# June 2002

## Question Paper of CS 51 – Operations Research of June 2002 from IGNOU

**Time**: 2 hours

Max. Marks: 75

Note: Question No 1 is compulsory. Attempt three more questions from questions numbered as 2 to 6.

Note: There are 6 questions in this paper. Question 1 is compulsory and carries 35 marks. From the remaining questions, attempt any two questions. Each of these carries 20 marks.

1. [15]

(a) Define the following terms very briefly, typically within one paragraph:

1. Dominance

2. Reasons for rising simulation

3. Safety Stock

4. Queue Discipline

5. Basic feasible solution

(b) List out the various steps involved in the Modified Distribution method for solving a given transportation problem. [10]

(c) Differentiate between Non-Linear Programming and Integer Programming. [10]

2. A firm buys castings of P and Q of parts and sells them as finished product after machining, boring and polishing. The purchasing cost for castings are Rs. 3 and Rs. 4 each for parts P and Q and selling costs are Rs. 8 and Rs. 10 respectively. The per hour capacity of machines used for machining, boring and polishing for the two products is given below:

Cac Parts

P Q

Machining 30 50

Boring 30 45

Polishing 45 30

The running costs for machining, boring and polishing are Rs. 30, Rs. 22.5 and Rs. 22.5 per hour respectively. Find out the product mix to maximize the profit using LP Method.

3. The following table shows all the necessary information on the availability supply to each warehouse, the requirement of each market and the unit transportation cost from each warehouse to each market/ [20]

I II III IV Supply

A 5 2 4 3 22

B 4 8 1 6 15

C 4 6 7 5 8

Requirement 7 12 17 9

The shipping clerk has worked out the following schedule from his experience:

12 Units from A to II

1 unit from A to III

9 units from A to IV

15 units from B to III

7 units from C to I and

1 unit from C to III

You are required to answer the following:

1. Check and see if the clerk has the optimal schedule

2. Find the optimal schedule and minimum total shipping cost and

3. If the clerk is approached by a carrier of route C to II, who offers to reduce his rate in the hope of getting new business, by how much

should the rate be reduced before the clerk should consider giving him an order?

4. (a) Determine the optimal strategies and the value of the game from the following 2 x m pay-off matrix game for X: [10]

Y

6 3 -1 0 -3

X

3 2 -4 2 -1

(b) An item is sold for Rs. 25 per unit and it costs Rs. 10. Unsold items can be sold for Rs. 4 each. It is assumed that there is no shortage penalty cost besides the lost revenue. The demand is known to be any value between 600 and 1000 items. Determine the optimal number of units of the item to be stocked. [10]

5. A computer is proposed to be used for scheduling of patients in a hospital operating room. In order to do so, arrival times, operating times and clean-up times are to be generated. What computer procedures would you use for this purpose? [20]

6. (a) In an assignment problem, there are 12 workers and 12 jobs to be done. Only one man can work in any one job. What is the total number of different possible ways of assignment of the jobs to the workers? [10]

(b) Draw a flow char and write in a pseudo-code format, how an ABC classification can be carried out using a computer? What is special about A class items in an inventory?