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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI 600 034
B.Sc. DEGREE EXAMINATION COMPUTER SCIENCE
FIFTH SEMESTER NOVEMBER 2017
CS 5402 OPERATIONS RESEARCH
Date: 13-11-2017 Dept. No. Max. 100 Marks
Time: 09:00-12:00
SECTION-A
ANSWER ALL THE QUESTIONS: (10X2=20)
1. Define Operation Research.
2. Write a note on slack and surplus variables.
3. When is transportation problem said to be unbalanced? Give an example.
4. State job sequencing problem.
5. Write down the route condition for the traveling salesman problem.
6. What is total elapsed time?
7. What is the objective of CPM?
8. Define dummy Activity
9. Define Inventory.
10. What is setup cost?
SECTION-B
ANSWER ALL THE QUESTIONS:
11. A company manufacturers two products A and B in two departments namely assembly
department and painting department. It takes two hours in the assembling department and one hour in
painting department to manufacture one unit of product A. It takes two hours in the assembling
department and 2 hours in painting department for manufacturing one unit of product B. The
assembling department works for three 8 hours shift per day and painting department works two 8
hours shift per day. The profit of the product A is Rs.100 and the profit of the product B is Rs.150
per unit. How many units of product A and B to be manufactured so as to maximize the profit for the
company?

Solve the following LPP by Graphical method:
Max Z 3x1 5 x2 Subject to the constraints:
x1 +2x2 ≤2000 x1 x2 ≤1500 x2 600 x1,x2
12. Obtain an initial basic feasible solution to the following transportation
Problem using Least cost method.
D E F G Available
A 1 2 3 4 6
B 4 3 2 0 8
C 0 2 2 1 10
Requirements 4 6 8 6

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Solve the following Traveling salesman problem.
A B C D E
A 4 7 3 4
B 4 6 3 4
C 7 6 7 5
D 3 3 7 7
E 4 4 5 7
13. Solve the following assignment problem:
A B C D
I 1 4 6 3
II 9 7 10 9
III 4 5 11 7
IV 8 7 8 5

Find the sequence that minimizes the total elapsed time (in Hrs) required to complete the following
task on 2 machines. Also find the total elapsed time and idle time of each machine.
Jobs J1 J2 J3 J4 J5 J6
Machine A 3 12 5 2 9 11
Machine B 8 10 9 6 3 1
14. A is the operation on the project. B&C can be done concurrently both must follow A.
B must proceed D. E can not begin until both B&C are completed. F is dependent on the
completion of both D&E. F is the last operation on the project. Draw the arrow network
and number the nodes according to Fulkerson's Rule.

Write down the difference between PERT CPM.
15. Find the optimum order quantity for a product for which the price breaks are as follows:
Quantity Purchasing cost per unit
0 Q1 100 20
100 Q2 200 18
200 Q3 16
The monthly demand for the product is 400 units. The storage cost is 20% of the
unit cost of the product and the cost of ordering is Rs.25 per month.

A stockiest has to supply 12,000 units of a product per year to his customer. The demand is
fixed and known and the shortage cost is assumed is to be infinite. The inventory holding
cost is Re.0.20 per unit per month and the ordering cost per order is Rs.350. Determine the
following
The optimum lot size q0
Optimum scheduling period t0
Minimum total variable yearly cost.
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SECTION-C
ANSWER ANY TWO QUESTIONS: (2X20=40)
16. Solve by Simplex method
Max Z 3x1 2x2+ 5x3 Subject to the constraints:
x1 +2x2 x3 430, 3x1 2x3 460 x1 4x2 420 x1,x2
ii) A steel firm has 4 plants which purchase coal for their production from 3 mines. The cost of shipping
(in 100's of RS.) one ton of coal from each mine to each plant are given below:
Plants Capacity
Mines
P1 P2 P3 P4
M1 3 1 4 5 50
M2 7 3 8 6 50
M3 2 3 9 2 75
Requirements 40 55 60 20
How much coal should the firm purchase from each mine in order to satisfy the demand of the plants at
minimal shipping expenses.(Using Matrix minimum method)
17. Find the sequence that minimizes the total elapsed time (in Hrs) required to complete the following
task on 2 machines. Also find the total elapsed time and idle time of each machine.
Jobs J1 J2 J3 J4 J5 J6
Machine A 3 12 5 2 9 11
Machine B 8 10 9 6 3 1
ii) Given the following information:
Activity 1-2 1-3 2-3 2-4 2-5 3-4 4-7 5-6 5-7 6-7
a 3 1 6 0 2 3 6 1 2 4
m 4 2 8 0 5 5 9 1 5 8
b 5 3 10 0 8 7 12 1 8 12
Draw the Project Network
ii) Find the length and variance of each activity.
iii) Find the critical path.
iv) Find the length and variance of the critical path.
18. Define the following Terms:
Reorder Level Reorder Point
Safety stock Shortage
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 procurement is Rs.150/- determine the following Economic order
quality time between two consecutive orders number of order per year the optimal total cost.