Download OU (Osmania University) B.Sc Computer Science 6th Sem Operations Research Important Question Bank For 2021 Exam
Subject Title: Operations Research
Prepared by: E.Sukanya
Year: III
Semester: VI
Updated on: 25-03-
Unit - I:
1. Definitions of (i) Operations Research (ii) Deterministic model (iii) Probability model
2. Definitions of (i) Decission Variable (ii) Convex sets (iii) Extreme points of Convex Sets.
3. Definitions of (i) Solution (ii) Feasible solution (iii) Basic Solution (iv) Basic Feasible Solution
(v) Degenerate Solution (vi) Non-degenerate Solution (vii) Optimum Solution (viii)
unbounded solution.
4. Explain about the Fundamental theorem of LPP.
5. Describe about the Graphical Method Algorithm.
6. Describe about the Simplex Method Algorithm.
7. Explain the Characteristics of Standard Form of LPP.
8. Solve the following LP problem by Graphical Method:
Max z=5
+ 7
; STC:
+
4, 3
+ 8
24, 10
+ 7
35,
,
0
9. Solve the LP problem by Simplex Method:
Maxz=3
+ 5
+ 4
;
:2
+ 3
8, 2
+ 5
10, 3
+ 2
+ 4
15
,
,
0
10. Solve the LP problem by Simplex Method:
Maxz=
- 3
+ 2
:3
-
+ 3
7, -2
+ 4
12, -4
+ 3
+ 8
10
,
,
0
Unit - II:
11. Describe the algorithm of Big M or Penalty method.
12. Describe the algorithm of Two Phase Method
13. Describe the algorithm of Duality.
14. Explain the dual of the Dual is Primal.
15. Definition of (i) Artificial variable (ii) Degeneracy in LPP (iii) Duality of LPP (iv) Primal and
Dual pairs.
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16. Solve the following LP problem by Big M method.
Max z=
+ 2
+ 3
-
; STC:
+ 2
+ 3
= 15;2
+
+ 5
= 20;
+ 2
+
+
=10 and
,
,
,
0
17. Solve the following problem by Two-Phase Simplex Method:
Min z=
+
;
: 2
+
4,
+ 7
7
,
0
18. Write the Dual of the following LP problem:
Min z=3
- 2
+ 4
;
: 3
+ 5
+ 4
7, 6
+
+ 3
4; 7
- 2
-
10;
- 2
+ 5
4; 4
+ 7
- 2
2
,
,
0.
19. Obtain the dual of the LP problem:
Min z=
+
+
;
:
- 3
+ 4
= 5;
- 2
3, 2
-
4,
,
0
is
unrestricted.
20. Solve the following problem by Dual Simplex Method:
Min z= 2
+
;
:3
+
3, 4
+ 3
6,
+ 2
3
,
0
Unit - III:
21. Definitions of (i) Feasible Solution (ii) Basic Feasible Solution (iii) Degenerate basic feasible
solution (iv) Optimum basic feasible solution (v) Transhipment problem
22. Describe the algorithm of North West Corner Rule (NWCR)
23. Describe the algorithm of Matrix Minima method or Least Cost Method.
24. Describe the algorithm of VAM.
25. State the algorithm of Stepping stone method
26. State The Algorithm Of UV Method or MODI Method
27. Obtain an Initial Feasible Solution by NWCR
D1
D2
D3
D4
O1
4
6
8
13
500
O2
13
11
10
8
700
O3
14
4
10
13
300
O4
9
11
13
3
500
400
350
1050
200
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28. Obtain an Initial Basic Feasible Solution by Least cost Entry method to the following
transportation problem.
Destinations
origins
1
2
3
4
Availability
I
20
22
17
4
120
II
24
37
9
7
70
III
32
37
20
15
50
60
40
30
110
29. Obtain an Initial Basic Feasible Solution by using VAM to the following Transportation
problem
Destinations
origins
D1
D2
D3
D4
Capacities
I
6
6
4
4
5
II
7
9
1
2
7
III
6
5
16
7
8
IV
11
9
10
2
10
10
5
10
5
30. Obtain an Optimum Basic Feasible Solution by using Stepping Stone Method
Destinations
origins
I
II
III
IV
Availability
A
4
6
8
6
700
B
3
5
2
5
400
C
3
9
6
5
600
400
450
350
500
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31. Solve the following Transportation problem using UV ?method/ MODI method
B1
B2
B3
B4
B5
Availability
A1
3
4
6
8
9
20
A2
2
10
1
5
8
30
A3
7
11
20
40
3
15
A4
2
1
9
14
16
13
40
6
8
18
6
32. Resolve Degeneracy if occurs and solve the following Transportation problem
D1
D2
D3
Availability
O1
8
5
6
120
O2
15
10
12
80
O3
3
9
10
80
Req
150
80
50
33. Consider a Transhipment problem with two sources, three destinations, the cost for shipment
in rupees are given below. Determine the Optimum Schedule
S1
S2
D1
D2
D3
Availability
S1
0
65
1
3
15
150
S2
1
0
3
5
25
300
D1
3
15
0
23
1
-
D2
25
3
1
0
3
-
D3
45
55
65
3
0
-
Unit - IV
34. Describe the Hungarian method for an assignment problem.
35. Describe the algorithm of Johnson's algorithm to obtain optimum sequence for n jobs and
two machines
36. Describe the algorithm of n jobs through three machines
37. Describe the algorithm of n jobs through K machines
38. A department has four sub ordinates and four tasks have to be performed. Subordinates
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differ in efficiency and tasks differ in their intrinsic difficulty. Time each man would take to
perform each task is given in the effectiveness matrix. How the tasks should be allocated to
each person so as to minimize the total man-hours?
I
II
III
IV
Task
A
8
26
17
11
B
13
28
4
26
C
38
19
18
15
D
19
26
24
10
39. The owner of a small machine shop has four machinists available to do jobs for the day.Five
jobs are offered with expected profit for each machinist on each job as follows.
1
2
3
4
A
32
41
57
18
B
48
54
62
34
C
20
31
81
57
D
71
43
41
47
E
52
29
51
50
Find by using an assignment method, the assignment of machinists to jobs that will result a
maximum profit. Which job should be declined.
40. A company has 4 machines on which to do 3 jobs. Each job can be assigned to one and only
one machine. The cost of each job on each machine is given in the following table.
Machine
W
X
Y
Z
Job
A
18
24
28
32
B
8
13
17
19
C
10
15
19
22
What are the job assignment which will minimize the cost?
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41. We have 5 jobs, each of which has to be processed on two machines A and B in the order
AB. Processing times are given in the following table (in hours)
Jobs
1
2
3
4
5
Mach A
6
2
10
4
11
Mach B
3
7
8
9
5
Determine an order in which these jobs should be processed so as to minimize the total
elapsed time.
42. Determine the optimal sequence of jobs that minimizes the total elapsed time base on the
given processing times
Jobs
1
2
3
4
5
6
7
Mach A
3
8
7
4
9
8
7
Mach B
4
3
2
5
1
4
3
Mach C
6
7
5
11
5
6
12
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This post was last modified on 23 January 2021