Download GTU (Gujarat Technological University Ahmedabad) B.Tech/BE (Bachelor of Technology/ Bachelor of Engineering) 2020 Winter 7th Sem 2171901 Operation Research Previous Question Paper
Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE- SEMESTER?VII (NEW) EXAMINATION ? WINTER 2020
Subject Code:2171901 Date:25/01/2021
Subject Name:Operation Research
Time:10:30 AM TO 12:30 PM Total Marks: 56
Instructions:
1. Attempt any FOUR questions out of EIGHT questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
MARKS
Q.1 (a) Discuss various areas for the application of operations research techniques.
03
(b) Differentiate CPM & PERT.
04
(c) Explain the set of assumptions for Linear Programming in details.
07
a
nerations research problem.
Graphically represent following cases in linear programming.
Q.2 (a)
03
(1) Un-bounded solution (2) Multiple optimal solution
A company is manufacturing two different types of products, A and B. Each
(b) product has to be processed on two machines M1 and M2.Product A requires 2
04
details P
hours
roble
on mac m, in
hine de
M1 tail.
an
d 1 hour on machine M2, Product B requires 1 hours on
machine M1 and 2 hour on machine M2.The available capacity of machine M1 is
104 hours and that of machine M2 is 76 hours. Profit per unit for product A is
Rs.6 and that for B is Rs.11.Formulate the problem.
(c) Maximize Z = 40 x1 + 35 x2
Subject to constraints, 2x1 + 3x2 60,
07
4x1 + 3x2 96,
x1, x2 0
Q.3 (a) What is assignment problem? Show the assignment problem is special case of
transportation problem.
03
(b) Describe the various steps in Hungarian method used for solving the
assignment problem.
04
(c) The captain of a cricket team has to allot five middle order batting
positions 07
07
to 5 batsmen available for selection. The average runs scored by each
batsman at these positions are summarized in a table below. Using
Assignment model, determine the assignment of batsmen to positions
which would give maximum runs in favor of team.
Batsman
Batting positions
I
II
III
IV
V
A
40
46
48
36
48
B
48
32
36
29
44
C
49
35
41
38
45
D
30
46
49
44
44
E
37
41
48
43
47
Q.4 (a) What is degeneracy in transportation problem?
03
(b) Discuss group replacement policy with suitable example.
04
1
(c) Five jobs are to be assigned to five machines with an objective to minimize
total
man-hours. The time (in hours) that each man takes to perform each job is given below.
07
Find the optimum assignment.
Employees
I
II
III
IV
V
A
10
5
13
15
16
Jobs
B
3
9
18
13
6
C
10
7
2
2
2
D
7
11
9
7
12
E
7
9
10
4
12
Q.5 (a) What is inventory? Classify the inventory.
03
(b) Write a short note on "ABC analysis" of inventory control technique.
04
(c) The annual demand for an item is 3200 units. The unit cost is Rs.6 and
inventory carrying charges 25 % per annum.If the cost of one
07
procurement is Rs.150, then determine the 1) EOQ 2) No. of order
per year 3) Time between two consecutive order 4) The optimal
cost.
Q.6 (a) Define the following terms relating the customer's behavior in Queue.
03
(A)Balking (B) Jockeying (C) Reneging
(b) Explain Kendall's notation for queuing system.
04
(c) In a bank counter, customers arrive at a rate of 30 customers per day. Assuming
that the inter arrival time follows an exponential distribution and service time
distribution is also exponential with an average of 36 minutes. Calculate:
07
Expected queue size
Probability that the queue size exceeds 10
Q.7 (a) What is "Strategy"? Explain the difference between pure strategy and
03
mixed 03strategy.
Strategy?
(b) Discuss various costs involved in an Inventory model.
04
(c) Explain the steps of a Travelling Salesman Problem.
07
Q.8 (a) What is replacement? Describe some important replacement situations.
03
(b) How would you deal with assignment problems, where (a) the objective
04
Function is to be maximized? (b) Some assignments are prohibited?
(c) Explain the different methods useful for decision making under certainty.
07
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This post was last modified on 04 March 2021