MS51 Operations Research June 2005

MANAGEMENT PROGRAMME
Term-End Examination

June, 2005

MS51 : OPERATIONS RESEARCH

Time: 3 hours
Maximum Marks: 100
(Weightage 70%)
Note : (i) Section A has five questions carrying 20 marks each. Attempt any three.
(ii) Section B is compulsory and carries 40 marks.
(iii) Graph paper will be supplied on demand.

SECTION A

1. Describe the origin and development of Operations Research (OR). Discuss the early Indian scene. Also highlight, how you use OR in day-to-day decision making process. (20)

2. Maximise z = 30x1 + 40x2
Subject to
60x1 + 120x2 ≤ 12,000
8x1+5x2 ≤ 600
3x1+4x2 ≤ 500
x1, x2 ≥ 0 (20)

3. Consider the game of matching coins. Two players A and B each put down a coin. If the coins match i.e. both are heads or both are tails, A gets rewarded otherwise B gets rewarded. However, matching on heads gives double premium. Obtain the best strategies for both players and the value of the game. (20)

4. A company buys in lots of 500 boxes which is a 3-month supply. The cost per box is Rs. 125 and the ordering cost is Rs. 150. The inventory cost is estimated at 20% of unit value.

(a) What is the total annual cost of the existing inventory policy ?
(b) How much money could be saved by employing the economic order quantity? (20)

5. Write short notes on any four of the following : (20)

(a) Random Variable
(b) Sensitivity Analysis
(c) Kuhn Tucker's conditions
(d) ABC Classification
(e) Steps in the simulation process

SECTION B

6. Solve the following transportation problem by Least Cost method and check the feasibility of the solution. The unit costs of shipment are given in the cells below : (20)
To D E F Supply
From
A 6 4 1 50
B 3 8 7 40
C 4 4 2 60
Demand 20 95 35 150

7. Belt snapping for conveyors in an open cast mine occurs at the rate of 2 per shift. There is only one hot plate available for vulcanising, and it can vulcanise on an average 5 belt-snaps per shift.

(a) What is the probability that when a belt snaps, the hot plate is readily available?
(b) What is the average number of belts in the system ?
(c) What is the average waiting time of an arrival ?
(d) What is the average waiting time plus vulcanising time ? (20)