and transportation Problem. Level 2 Understanding
19. What do you mean by Travelling Salesman Problem? Level 1 Remembering
20. What is Restricted Assignment? Level 1 Remembering
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Solve and find the Transportation Problem and Which method will
you select if you want toMinimize Cost?
Destination Supply
1 2 3 4
I 21 16 25 13 11
II 17 18 14 23 13
III 32 27 18 41 19
Demand 6 10 12 15
Level 1 Remembering
2. Find the Initial Basic Feasible solution for following TP. Using NW
Rule, LCM, and VAM. Which method will you select if you want to
Minimize Cost?
D1 D2 D3 Supply
S1 7 3 2 2
S2 2 1 3 3
S3 3 4 6 5
Demand 4 1 5 10
Level 2 Understanding
3.
(i)
Analyze the transportation problem with unit transportation
costs,demand, and supply as given below:
Destination
Supply
Source
D1 D2 D3 D4
S1
6 1 9 3
70
11 5 2 8
S2 55
10 12 4 7
S3
70
Demand 85 35 50 45
Apply VAM for Initial solution.
(5)
Level 3 Applying
(ii)
Construct the final Solution by using MODIMethod.
(8)
4.
(i)
Analyze & solve the following transportation problem to maximize
profit.
A B C D Supply
1
Source 2
3
Demand
15 51 42 33 23
80 42 26 81 44
90 40 66 60 33
23
31
16
30
100
Examine Initial solution using VAM.
(5)
Level 4 Analysing
(ii)
Analyze and find out the final Solution by using MODI Method.
(8)
5. Solve the following transportation problem using Vogel?s
method
Factory? Warehouse ?Available
A B C D E F
1 9 12 9 6 9 10 5
2 7 3 7 7 5 5 6
3 6 5 9 11 3 11 2
4 6 8 11 2 2 10 9
4 4 6 2 4 2
Requirement?
(5)
Level 5 Evaluating
6. (i) Solve the transportation problem and decide using VAM for initial
solution.
(5) Level 6 Creating
(ii) Evaluate using NWC and Least Cost method for initial solution?
Destination Supply
I 2 1 25 13 11
II 1 1 14 23 13
III 3 2 18 41 19
Demand 6 1 22 15
(8)
7.
Maximize profit from the following transportationproblem.
A B C D Supply
I 40 25 22 33 100
SourceII 44 35 30 30 30
III 38 38 28 30 70
Demand 40 20 60 30
Level 1 Remembering
(i) How will you convert maximization problem to minimization.
Find the maximum profit
(8)
(ii) Explain stepping stone method for checking the
solution for optimality transportation problems.
(5)
8. A company has one surplus truck in each of the cities A, B, C, D, &
E and one deficit trucks in each of the cities 1,2,3,4,5,6. The
distance between the cities in kms is shown in the matrix below.
Can you select the assignment of trucks from cities in surplus to
cities in deficiency .so that total distance covered by the vehicles is
minimum?
1 2 3 4 5 6
A 12 10 15 22 18 8
B 10 18 25 15 16 12
C 11 10 3 8 5 9
D 6 4 10 13 13 12
E 8 12 11 7 13 10
Level 2 Understanding
9.
Consider the problem of assigning five jobs to five persons. The
assignment costs are given as follows:
PERSONS?JOBS ?
1 2 3 4 5
A 8 4 2 6 1
B 0 9 5 5 4
C 3 8 9 2 6
D 4 3 1 0 3
Level 3 Applying
E 9 5 8 9 5
Determine the optimum assignment schedule.
10. The assignment cost of assigning any one operator to any one
machine is given in the following table.
MACHINE?OPERATORS ?
I II III IV
A 10 5 13 15
B 3 9 18 3
C 10 7 3 2
D 5 11 9 7
Find the optimal assignment by Hungarian method.
Level 4 Analysing
11. A machine shop purchased a drilling machine and two lathes of
different capacities. The Positioning of the machines among 4
possible locations on the shop floor is important forms the
standard of materials handling. Given the cost estimate per unit
time of materials below, find the optimum location of the
machines.
LOCATIONS
1 2 3 4
Lathe 1 12 9 12 9
Drill 15 Not
suitable
13 20
Lathe 2 4 8 10 6
Level 1 Remembering
12.
Solve the assignment problem for maximization given profit
matrix(profit in rupees).
Machines
P Q R S
JOB
51 53 54 50
47 50 48 50
49 50 60 61
63 64 60 60
Level 2 Understanding
PART - C
S.No Questions Marks BT
Level
Competence
1.
a
Assume that you are an OR specialist. Identify the procedure
for each of the following Method to the employees in order to
help them achieve solution to Transportation Problems.
Northwest Corner Cell Method
(3)
Level 1 Remembering
b Least Cost cell Method (4)
c Vogel?s Approximation Method (4)
d U V Method. (4)
13. The processing time in hours for the jobs when allocated to the
different machines is indicated below. Select the best assignment
of the machines for the jobs so that the total processing time is
Minimum.
Machines
M1 M2 M3 M4 M5
J1 9 22 58 11 19
JOB J2 43 78 72 50 63
J3 41 28 91 37 45
J4 74 42 27 49 39
J5 36 11 57 22 25
Level 4 Analysing
14. For the given travelling salesman problem, Minimize the total cost.
To
1 2 3 4
From A - 46 16 40
B 41 - 50 40
C 82 32 - 60
D 40 40 36 -
Level 1 Remembering
(i) Observe the above travelling salesman
problem and find out minimize the cost per
cycle.
(8)
(ii) Find whether path is satisfied. (5)
2.
Solve the following transportation problem, in which a
i
is the
availability at Origin
O
i
and b
j
is the requirement at the destination D
j
and cell entries
are unit costs of transportation from any origin to any
destination:
D1 D2 D3 D4 D5 a
j
O1 4 7 3 8 2 4
O2 1 4 7 3 8 7
O3 7 2 4 7 7 9
O4 4 8 2 4 7 2
b
j
8 3 7 2 2
Predict the allocation to minimize the cost.
Level 2 Understanding
3. A company has a team of 4 Salesman and the company wants to
do in 4 districts. Considering the capabilities of salesmen
and nature of the district, the company has estimated the profit per
day in Rs. For each salesmen in each district as follows.
District
s
Salesmen 1 2 3 4
A 16 10 14 11
B 14 11 15 15
C 15 15 13 12
D 13 12 14 15
Develop the best assignment schedule and analyze the total cost.
Level 3 Applying
4. Five operators have to be assigned to Five Machines. The
assignment costs are given in thetablebelow.
Analyse using Hungarian algorithm & find out the assignment to
minimize the cost.
Machine
I II III IV V
Operator
A 5 5 - 2 6
B 7 4 2 3 4
C 9 3 5 - 3
D 7 2 6 7 2
E 6 5 7 9 1
Level 4 Analyzing
UNIT ? III ? INTEGER PROGRAMMING AND GAME THEORY
SYLLABUS: Integer Programming ? Introduction and types - Game Theory-Two-person Zero sum
games-Saddle point, Dominance Rule, graphical and LP solutions, Nash Equilibrium
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. What do you mean by integer programming problem?
Level 1 Remembering
2. In what respect a mixed IPP differs from pure IPP?
Level 2 Understanding
3. What is Nash Equilibrium?
Level 3 Applying
4. Classify the different types of strategy.
Level 4 Analysing
5. Compile the Characteristics of game.
Level 5 Evaluating
6. Can you assess the applications of integer
programming?
Level 6 Creating
7. Define Game.
Level 1 Remembering
8. Compare Mixed Strategy and Pure Strategy.
Level 2 Understanding
9. How would you make use of the concept of Game theory
in Managerial Decision Making?
Level 3 Applying
10. Conclude your understanding about Payoff Matrix.
Level 4 Analysing
11. How will you find the optimal strategies and value of the
following game?
Player B
Player
A
H T
H 2 -1
T -1 0
Level 5 Evaluating
12. Interpret the concept of two person zero sum game.
Level 6 Creating
13. What is Saddle point?
Level 1 Remembering
14. Compare Dominance Principle of Rows and Columns.
Level 2 Understanding
15. Identify the basic assumptions of the Game.
Level 3 Applying
16. Conclude the advantages of Game theory.
Level 4 Analysing
17. What are the Methods of Matrices?
Level 1 Remembering
18. Summarize how graphs and LP solution are used in
Game theory.
Level 2 Understanding
19. What is a Decision Tree?
Level 1 Remembering
20. Define Dominance principle.
Level 1 Remembering
S.N
O
PART - B QUESTIONS MA
RK
S
BT
LEVEL
COMPETENCE
1. (i) What do you mean by Pure IPP? (3) Level 1 Remembering
(ii) What do you mean by Mixed IPP? (5)
(iii)
List out the difference between Pure and Mixed IPP.
(5)
2. (i) For what value of ?,the game with the following
matrix is strictly determined
B
1
B
2
B
3
A
1
? 6 2
A
2
-1 ? -7
A
3
-2 4 ?
(8) Level 2 Understanding
(ii) Write down the assumptions of game theory. (5)
3. (i) Solve the game whose pay-off matrix is given by
B
1
B
2
B
3
A
1
1 3 1
A
2
0 -4 -3
A
3
1 5 -1
(8)
Level 3 Applying
(ii) Explain the concept of Nash Equilibrium. (5)
4.
Analyze the Value of the game graphically
B1 B2
A1 4 4
A2 2 7
A3 5 3
A4 6 2
Level 4 Analysing
5.
What inference can be made using Dominance
Principle to reduce the following game and estimate
the game value?
B1 B2 B3 B4
A1 3 2 4 0
A2 3 4 2 4
A3 4 2 2 0
A4 2 1 6 3
Level 5 Evaluating
6.
How would you evaluate the following game whose
Pay-Off matrix is Given Below?
9 3 1 8 0
6 5 4 6 7
2 4 3 3 8
5 6 2 2 1
Level 6 Creating
7.
(i)
Two players A&B match coins. If the coins match
then A wins one unit value, if the coins do not
match then B wins one unit of value.
Determine pay-off matrix which strategy is to be
chosen
(5)
Level 1 Remembering
(ii)
Find the value of game. (8)
8.
Predict the Value of the Game given above Pay
OffMatrix.
Player B
B1 B2 B3
A1 -2 5 -3
Player A A2 1 3 5
A3 -3 -7 11
Level 2 Understanding
9.
Apply graphical analysis to Solve the game.
A/
B
B1 B2 B3 B4
A1 3 3 4 0
A2 5 4 3 7
Level 3 Applying
10. Solve the following game by graphical method.
Player B
1 2 3
1 6 4 3
Player A 2 2 4 8
Level 4 Analysing
11.
(i)
A and B play a Match(Game) in which each has 3
coins 5 paise, 10 paise and 20 paise. Each player
selects a coin without the knowledge of others
choice. IF the sum is even, B wins A?s Coin. If sum
is Odd, A wins B?s coin.
How will you find the pay-off matrix ?
(5)
Level 1
Remembering
(ii)
Find the Best Strategy & value of the Game. (8)
12.
Consider the Pay Off Matrix of player A as shown in
the table below and solve it optimally using the
graphical method .
Player A
Player
B
1 2 3 4 5
1 3 6 8 4 4
2 -7 4 2 10 2
Level 2 Understanding
13.
(i)
Analyze the Game Graphically:
Player A
Player
A
B1 B2
A1 -3 1
A2 5 3
A3 6 -1
A4 1 4
A5 2 2
A6 0 -5
Plot the graph
(5)
Level 4 Analysing
(ii)
Analyse and find the value of the game.
(8)
14.
Which one is the best strategy using Dominance
Principle?
B1 B2 B3 B4 B5 B6
A1
4 2 0 2 1 1
A2
4 3 1 3 2 2
A3
4 3 7 -5 1 2
A4
4 3 4 -1 2 2
A5
4 3 3 -2 2 2
Level 1 Remembering
PART-C
S.No Questions BT
Level
Competence
1.
Using Dominance property Solve.
B
A
I II IIIIV
1 -5 3 1 20
2 5 5 4 6
3 -4 -2 0 -5
Level 1 Remembering
2. Examine the 2 * n Game by the Method of Sub Game:
B1 B2 B3
A1 1 3 11
A2 8 5 2
Level 2 Understanding
3. In a game of matching coins with 2 players, A wins 1 unit value
when there are 2 heads, wins nothing when there are 2 tails
and looses ? unit value when there are one head and one tail.
Develop Pay Off matrix and value of the game.
Level 3 Applying
4.
i
ii
iii
Assume you have to choice of 3 strategies for advertising
and you have one major
Analyse the theory on Two-person sum games competitor
with 3 strategies.
(5)
Level 4 Analysing
What are the assumptions of Game? (5)
Find value of game.
B1 B2 B3
A1 80 70 60
A2 90 80 100
A3 40 30 40
(5)
UNIT - IV INVENTORY MODELS, SIMULATION AND DECISION THEORY
SYLLABUS: Inventory Models ? EOQ and EBQ Models (With and without shortages), Quantity Discount
Models. Decision making under risk ? Decision trees ? Decision making under uncertainty. Monte-carlo
simulation.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define inventory. Level 1 Remembering
2.
Classify the Forms of inventory.
Level 2 Understanding
3.
Identify the Objectives/significance of inventory model.
Level 3 Applying
4.
Highlight the importance of Reorder level.
Level 4 Analysing
5.
Discuss the concept of Lead time.
Level 5 Evaluate
6.
Interpret the Types of stock replenishment.
Level 1 Remembering
7.
List the Basic inventory models.
Level 2 Understanding
8.
Compare Ordering Cost and Carrying Cost.
Level 3 Appyling
9.
Identify when shortage cost and stock out cost arises?
Level 5 Evaluating
10.
Analyze why safety stock is maintained.
Level 1 Remembering
11.
Discuss the concept of Quantity Discount Model.
Level 2 Understanding
12.
Interpret the meaning of EOQ & EBQ.
Level 3 Applying
13.
What are random and pseudo random numbers?
Level 4 Analysing
14.
Explain Monte Carlo Method.
Level 5 Evaluating
15.
Summarize the concept of EMV.
Level 1 Remembering
16.
What inference can you make about holding cost ?
Level 2 Understanding
17.
What is Shortage Cost?
Level 3 Applying
18. Classify and explain the various conditions under which
decisions are made.
Level 1 Remembering
19. What is meant by the following terms in inventory
management: i)Carrying cost ii) shortage costs
Level 2 Understanding
20. What is Decision theory? List the problems that can be solved
by Simulation.
Level 3 Applying
S.NO PART - B QUESTIONS Marks BT
LEVEL
COMPETENCE
1.
(i)
Alpha industry needs 5400 units per year of a bought out
component which will be
used in its main product. The ordering cost is Rs.250
per order and the carrying cost per unit per year is
Rs.30.
Which is the best order quantity?
(8)
Level 1 Remembering
(ii)
Find the number of order per year and Frequency of
orders?
(5)
2.
(i)
A stockiest has to supply 12000 units of a product per
year to his customer. Demand is
fixed and known. Shortage cost is assumed to be
infinite. Inventory holding cost is 20 paise per unit per
month. Ordering Cost is Rs. 250 and purchase price
is Rs.10 per unit.
Estimate the EOQ
(8)
Level 2 Understanding
(ii)
Find the Frequency of orders and total inventory cost. (5)
3.
ABC manufacturing company purchases 9000 parts of a
machine for its annual requirement. Each part costs
Rs.20. The ordering cost per order is Rs.15 and the
carrying charges are 15% of the average inventory per
year. Apply EOQ formulae and find out EOQ, No of
orders ,Total Inventory Cost and total cost.
Level 3 Applying
4.
(i)
Demand for an item in a company is 18,000 units per
year. The company can produce the items at a rate of
3000 units per month. The Cost of one setup is Rs.500
and the holding cost of one unit per month is 15 paise.
Shortage cost of one unit is Rs.20 per year.
Analyze and find the optimum manufacturing quantity.
(8)
Level 4 Analysing
(ii)
Find the number of shortages and frequency of
Production run.
(5)
5. A company has a demand of 12000 units/year for an
item and it can produce 2000 units per month. The
cost of one setup is Rs.400 and the holding
cost/unit/month is 15 paise. Select the optimum lot
size and total cost per year assuming the cost of 1 unit
as Rs.4. Find EBQ, the number of set ups & total cost.
Level 5 Evaluating
6.
(i)
Find the optimal order quantity for a product when the
annual demand for the product is 500 units. The Cost of
storage per unit per year is 10% of the unit cost. Ordering
cost per order is Rs. 180.
Determine EOQ
(8)
Level 6 Creating
(ii)
Evaluate the Total Cost
(5)
The unit cost are given below:
Quantity Unit Cost(Rs.)
O
1500<=Q3<3000 24.60
3000<=Q4 24.40
7. (i)
Formulate the Optimal order quantity for a product for
which the price breaks are as follows
(8)
Level 1 Remembering
(ii)
Also find the Total cost.
Quantity Unit Cost(Rs.)
O
750<=Q 875
(5)
8.
Compute the EOQ and the total variable cost for the
following:
Annual demand: 25 units
Unit price: Rs.2.50
Order cost: Rs.4.00
Storage rate: 1% per year
Level 2 Understand
9.
(i)
Identify the profit under three states of nature & three
decision alternative.
State of
Nature
State of
Nature
State of
Nature
N1 N2 N3
Decision
Naking
D1 150 250 300
Decision
Naking
D2 450 250 200
Decision
Naking
D3 100 180 290
Hurwitz criterion for alpha=0.5
(3)
Level 3 Applying
(ii)
Laplace condition
(5)
(iii)
Minimax Condition
(5)
10.
A Bakery keeps a stock of particular brand of cake. Daily
demand of past experience.
Daily
demand
0 15 25 35 45 50
Probability 0.01 0.15 0.20 0.50 0.12 0.02
Consider the following sequence of random numbers.
48 78 9 51 56 77 15 14 68 9
Using this sequence simulate the demand for next 10
days.
Find the stock situation if the owner makes 35 cakes
every day. Examine the daily average demand.
Level 1 Remembering
11.
Given above is the following pay off matrix.
Using EMV criterion . Decide which of the act can be
chosen at the best. FindEVPI & EOL.
Nature
Probability
Don?t
Expand
Expand
200
Expand
400
High
Demand
0.4 2500 3500 5000
Medium
Demand
0.4 2500 3500 2500
Low
Demand
0.2 2500 1500 1000
Level 2 Understanding
12.
A sample of 100 arrivals of customers at a retail sales
depot is according to the following distribution.
Time between arrivals(mins) Frequency
0.5 2
1.0 6
1.5 10
2.0 25
2.5 20
3.0 14
3.5 4
4.0 7
4.5 4
5.0 2
Use random numbers and predict the average time
between arrivals.
48 78 9 51 56 77 15 14 68 9
Level 3 Applying
13.
(i)
A departmental store purchases sprays which can be
ordered only in lots of 10. Each spray cost Rs.75 and
sells at Rs.90 each. Used sprays, however have \no
salvage value.
Demand 10 20 30 40 50
Probability 0.2 0.35 0.25 0.15 0.05
The probability distribution obtained from analysis of past
sales data is given below.
Analyse the payoff table.
(5)
Level 4 Analysing
(ii) How much quantity should the departmental store buy to
maximize its profit?
(8)
14. (i)
A company uses annually 50,000 units of an item each
costing Rs.1.20. Each order costs Rs.45 and inventory
carrying costs are 15% of the annual average inventory
value.
Find EOQ.
(3)
Level 2 Understanding
(ii) If the company operates 250 days a year and the
procurement time is 10 days and safety stock is 500
units, find reorder level, maximum, minimum and
average inventory
(10)
PART - C
S.No Questions BT
Level
Competence
1.
A contractor has to supply 10000 bearings per day to an
automobile manufacturer. He finds that when he starts a
production run he can produce 25000 bearings per day. The
cost of holding a bearing in stock for one year is 2 paise and
the set up cost of the production run is Rs.18. How frequently
should production run be made and which is the Best
Economic Batch Quantity? How much would be the No. of
Setup and Total Inventory Cost.
Level 1 Remembering
2.
A stockist has to supply 400 units of a product every
Monday to his customer.
He gets the product at Rs.50 per unit from the
manufacturer. The cost of ordering and transportation
from the manufacturer is Rs.75 per order. The cost of
carrying inventory is 7.5% per year of the cost of product.
Predict EOQ, Frequency of orders and Number of Orders,
Total Incremental cost and Total Cost.
Level 2 Understanding
3. (i) Identify the profit under three states of nature & three
decision alternative.
State of
Nature
N1 N2 N3
Decision
Making
D1 100 200 300
D2 400 200 200
D3 200 160 390
Hurwitz criterion for alpha=0.5
(5) Level 3 Applying
(ii)
Laplace Condition
(5)
(iii) Mininmax Condition (5)
4.
An automobile production line turns out about 100 cars a
day, but deviation occur owing to many causes. The
production is more accurately described by the
probability distribution given below;
Production/
Day
Probability
95 0.03
96 0.05
97 0.07
98 0.10
Level 4 Analysing
99 0.15
100 0.20
101 0.15
102 0.10
103 0.07
104 0.05
105 0.03
Use the random numbers &find the average demand
48 78 9 51 56 77 15 14 68 9
UNIT - V QUEUING THEORYAND REPLACEMENT MODELS
SYLLABUS:Queuing Theory ?Single and Multi-Channel models-infinite number of customers and
infinite calling resource Replacement Models-Individuals replacement Models (With and without time
value of money) ? Group Replacement Models.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define Queue.
Level 1 Remembering
2. How do you show your understanding on replacement theory?
Level 2 Understanding
3. In a bank, 20 customers on an average are served by a
cashier in an hour. If the service time has exponential
distribution, what is the probability that it will take more than
10 minutes to serve a customer?
Level 3 Applying
4. Classify the types of Queue.
Level 4 Analysing
5. How waiting time cost is related to queuing system?
Level 5 Evaluating
6. Interpret the Characteristics Of Queuing Models.
Level 4 Evaluating
7. How would you explain consumer behavior in queues?
Level 1 Remembering
8. Compare Serial and parallel Queue with Examples. Level 2 Understanding
9. Classify the types of Replacement model.
Level 3 Applying
10. Describe Kendall?s Notation for identifying a Queue Model with
single channel, Poisson arrivals, exponential service unlimited
queue and infinite calling population.
Level 4 Analysing
11. GRP includes IRP .Do You Agree?
Level 5 Evaluating
12. What is GRP &IRP?
Level 6 Creating
13. Distinguish between breakdown maintenance and preventive
maintenance.
Level 1 Remembering
14. How do you show your understanding on Little?s formula in
queuing theory?
Level 2 Understanding
15. Categorize Queue Discipline.
Level 3 Applying
16. Develop Kendall?s Notation of a Queue.
Level 4 Analysing
17. What is ?Collusion? in Queue Discipline?
Level 1 Remembering
18. Compare the Queue Length and No. of Customers in the System.
Level 2 Understanding
19. Distinguish between individual replacement and group
replacement?
Level 3 Applying
20. Describe Kendall?s Notation for identifying a Queue Model with
two channels, Poisson arrivals, exponential service Unlimited
Queue and infinite calling population.
Level 1 Remembering
S.No
PART - B QUESTIONS Marks
BT
LEVEL
COMPETENCE
1. The cost of machine is Rs.16, 00 and scrap value is
Rs.1,100. Maintenance Cost form for machine are as
follows:
Year 1 2 3 4 5 6 7 8
Maintenance
cost
300 459 600 800 100 1200 1500 2000
When should the machine be the replaced?
Level 1 Remembering
2.
The following table gives to cost of spares per year,
overhead cost of maintenance per year and resale value of
certain equipment whose purchase price is Rs. 50,000:
Illustrate when the machine can be replaced.
Year 1 2 3 4 5
Cost of Spares 10000 12000 14000 15000 17000
Overhead
Maintenance
Cost
5000 5000 6000 6000 8000
Resale Value 40000 32000 28000 25000 22000
Level 2 Understanding
3.
A Taxi owner estimates from his past records that the cost
per year for operating a taxi whose purchase price when
new is Rs.60,000 are as follows.
Age 1 2 3 4 5
Operating cost 10000 12000 15000 18000 20000
After 5 years the operating cost is Rs.6000 x K, Where ?k?
is 6,7,8,9,10(age). If the resale value decreases by 10% of
Level 3 Applying
purchase price each year, calculate the best time of
replacement if time value is not implemented?
4.
(i)
A cost of a machine is 6100 and its scrap value is Rs.
100. The maintenance Cost from the experience are as
follows:
Year 1 2 3 4 5 6 7 8
Maintenance
cost
100 250 400 600 900 1200 1600 2000
Examine the average cost of replacement
(8)
Level 4 Analysing
(ii) Analyze when the asset can be replaced (5)
5.
(i)
Week 1 2 3 4 5 6 7
Conditional
Probability
0.07 0.15 0.25 0.45 0.75 0.9 1
IRP
Co
st
is Rs.1.25 per item
GRP Cost is Rs.60 Paise Per item.
Estimate the IRP Cost
(5)
Level 5 Evaluating
(ii)
Predict GRP cost and Determine whether GRP or IRP is the
Best Policy
(8)
6.
Machine A Costs Rs.9000. Annual Operating Cost is
Rs.200 for the 1
st
year and then increases by 2000 every
year. Determine the best age at which to replace the
machine. Assume the machine has no resale value.
Machine B Costs Rs.10,000 . Annual operating cost is
Rs.400 for the 1
st
year and then increases by 800 every
year. No resale value. You have now a machine of type A
which is one year old. Conclude if M/c A can be replaced
by M/c B. Is so, When?
Level 6 Creating
7.
A manufacturer is offered two machines A and B. A has
cost price of Rs.2,500, its running cost is Rs. 400 for each
of first years and increased by Rs. 100 every subsequent
year, Taking money?s value as 10% per year, when
machine should be replaced?
Level 1 Remembering
8.
The maintenance cost and resale value per year of a
machine whose purchase price is Rs.7000 is given below :
Year Operating Cost Resale Value
1 900 400
2 1200 2000
3 1600 1200
4 2100 600
5 2800 500
6 3700 400
7 4700 400
8 5900 400
When should the machine be replaced ?
Level 2 Understanding
10.
(i)
IRP cost Rs 4/item. GRP cost is
80paise/item.
Week 1 2 3 4 5 6
Probability
0.09
0.25
0.49
0.85
0.97
1
Find the IRP cost
5
Level 4 Analysing
(ii) Compare IRP or GRP and conclude which is best. 8
11. A machine owner finds from his past records that the
cost per year of maintaining a machine, whose purchase
price is Rs.6,000 are as given below.
Year 1 2 3 4 5 6 7 8
Maint
en
Ance
Cost
100 1200 140
0
180
0
230
0
280
0
340
0
400
0
Resal
e
Price
3000 150
0
750 375 200 200 200 200
Find at what age a replacement is due, assuming time
value is 10%
Level 1 Remembering
12.
(i)
(ii)
Cars arrive at a petrol pump, having one petrol
unit, in poisson fashion with an average of 10 cars
per hour. The service time is distributed
exponentially with a mean of 3 minutes.
(3)
Level 2 Understanding
PredictAverage number of cars in the system
Average waiting time in the queue
(3)
(iii)
Average queue length
(3)
(iv) The probability that the number of cars in the system is (4)
13.
(i)
In a public telephone booth, the arrivals are on the
average 15 per hour. A call on the average takes 3
minutes. If there is just one phone, Analyse and find:
The expected number of callers in the booth at any
time.
(6)
Level 4 Analysing
(ii) The proportion of the time the booth is expected tobe
idle
(7)
9.
A truck owner finds from his past experience that the
maintenance costs rs.200 for the first year and then
increases by rs.2000 every year, The cost of the truck type
A is rs.9000. Determine the best age at which to replace
the truck. Truck B type cost rs.10000.Annual Maintenance
costs are rs.400 and increased by Rs.800 every year. The
truck owner now has truck type A which is one year old
and should be replaced by Type B and if so when?
Level 3 Applying
14.
A T.V repairman finds that the time spent on his job has
an exponential distribution with mean 30 minutes. If he
repairs sets in the order in which they came in and if the
arrival of sets is poisson with an average rate of 10 per
8 hour day, how will you calculate the expected idle
time day? How much is the queue length and how
many TV sets would be in the shop ?
Level 1 Remembering
PART - C
S.No Questions Mar
ks
BT
Level
Competence
1.
(i)
Assume an insurance company has three claims adjusters
in its branch office. People with claims against the company
are found to arrive in a Poisson fashion, at an average rate
of20 per 8-hour day. The amount of time that an adjuster
spends with a claimant is found to have an exponential
distribution, with mean service time 40 minutes. Claimants
are processed in the order of their appearance.
How many hours a week can an adjuster
expect to spend with claimants?
(8)
Level 1 Remembering
(ii) How much time, on the average, does a claimant spend in
the branch office?
(7)
2.
(i)
In a reservation counter with a single server, customer arrive
with the inter-arrival time as the exponential distribution with
mean 10 minutes. The service time is also assumed to be
exponential with mean 8 minutes. Predict the idle time of the
server
(5) Level 2
Understanding
(ii) The average length of the Queue.
(5)
(iii) Expected time that a customer spends in the system.
(5)
3.
An electronic equipment contains 500 resistors. When any
resistor fails, it is replaced. The cost of replacing a resistor
individually is Rs.20. If all the resistors are replaced at the
same time, the cost per resistor is Rs. 5. The percentage
of surviving, S(i) at the end of month i is given below; Apply
IRP &GRP & Find which is best.
Month I 0 1 2 3 4 5
S (i) 100 90 75 55 30 0
Level 3 Applying
FirstRanker.com - FirstRanker's Choice
(An
?
DEPARTMENT OF MANAGEMENT STUDIES
QUESTION BANK
II SEMESTER
1915201? APPLIED OPERATIONS RESEACH
Regulation ? 2019
Academic Year 2019 - 2020
Prepared by
Dr. Radha Ganesh Kumar ? Asst. Professor (Sel.G) and HOD
Mr.B. Sam Paul ? Asst. Professor (OG)
(An
? .
DEPARTMENT OFMANAGEMENT STUDIES
QUESTION BANK
SUBJECT :1915201 ?APPLIED OPERATIONS RESEACH
SEM / YEAR : IISemester / IYear
UNIT ? I ?INTRODUCTION TO LINEAR PROGRAMMING (LP)
SYLLABUS: Introduction to applications of operations research in functional areas of management.
Linear Programming-formulation, solution by graphical and simplex methods, Special cases. Dual
simplex method. Principles of Duality. Sensitivity Analysis.
PART- A
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Define Operations Research (OR). Level 1 Remembering
2. Differentiate between Simplex and Big M Method Level 2 Understanding
3. How do you show your understanding unbounded solution? Level 3 Applying
4. Categorize the forms of LPP. Level 4 Analysing
5.
Discuss why is two phase method is better than Big M
method?
Level 5 Evaluating
6. Interpret the usage of Sensitivity Analysis in LPP. Level 6 Creating
7. What are the assumptions and requirements of LPP? Level 1 Remembering
8. Compare Dual Simplex and Duality. Level 2 Understanding
9. Identify the Advantages of duality. Level 3 Applying
10. What do you think about Infeasible solution? Level 4 Analysing
11. How will you solve LPP graphically? Level 5 Evaluating
12.
Conclude your understanding on the mathematical
formulation of LPP.
Level 6 Creating
13. Define basic variables and artificial variables. Level 1 Remembering
14. Compare Slack variable & Surplus Variable. Level 2 Understanding
15.
Give some example for the role of Surplus variable & Slack
Variable in the simplex method
Level 3 Applying
16. How would you apply Artificial variable? Level 4 Analysing
17. What is Big M Method? Level 1 Remembering
18. Distinguish simplex and Big M method Level 2 Understanding
19.
What do you mean by Duality? List the Rules for primal and
dual.
Level 1 Remembering
20. What is Shadow price? Level 1 Remembering
PART- B
S.NO
QUESTIONS
BT
LEVEL
COMPETENCE
1.
(i)
Maximise Z=3x+4y subject to
2x+5y ?60,
4x+2y ?40.
x, y >0. Solve by Graphical Method
Plot the graph
(8)
Level 1 Remembering
(ii) Which one is the best solution? (5)
2.
(i)
Min Z= 20x
1
+10 x
2
subject to
x
1
+2x
2
? 40,
3x
1
+x
2
? 30,
4x
1
+3x
2
? 60,
x
1
,x
2
? 0.
Solve by Graphical Method,
Plot the graph
(8)
Level 2 Understanding
(ii) Predict the value of x & y. (5)
3 Max Z= 5x1+4x2 subject to
x
1
-2x
2
? 1,
x
1
+2x
2
?3,
x
1
,x
2
? 0. Solve Graphically. Which one is the best
solution?
Level 3 Applying
4.
(i)
A Plant Manufacturer 2 Product A & B. The Profit Contribution
of each product has been estimated as Rs.300 for product A
and Rs.400 for Product B. Each Product passes through 3
departments of the plant. The time required for each product
and total time available in each department is as follows.
Department Hours
Required
Hours
Required
Available
Hours
during
month
Product
A
Product
B
I 2 3 1600
II 3 2 1500
III 1 1 700
The company has a contract to supply atleast 300 units of
Product B per month.
Formulate the LPP
(5)
Level 4
Analysing
(ii) Solve through Graphical Method
(8)
5. Solve the following LPP by graphical method.
Maximize Z= 3x
1
+2x
2
Subject t o
- 2x
1
+x
2
?1,
x
1
? 2,
x
1
+ x
2
? 3
and x
1
,x
2
? 0
Level 5 Evaluating
6. (i) Max Z= 1000x
1
+4000x
2
+5000x
3
Subject to 3x1+3x
3
?22,
x1+2x2+3x
3
? 14,
3x1+2x2 ? 14
& x1,x2 ? 0
Develop a Simplex Table
(5)
Level 6 Creating
(ii) Analyse and find the value of x
1
, x
2
? (8)
7. Analyze the following LPP by Simplex Method:
Min Z = -10y
1
-15y
2
-20y
3
Subject to 2y
1
+4y
2
+6y
3
? 24,
3y
1
+9y
2
+6y
3
? 30,
& y
1
, y
2
, y
3
? 0.
Level 1 Remembering
(i)
Develop a Simplex Table (5)
(ii) Solve and find the value of y1 ,y2 and y3
(8)
8.
Solve By Graphical Method
Minimize Z= 40x
1
+24x
2
Subject to, 20x
1
+50 x
2
> 4,800
80 x
1
+50x
2
> 7,200
x
1
,x
2
>0
Level 2 Understanding
9. Solve the following LPP by simplex method:
Minimize Z= 8x
1
-2x
2
Subject to -4x
1
+2x
2
?1,
5x
1
-4x
2
?3,
and x
1
,x
2
? 0
Level 3 Applying
10. Solve the following LPP by simplex method:
Maximize Z= 3x1+2x
2
Subject to
2x
1
+x
2
?2,
3x
1
+4x
2
?12,
x
1
,x
2
? 0
Level 4 Analyzing
11. Review the LPP and solve by simplex method
Max Z= 25x+10y
Subject to the constraints
x+0.5y? 20
x+y? 50
x,y ? 0
Level 1 Remembering
12. A firm produces three products. These products are
processors on 3 different machines. The time required for
manufacturing one unit of cost of the products and the daily
capacity of the three machines is given in the table below.
Analyse and find the optimum solution.
Mac
hine
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Time/Unit
(Minutes)
Machine
Capacity
Min /Day
Product1 Product 2 Product 3
M1 2 8 2 940
M2 4 - 8 970
M3 2 5 - 430
It is required to determine the daily no. of units to be
manufactured for each product. The profit for unit for
Level 2 Understanding
product 1,2,3 is Rs.4,Rs.8,Rs.6 respectively. It is assumed
that all the amount produced are consumed in the market
13. Using dual simplex method , solve and find the optimum
solution for the given LPP.
Maximize Z=6x
1
+4x
2
+4x
3
Subject to 3x
1
,x
2
+2x
3
? 2
2x
1
+x
2
-x
3
? 1
-x
1
+x
2
+2x
3
? 1 &
x
1
,x
2
,x
3
? 0
Level 4 Analysing
14.
(i)
Evaluate by using dual simplex method and solve the LPP.
Minimize Z=2x
1
+x
2
Subject to 3x
1
+2x
2
? 3
4x
1
+3x
2
? 6
x
1
+x
2
? 5 & x
1
,x
2
?
Determine the dual simplex table
(5)
Level 1 Remembering
(ii)
Find the value of x
1
, x
2
(8)
PART - C
S.No Questions BT
LEVEL
COMPETENCE
1.
Max Z=300x+400y subject to
2x+3y ? 1600,
3x+2y ? 1500,
x+y ? 700,
y ? 300, x,y ? 0 Solve by Graphical Method, choose the
value of x & y which maximizes profit.
Level 1 Remembering
2. Solve the following LPP by graphical method.
Minimize Z= 6000x1+4000x
2
Subject t o
3x+x
2
? 40,
x
1
+2.5 x
2
? 22
3x
1
+3 x
2
? 40
and x
1
,x
2
? 0
Level 2 Understanding
3. Develop a Simplex Table and Solve
Max Z = 3 x1+2 x2,
Subject to
x1+ x2 ?4,
x1- x2 ? 2;
x1, x2 ?0.
Level 3 Applying
4. Solve by using Simplex Method.
Maximize Z= 3x+5y
Subject to the constraints
x+y? 60
x? 40
y ? 30
x,y ? 0
Level 1 Remembering
UNIT - II LINEAR PROGRAMMING EXTENSIONS
SYLLABUS: Transportation Models (Minimizing and Maximizing Problems) ? Balanced and unbalanced
Problems ? Initial Basic feasible solution by N-W Corner Rule, Least cost and Vogel?s approximation methods.
Check for optimality. Solution by MODI /. Case of Degeneracy. Trans-shipment Models. Assignment Models
(Minimising and Maximising Problems) ? Balanced and Unbalanced Problems. Solution by Hungarian and
Branch and Bound Algorithms. Travelling Salesman problem.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define Transportation & Transhipment. Level 1 Remembering
2. Differentiate balanced transportation problem & Unbalanced
Transportation Problem.
Level 2 Understanding
3. How would you show your understanding on unbalanced
transportation problem?
Level 3 Applying
4. Categorize the Phases of transportation model. Level 4 Analysing
5. Construct the basic feasible solution for the following
transportation problem.
1 2 3 4 SUPPLY
1 2 3 11 7 6
2 1 0 6 1 1
3 5 8 15 9 10
DEMAN D 7 5 3 2
Level 5 Evaluating
6 Interpret the need for Optimum solution in transportation. Level 6 Creating
7. What do you mean by Least cost method (LCM)? Level 1 Remembering
8. Compare Vogel approximation method (VAM) & Least Cost
Method.
Level 2 Understanding
9. How do you represent a travelling salesman problem
through mathematical formulation?
Level 3 Applying
10. Analyse the rules of travelling salesman Problem. Level 4 Analysing
11. Discuss the meaning of Assignment Level 5 Evaluating
12. Compare Balanced assignment problem & Unbalanced
Assignment Problem.
Level 6 Creating
13. What example can you give for Unbalanced assignment
problem?
Level 1 Remembering
14. How will you resolve degeneracy in Transportation Problem? Level 2 Understanding
15. Classify transportation problem. Level 3 Applying
16. Examine the Steps in Hungarian algorithm. Level 4 Analysing
17. What is Branch and bound algorithm in Assignment? Level 1 Remembering
18. Compare Assignment and transportation Problem. Level 2 Understanding
19. What do you mean by Travelling Salesman Problem? Level 1 Remembering
20. What is Restricted Assignment? Level 1 Remembering
S.NO QUESTIONS
BT
LEVEL
COMPETENCE
1. Solve and find the Transportation Problem and Which method will
you select if you want toMinimize Cost?
Destination Supply
1 2 3 4
I 21 16 25 13 11
II 17 18 14 23 13
III 32 27 18 41 19
Demand 6 10 12 15
Level 1 Remembering
2. Find the Initial Basic Feasible solution for following TP. Using NW
Rule, LCM, and VAM. Which method will you select if you want to
Minimize Cost?
D1 D2 D3 Supply
S1 7 3 2 2
S2 2 1 3 3
S3 3 4 6 5
Demand 4 1 5 10
Level 2 Understanding
3.
(i)
Analyze the transportation problem with unit transportation
costs,demand, and supply as given below:
Destination
Supply
Source
D1 D2 D3 D4
S1
6 1 9 3
70
11 5 2 8
S2 55
10 12 4 7
S3
70
Demand 85 35 50 45
Apply VAM for Initial solution.
(5)
Level 3 Applying
(ii)
Construct the final Solution by using MODIMethod.
(8)
4.
(i)
Analyze & solve the following transportation problem to maximize
profit.
A B C D Supply
1
Source 2
3
Demand
15 51 42 33 23
80 42 26 81 44
90 40 66 60 33
23
31
16
30
100
Examine Initial solution using VAM.
(5)
Level 4 Analysing
(ii)
Analyze and find out the final Solution by using MODI Method.
(8)
5. Solve the following transportation problem using Vogel?s
method
Factory? Warehouse ?Available
A B C D E F
1 9 12 9 6 9 10 5
2 7 3 7 7 5 5 6
3 6 5 9 11 3 11 2
4 6 8 11 2 2 10 9
4 4 6 2 4 2
Requirement?
(5)
Level 5 Evaluating
6. (i) Solve the transportation problem and decide using VAM for initial
solution.
(5) Level 6 Creating
(ii) Evaluate using NWC and Least Cost method for initial solution?
Destination Supply
I 2 1 25 13 11
II 1 1 14 23 13
III 3 2 18 41 19
Demand 6 1 22 15
(8)
7.
Maximize profit from the following transportationproblem.
A B C D Supply
I 40 25 22 33 100
SourceII 44 35 30 30 30
III 38 38 28 30 70
Demand 40 20 60 30
Level 1 Remembering
(i) How will you convert maximization problem to minimization.
Find the maximum profit
(8)
(ii) Explain stepping stone method for checking the
solution for optimality transportation problems.
(5)
8. A company has one surplus truck in each of the cities A, B, C, D, &
E and one deficit trucks in each of the cities 1,2,3,4,5,6. The
distance between the cities in kms is shown in the matrix below.
Can you select the assignment of trucks from cities in surplus to
cities in deficiency .so that total distance covered by the vehicles is
minimum?
1 2 3 4 5 6
A 12 10 15 22 18 8
B 10 18 25 15 16 12
C 11 10 3 8 5 9
D 6 4 10 13 13 12
E 8 12 11 7 13 10
Level 2 Understanding
9.
Consider the problem of assigning five jobs to five persons. The
assignment costs are given as follows:
PERSONS?JOBS ?
1 2 3 4 5
A 8 4 2 6 1
B 0 9 5 5 4
C 3 8 9 2 6
D 4 3 1 0 3
Level 3 Applying
E 9 5 8 9 5
Determine the optimum assignment schedule.
10. The assignment cost of assigning any one operator to any one
machine is given in the following table.
MACHINE?OPERATORS ?
I II III IV
A 10 5 13 15
B 3 9 18 3
C 10 7 3 2
D 5 11 9 7
Find the optimal assignment by Hungarian method.
Level 4 Analysing
11. A machine shop purchased a drilling machine and two lathes of
different capacities. The Positioning of the machines among 4
possible locations on the shop floor is important forms the
standard of materials handling. Given the cost estimate per unit
time of materials below, find the optimum location of the
machines.
LOCATIONS
1 2 3 4
Lathe 1 12 9 12 9
Drill 15 Not
suitable
13 20
Lathe 2 4 8 10 6
Level 1 Remembering
12.
Solve the assignment problem for maximization given profit
matrix(profit in rupees).
Machines
P Q R S
JOB
51 53 54 50
47 50 48 50
49 50 60 61
63 64 60 60
Level 2 Understanding
PART - C
S.No Questions Marks BT
Level
Competence
1.
a
Assume that you are an OR specialist. Identify the procedure
for each of the following Method to the employees in order to
help them achieve solution to Transportation Problems.
Northwest Corner Cell Method
(3)
Level 1 Remembering
b Least Cost cell Method (4)
c Vogel?s Approximation Method (4)
d U V Method. (4)
13. The processing time in hours for the jobs when allocated to the
different machines is indicated below. Select the best assignment
of the machines for the jobs so that the total processing time is
Minimum.
Machines
M1 M2 M3 M4 M5
J1 9 22 58 11 19
JOB J2 43 78 72 50 63
J3 41 28 91 37 45
J4 74 42 27 49 39
J5 36 11 57 22 25
Level 4 Analysing
14. For the given travelling salesman problem, Minimize the total cost.
To
1 2 3 4
From A - 46 16 40
B 41 - 50 40
C 82 32 - 60
D 40 40 36 -
Level 1 Remembering
(i) Observe the above travelling salesman
problem and find out minimize the cost per
cycle.
(8)
(ii) Find whether path is satisfied. (5)
2.
Solve the following transportation problem, in which a
i
is the
availability at Origin
O
i
and b
j
is the requirement at the destination D
j
and cell entries
are unit costs of transportation from any origin to any
destination:
D1 D2 D3 D4 D5 a
j
O1 4 7 3 8 2 4
O2 1 4 7 3 8 7
O3 7 2 4 7 7 9
O4 4 8 2 4 7 2
b
j
8 3 7 2 2
Predict the allocation to minimize the cost.
Level 2 Understanding
3. A company has a team of 4 Salesman and the company wants to
do in 4 districts. Considering the capabilities of salesmen
and nature of the district, the company has estimated the profit per
day in Rs. For each salesmen in each district as follows.
District
s
Salesmen 1 2 3 4
A 16 10 14 11
B 14 11 15 15
C 15 15 13 12
D 13 12 14 15
Develop the best assignment schedule and analyze the total cost.
Level 3 Applying
4. Five operators have to be assigned to Five Machines. The
assignment costs are given in thetablebelow.
Analyse using Hungarian algorithm & find out the assignment to
minimize the cost.
Machine
I II III IV V
Operator
A 5 5 - 2 6
B 7 4 2 3 4
C 9 3 5 - 3
D 7 2 6 7 2
E 6 5 7 9 1
Level 4 Analyzing
UNIT ? III ? INTEGER PROGRAMMING AND GAME THEORY
SYLLABUS: Integer Programming ? Introduction and types - Game Theory-Two-person Zero sum
games-Saddle point, Dominance Rule, graphical and LP solutions, Nash Equilibrium
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. What do you mean by integer programming problem?
Level 1 Remembering
2. In what respect a mixed IPP differs from pure IPP?
Level 2 Understanding
3. What is Nash Equilibrium?
Level 3 Applying
4. Classify the different types of strategy.
Level 4 Analysing
5. Compile the Characteristics of game.
Level 5 Evaluating
6. Can you assess the applications of integer
programming?
Level 6 Creating
7. Define Game.
Level 1 Remembering
8. Compare Mixed Strategy and Pure Strategy.
Level 2 Understanding
9. How would you make use of the concept of Game theory
in Managerial Decision Making?
Level 3 Applying
10. Conclude your understanding about Payoff Matrix.
Level 4 Analysing
11. How will you find the optimal strategies and value of the
following game?
Player B
Player
A
H T
H 2 -1
T -1 0
Level 5 Evaluating
12. Interpret the concept of two person zero sum game.
Level 6 Creating
13. What is Saddle point?
Level 1 Remembering
14. Compare Dominance Principle of Rows and Columns.
Level 2 Understanding
15. Identify the basic assumptions of the Game.
Level 3 Applying
16. Conclude the advantages of Game theory.
Level 4 Analysing
17. What are the Methods of Matrices?
Level 1 Remembering
18. Summarize how graphs and LP solution are used in
Game theory.
Level 2 Understanding
19. What is a Decision Tree?
Level 1 Remembering
20. Define Dominance principle.
Level 1 Remembering
S.N
O
PART - B QUESTIONS MA
RK
S
BT
LEVEL
COMPETENCE
1. (i) What do you mean by Pure IPP? (3) Level 1 Remembering
(ii) What do you mean by Mixed IPP? (5)
(iii)
List out the difference between Pure and Mixed IPP.
(5)
2. (i) For what value of ?,the game with the following
matrix is strictly determined
B
1
B
2
B
3
A
1
? 6 2
A
2
-1 ? -7
A
3
-2 4 ?
(8) Level 2 Understanding
(ii) Write down the assumptions of game theory. (5)
3. (i) Solve the game whose pay-off matrix is given by
B
1
B
2
B
3
A
1
1 3 1
A
2
0 -4 -3
A
3
1 5 -1
(8)
Level 3 Applying
(ii) Explain the concept of Nash Equilibrium. (5)
4.
Analyze the Value of the game graphically
B1 B2
A1 4 4
A2 2 7
A3 5 3
A4 6 2
Level 4 Analysing
5.
What inference can be made using Dominance
Principle to reduce the following game and estimate
the game value?
B1 B2 B3 B4
A1 3 2 4 0
A2 3 4 2 4
A3 4 2 2 0
A4 2 1 6 3
Level 5 Evaluating
6.
How would you evaluate the following game whose
Pay-Off matrix is Given Below?
9 3 1 8 0
6 5 4 6 7
2 4 3 3 8
5 6 2 2 1
Level 6 Creating
7.
(i)
Two players A&B match coins. If the coins match
then A wins one unit value, if the coins do not
match then B wins one unit of value.
Determine pay-off matrix which strategy is to be
chosen
(5)
Level 1 Remembering
(ii)
Find the value of game. (8)
8.
Predict the Value of the Game given above Pay
OffMatrix.
Player B
B1 B2 B3
A1 -2 5 -3
Player A A2 1 3 5
A3 -3 -7 11
Level 2 Understanding
9.
Apply graphical analysis to Solve the game.
A/
B
B1 B2 B3 B4
A1 3 3 4 0
A2 5 4 3 7
Level 3 Applying
10. Solve the following game by graphical method.
Player B
1 2 3
1 6 4 3
Player A 2 2 4 8
Level 4 Analysing
11.
(i)
A and B play a Match(Game) in which each has 3
coins 5 paise, 10 paise and 20 paise. Each player
selects a coin without the knowledge of others
choice. IF the sum is even, B wins A?s Coin. If sum
is Odd, A wins B?s coin.
How will you find the pay-off matrix ?
(5)
Level 1
Remembering
(ii)
Find the Best Strategy & value of the Game. (8)
12.
Consider the Pay Off Matrix of player A as shown in
the table below and solve it optimally using the
graphical method .
Player A
Player
B
1 2 3 4 5
1 3 6 8 4 4
2 -7 4 2 10 2
Level 2 Understanding
13.
(i)
Analyze the Game Graphically:
Player A
Player
A
B1 B2
A1 -3 1
A2 5 3
A3 6 -1
A4 1 4
A5 2 2
A6 0 -5
Plot the graph
(5)
Level 4 Analysing
(ii)
Analyse and find the value of the game.
(8)
14.
Which one is the best strategy using Dominance
Principle?
B1 B2 B3 B4 B5 B6
A1
4 2 0 2 1 1
A2
4 3 1 3 2 2
A3
4 3 7 -5 1 2
A4
4 3 4 -1 2 2
A5
4 3 3 -2 2 2
Level 1 Remembering
PART-C
S.No Questions BT
Level
Competence
1.
Using Dominance property Solve.
B
A
I II IIIIV
1 -5 3 1 20
2 5 5 4 6
3 -4 -2 0 -5
Level 1 Remembering
2. Examine the 2 * n Game by the Method of Sub Game:
B1 B2 B3
A1 1 3 11
A2 8 5 2
Level 2 Understanding
3. In a game of matching coins with 2 players, A wins 1 unit value
when there are 2 heads, wins nothing when there are 2 tails
and looses ? unit value when there are one head and one tail.
Develop Pay Off matrix and value of the game.
Level 3 Applying
4.
i
ii
iii
Assume you have to choice of 3 strategies for advertising
and you have one major
Analyse the theory on Two-person sum games competitor
with 3 strategies.
(5)
Level 4 Analysing
What are the assumptions of Game? (5)
Find value of game.
B1 B2 B3
A1 80 70 60
A2 90 80 100
A3 40 30 40
(5)
UNIT - IV INVENTORY MODELS, SIMULATION AND DECISION THEORY
SYLLABUS: Inventory Models ? EOQ and EBQ Models (With and without shortages), Quantity Discount
Models. Decision making under risk ? Decision trees ? Decision making under uncertainty. Monte-carlo
simulation.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define inventory. Level 1 Remembering
2.
Classify the Forms of inventory.
Level 2 Understanding
3.
Identify the Objectives/significance of inventory model.
Level 3 Applying
4.
Highlight the importance of Reorder level.
Level 4 Analysing
5.
Discuss the concept of Lead time.
Level 5 Evaluate
6.
Interpret the Types of stock replenishment.
Level 1 Remembering
7.
List the Basic inventory models.
Level 2 Understanding
8.
Compare Ordering Cost and Carrying Cost.
Level 3 Appyling
9.
Identify when shortage cost and stock out cost arises?
Level 5 Evaluating
10.
Analyze why safety stock is maintained.
Level 1 Remembering
11.
Discuss the concept of Quantity Discount Model.
Level 2 Understanding
12.
Interpret the meaning of EOQ & EBQ.
Level 3 Applying
13.
What are random and pseudo random numbers?
Level 4 Analysing
14.
Explain Monte Carlo Method.
Level 5 Evaluating
15.
Summarize the concept of EMV.
Level 1 Remembering
16.
What inference can you make about holding cost ?
Level 2 Understanding
17.
What is Shortage Cost?
Level 3 Applying
18. Classify and explain the various conditions under which
decisions are made.
Level 1 Remembering
19. What is meant by the following terms in inventory
management: i)Carrying cost ii) shortage costs
Level 2 Understanding
20. What is Decision theory? List the problems that can be solved
by Simulation.
Level 3 Applying
S.NO PART - B QUESTIONS Marks BT
LEVEL
COMPETENCE
1.
(i)
Alpha industry needs 5400 units per year of a bought out
component which will be
used in its main product. The ordering cost is Rs.250
per order and the carrying cost per unit per year is
Rs.30.
Which is the best order quantity?
(8)
Level 1 Remembering
(ii)
Find the number of order per year and Frequency of
orders?
(5)
2.
(i)
A stockiest has to supply 12000 units of a product per
year to his customer. Demand is
fixed and known. Shortage cost is assumed to be
infinite. Inventory holding cost is 20 paise per unit per
month. Ordering Cost is Rs. 250 and purchase price
is Rs.10 per unit.
Estimate the EOQ
(8)
Level 2 Understanding
(ii)
Find the Frequency of orders and total inventory cost. (5)
3.
ABC manufacturing company purchases 9000 parts of a
machine for its annual requirement. Each part costs
Rs.20. The ordering cost per order is Rs.15 and the
carrying charges are 15% of the average inventory per
year. Apply EOQ formulae and find out EOQ, No of
orders ,Total Inventory Cost and total cost.
Level 3 Applying
4.
(i)
Demand for an item in a company is 18,000 units per
year. The company can produce the items at a rate of
3000 units per month. The Cost of one setup is Rs.500
and the holding cost of one unit per month is 15 paise.
Shortage cost of one unit is Rs.20 per year.
Analyze and find the optimum manufacturing quantity.
(8)
Level 4 Analysing
(ii)
Find the number of shortages and frequency of
Production run.
(5)
5. A company has a demand of 12000 units/year for an
item and it can produce 2000 units per month. The
cost of one setup is Rs.400 and the holding
cost/unit/month is 15 paise. Select the optimum lot
size and total cost per year assuming the cost of 1 unit
as Rs.4. Find EBQ, the number of set ups & total cost.
Level 5 Evaluating
6.
(i)
Find the optimal order quantity for a product when the
annual demand for the product is 500 units. The Cost of
storage per unit per year is 10% of the unit cost. Ordering
cost per order is Rs. 180.
Determine EOQ
(8)
Level 6 Creating
(ii)
Evaluate the Total Cost
(5)
The unit cost are given below:
Quantity Unit Cost(Rs.)
O
1500<=Q3<3000 24.60
3000<=Q4 24.40
7. (i)
Formulate the Optimal order quantity for a product for
which the price breaks are as follows
(8)
Level 1 Remembering
(ii)
Also find the Total cost.
Quantity Unit Cost(Rs.)
O
750<=Q 875
(5)
8.
Compute the EOQ and the total variable cost for the
following:
Annual demand: 25 units
Unit price: Rs.2.50
Order cost: Rs.4.00
Storage rate: 1% per year
Level 2 Understand
9.
(i)
Identify the profit under three states of nature & three
decision alternative.
State of
Nature
State of
Nature
State of
Nature
N1 N2 N3
Decision
Naking
D1 150 250 300
Decision
Naking
D2 450 250 200
Decision
Naking
D3 100 180 290
Hurwitz criterion for alpha=0.5
(3)
Level 3 Applying
(ii)
Laplace condition
(5)
(iii)
Minimax Condition
(5)
10.
A Bakery keeps a stock of particular brand of cake. Daily
demand of past experience.
Daily
demand
0 15 25 35 45 50
Probability 0.01 0.15 0.20 0.50 0.12 0.02
Consider the following sequence of random numbers.
48 78 9 51 56 77 15 14 68 9
Using this sequence simulate the demand for next 10
days.
Find the stock situation if the owner makes 35 cakes
every day. Examine the daily average demand.
Level 1 Remembering
11.
Given above is the following pay off matrix.
Using EMV criterion . Decide which of the act can be
chosen at the best. FindEVPI & EOL.
Nature
Probability
Don?t
Expand
Expand
200
Expand
400
High
Demand
0.4 2500 3500 5000
Medium
Demand
0.4 2500 3500 2500
Low
Demand
0.2 2500 1500 1000
Level 2 Understanding
12.
A sample of 100 arrivals of customers at a retail sales
depot is according to the following distribution.
Time between arrivals(mins) Frequency
0.5 2
1.0 6
1.5 10
2.0 25
2.5 20
3.0 14
3.5 4
4.0 7
4.5 4
5.0 2
Use random numbers and predict the average time
between arrivals.
48 78 9 51 56 77 15 14 68 9
Level 3 Applying
13.
(i)
A departmental store purchases sprays which can be
ordered only in lots of 10. Each spray cost Rs.75 and
sells at Rs.90 each. Used sprays, however have \no
salvage value.
Demand 10 20 30 40 50
Probability 0.2 0.35 0.25 0.15 0.05
The probability distribution obtained from analysis of past
sales data is given below.
Analyse the payoff table.
(5)
Level 4 Analysing
(ii) How much quantity should the departmental store buy to
maximize its profit?
(8)
14. (i)
A company uses annually 50,000 units of an item each
costing Rs.1.20. Each order costs Rs.45 and inventory
carrying costs are 15% of the annual average inventory
value.
Find EOQ.
(3)
Level 2 Understanding
(ii) If the company operates 250 days a year and the
procurement time is 10 days and safety stock is 500
units, find reorder level, maximum, minimum and
average inventory
(10)
PART - C
S.No Questions BT
Level
Competence
1.
A contractor has to supply 10000 bearings per day to an
automobile manufacturer. He finds that when he starts a
production run he can produce 25000 bearings per day. The
cost of holding a bearing in stock for one year is 2 paise and
the set up cost of the production run is Rs.18. How frequently
should production run be made and which is the Best
Economic Batch Quantity? How much would be the No. of
Setup and Total Inventory Cost.
Level 1 Remembering
2.
A stockist has to supply 400 units of a product every
Monday to his customer.
He gets the product at Rs.50 per unit from the
manufacturer. The cost of ordering and transportation
from the manufacturer is Rs.75 per order. The cost of
carrying inventory is 7.5% per year of the cost of product.
Predict EOQ, Frequency of orders and Number of Orders,
Total Incremental cost and Total Cost.
Level 2 Understanding
3. (i) Identify the profit under three states of nature & three
decision alternative.
State of
Nature
N1 N2 N3
Decision
Making
D1 100 200 300
D2 400 200 200
D3 200 160 390
Hurwitz criterion for alpha=0.5
(5) Level 3 Applying
(ii)
Laplace Condition
(5)
(iii) Mininmax Condition (5)
4.
An automobile production line turns out about 100 cars a
day, but deviation occur owing to many causes. The
production is more accurately described by the
probability distribution given below;
Production/
Day
Probability
95 0.03
96 0.05
97 0.07
98 0.10
Level 4 Analysing
99 0.15
100 0.20
101 0.15
102 0.10
103 0.07
104 0.05
105 0.03
Use the random numbers &find the average demand
48 78 9 51 56 77 15 14 68 9
UNIT - V QUEUING THEORYAND REPLACEMENT MODELS
SYLLABUS:Queuing Theory ?Single and Multi-Channel models-infinite number of customers and
infinite calling resource Replacement Models-Individuals replacement Models (With and without time
value of money) ? Group Replacement Models.
PART - A
S.NO QUESTIONS BT LEVEL COMPETENCE
1. Define Queue.
Level 1 Remembering
2. How do you show your understanding on replacement theory?
Level 2 Understanding
3. In a bank, 20 customers on an average are served by a
cashier in an hour. If the service time has exponential
distribution, what is the probability that it will take more than
10 minutes to serve a customer?
Level 3 Applying
4. Classify the types of Queue.
Level 4 Analysing
5. How waiting time cost is related to queuing system?
Level 5 Evaluating
6. Interpret the Characteristics Of Queuing Models.
Level 4 Evaluating
7. How would you explain consumer behavior in queues?
Level 1 Remembering
8. Compare Serial and parallel Queue with Examples. Level 2 Understanding
9. Classify the types of Replacement model.
Level 3 Applying
10. Describe Kendall?s Notation for identifying a Queue Model with
single channel, Poisson arrivals, exponential service unlimited
queue and infinite calling population.
Level 4 Analysing
11. GRP includes IRP .Do You Agree?
Level 5 Evaluating
12. What is GRP &IRP?
Level 6 Creating
13. Distinguish between breakdown maintenance and preventive
maintenance.
Level 1 Remembering
14. How do you show your understanding on Little?s formula in
queuing theory?
Level 2 Understanding
15. Categorize Queue Discipline.
Level 3 Applying
16. Develop Kendall?s Notation of a Queue.
Level 4 Analysing
17. What is ?Collusion? in Queue Discipline?
Level 1 Remembering
18. Compare the Queue Length and No. of Customers in the System.
Level 2 Understanding
19. Distinguish between individual replacement and group
replacement?
Level 3 Applying
20. Describe Kendall?s Notation for identifying a Queue Model with
two channels, Poisson arrivals, exponential service Unlimited
Queue and infinite calling population.
Level 1 Remembering
S.No
PART - B QUESTIONS Marks
BT
LEVEL
COMPETENCE
1. The cost of machine is Rs.16, 00 and scrap value is
Rs.1,100. Maintenance Cost form for machine are as
follows:
Year 1 2 3 4 5 6 7 8
Maintenance
cost
300 459 600 800 100 1200 1500 2000
When should the machine be the replaced?
Level 1 Remembering
2.
The following table gives to cost of spares per year,
overhead cost of maintenance per year and resale value of
certain equipment whose purchase price is Rs. 50,000:
Illustrate when the machine can be replaced.
Year 1 2 3 4 5
Cost of Spares 10000 12000 14000 15000 17000
Overhead
Maintenance
Cost
5000 5000 6000 6000 8000
Resale Value 40000 32000 28000 25000 22000
Level 2 Understanding
3.
A Taxi owner estimates from his past records that the cost
per year for operating a taxi whose purchase price when
new is Rs.60,000 are as follows.
Age 1 2 3 4 5
Operating cost 10000 12000 15000 18000 20000
After 5 years the operating cost is Rs.6000 x K, Where ?k?
is 6,7,8,9,10(age). If the resale value decreases by 10% of
Level 3 Applying
purchase price each year, calculate the best time of
replacement if time value is not implemented?
4.
(i)
A cost of a machine is 6100 and its scrap value is Rs.
100. The maintenance Cost from the experience are as
follows:
Year 1 2 3 4 5 6 7 8
Maintenance
cost
100 250 400 600 900 1200 1600 2000
Examine the average cost of replacement
(8)
Level 4 Analysing
(ii) Analyze when the asset can be replaced (5)
5.
(i)
Week 1 2 3 4 5 6 7
Conditional
Probability
0.07 0.15 0.25 0.45 0.75 0.9 1
IRP
Co
st
is Rs.1.25 per item
GRP Cost is Rs.60 Paise Per item.
Estimate the IRP Cost
(5)
Level 5 Evaluating
(ii)
Predict GRP cost and Determine whether GRP or IRP is the
Best Policy
(8)
6.
Machine A Costs Rs.9000. Annual Operating Cost is
Rs.200 for the 1
st
year and then increases by 2000 every
year. Determine the best age at which to replace the
machine. Assume the machine has no resale value.
Machine B Costs Rs.10,000 . Annual operating cost is
Rs.400 for the 1
st
year and then increases by 800 every
year. No resale value. You have now a machine of type A
which is one year old. Conclude if M/c A can be replaced
by M/c B. Is so, When?
Level 6 Creating
7.
A manufacturer is offered two machines A and B. A has
cost price of Rs.2,500, its running cost is Rs. 400 for each
of first years and increased by Rs. 100 every subsequent
year, Taking money?s value as 10% per year, when
machine should be replaced?
Level 1 Remembering
8.
The maintenance cost and resale value per year of a
machine whose purchase price is Rs.7000 is given below :
Year Operating Cost Resale Value
1 900 400
2 1200 2000
3 1600 1200
4 2100 600
5 2800 500
6 3700 400
7 4700 400
8 5900 400
When should the machine be replaced ?
Level 2 Understanding
10.
(i)
IRP cost Rs 4/item. GRP cost is
80paise/item.
Week 1 2 3 4 5 6
Probability
0.09
0.25
0.49
0.85
0.97
1
Find the IRP cost
5
Level 4 Analysing
(ii) Compare IRP or GRP and conclude which is best. 8
11. A machine owner finds from his past records that the
cost per year of maintaining a machine, whose purchase
price is Rs.6,000 are as given below.
Year 1 2 3 4 5 6 7 8
Maint
en
Ance
Cost
100 1200 140
0
180
0
230
0
280
0
340
0
400
0
Resal
e
Price
3000 150
0
750 375 200 200 200 200
Find at what age a replacement is due, assuming time
value is 10%
Level 1 Remembering
12.
(i)
(ii)
Cars arrive at a petrol pump, having one petrol
unit, in poisson fashion with an average of 10 cars
per hour. The service time is distributed
exponentially with a mean of 3 minutes.
(3)
Level 2 Understanding
PredictAverage number of cars in the system
Average waiting time in the queue
(3)
(iii)
Average queue length
(3)
(iv) The probability that the number of cars in the system is (4)
13.
(i)
In a public telephone booth, the arrivals are on the
average 15 per hour. A call on the average takes 3
minutes. If there is just one phone, Analyse and find:
The expected number of callers in the booth at any
time.
(6)
Level 4 Analysing
(ii) The proportion of the time the booth is expected tobe
idle
(7)
9.
A truck owner finds from his past experience that the
maintenance costs rs.200 for the first year and then
increases by rs.2000 every year, The cost of the truck type
A is rs.9000. Determine the best age at which to replace
the truck. Truck B type cost rs.10000.Annual Maintenance
costs are rs.400 and increased by Rs.800 every year. The
truck owner now has truck type A which is one year old
and should be replaced by Type B and if so when?
Level 3 Applying
14.
A T.V repairman finds that the time spent on his job has
an exponential distribution with mean 30 minutes. If he
repairs sets in the order in which they came in and if the
arrival of sets is poisson with an average rate of 10 per
8 hour day, how will you calculate the expected idle
time day? How much is the queue length and how
many TV sets would be in the shop ?
Level 1 Remembering
PART - C
S.No Questions Mar
ks
BT
Level
Competence
1.
(i)
Assume an insurance company has three claims adjusters
in its branch office. People with claims against the company
are found to arrive in a Poisson fashion, at an average rate
of20 per 8-hour day. The amount of time that an adjuster
spends with a claimant is found to have an exponential
distribution, with mean service time 40 minutes. Claimants
are processed in the order of their appearance.
How many hours a week can an adjuster
expect to spend with claimants?
(8)
Level 1 Remembering
(ii) How much time, on the average, does a claimant spend in
the branch office?
(7)
2.
(i)
In a reservation counter with a single server, customer arrive
with the inter-arrival time as the exponential distribution with
mean 10 minutes. The service time is also assumed to be
exponential with mean 8 minutes. Predict the idle time of the
server
(5) Level 2
Understanding
(ii) The average length of the Queue.
(5)
(iii) Expected time that a customer spends in the system.
(5)
3.
An electronic equipment contains 500 resistors. When any
resistor fails, it is replaced. The cost of replacing a resistor
individually is Rs.20. If all the resistors are replaced at the
same time, the cost per resistor is Rs. 5. The percentage
of surviving, S(i) at the end of month i is given below; Apply
IRP &GRP & Find which is best.
Month I 0 1 2 3 4 5
S (i) 100 90 75 55 30 0
Level 3 Applying
4.
(i)
The failure rates of 1000 street bulbs in a colony are
summarized in table:
End Of
Month
1 2 3 4 5 6
Probability
of failure
to Date
0.05 0.2
0
0.40 0.65 0.85 1.00
The cost of replacing an individual bulb is Rs.60. If all the
bulbs are replaced simultaneously it would cost Rs.25 Per
bulb. Any one of the following two options can be followed
to replace the bulbs.Replace the bulbs individually when
they fail (Individual replacementpolicy) (8)
Level 4 Analysing
(ii)
Replace all the bulbs simultaneously at fixed intervals and
replace the individual bulbs as and when they fail in service
during the fixed interval (Group replacementpolicy).
Analyse & find out the optimal replacement policy, i.e.,
Individual replacement policy or group replacement policy? If
group replacement policy is optimal, then find at what equal
intervals should all bulbs are replaced?
(7)
FirstRanker.com - FirstRanker's Choice
This post was last modified on 29 February 2020