MS51 Operations Research December 2006

MANAGEMENT PROGRAMME
Term-End Examination

June, 2005

MS51 : OPERATIONS RESEARCH

Time: 3 hours
Maximum Marks: 100
(Weightage 70%)

Note : Answer any four questions

1 . (a) Express the linear Programming Problem in its general form with Matrix Notation. 10+15=25

(b) Solve the following LP - problem by SIMPLEX Method.

Minimize z = x₁ - 3x₂ + 2x₃

subject to

3x₁ - x₂ + 3x₃ ≤ 7

- 2x₁ + 4x₂ ≤ 12

- 4x₁ + 3x₂ + 5x₃≤ 10

x₁ ; x₂ ; and x₃ ≥ 0

2. Find the optimum solution for the following transportation problem. 25

From \ To	A	B	C	Total
I	1*	2	3	50
II	3	2	1	80
III	4	5	6	75
IV	3	1	2	95
Total	120	80	100

*This is unit transportation cost.

3. (a) Explain the difference between pure strategy and rnixed strategy.

(b) In a game of matching coins with two players, suppose A wins one unit of value when there are two heads, wins nothing when there are two tails and loses 1/2 unit of value when there is one head and one tail. Determine PAY - OFF matrix, the best strategy for each player and the value of the game to A. 10+15=25

4. (a) Discuss the costs associated with queuing system. Also explain the concept of optimum servicing rate and optimum cost.

(b) In a railway marshalling yard, goods trains arrive at a rate of 30 trains / day. Assuming that inter - arrival time follows exponential distribution and the service time distribution is also exponential with average 36 minutes, calculate the following :

(i) Average number of trains in the yard.

(ii) Probability of queue exceeding 10.

(iii) Utilization rate of the yard. 10+15=25

5. (a) Write down the general form of Integer Programming Problem as LP.

(b) Explain the branch and bound method of solving Integer Programming Problem.

(c) Discuss the effect of "ROUNDING - OFF" a continuous optimal solution of an LP - problem to obtain an integer solution. 9+9+7=25

6. (a) Discuss the various Inventory Control systems.

(b) A manufacturer requires 15000 units of a part annually for assembly. Manufacturer can produce this at the rate of 100 per day. Set - up cost for each production run is Rs. 24 /-.To hold one unit of this part, inventory cost of manufacturer is Rs. 5 /- for a year: Assume 250 working days per year. Find out the economic batch quantity and economic run length. 10+15=25

7 . Write short notes on any two of the following : 25

(i) Goal Programming

(ii) Non - Linear Programming

(iii) Selective Inventory Control

(iv) Simulation