MCA CS-15 TMA Operations Research

MCA CS-15 TMA Operations Research

Course Code : CS-51
Course Title : Operations Research
Assignment Number : MCA (3)-51/Project/04
Maximum Marks : 15
Last Date of Submission : 30th April, 2004

This is a Project Assignment. You may use illustrations and diagrams to enhance explanations. Answer the following question.

Question 1: Using Stepping Stone Method, solve the following transportation problem (cost in rupees) for minimum cost of transportation:

Depot

Factory

D E F G Capacity

A

4 6 8 6 700

B

3 5 2 5 400

C

3 9 6 5 600

Requirement

400 450 350 500 1700

(2 marks)

Question 2(a): Two products are manufactured on two sequential machines. The following table gives the matching times in minutes per unit for the two products.

Machine

Product 1 Product 2

1

5 3

2

6 2

The daily production quota for the two products are 80 and 60 units, respectively. Each machine runs 8 hours a day. Overtime, though not desirable, may be used if necessary to meet production quota.
Formulate the above problem as a goal programming model.

(2 Marks)

(b): Formulate the following as an Integer Programming Problem:

We have landed in a treasure island full of three types of valuable stones: Emerald (E), Ruby (R) and Topaz (T). Each piece of E, R and T weighs 3, 2, 2 kilogram respectively and is known to have a value of 4 crore, 3 crore and 1 crore respectively. We have got a bag with us that can carry a maximum of 11 kg. Our problem is to decide on how many pieces of each type to carry, within the capacity of our bag, so as to maximize the total value carried. The stones cannot be broken.
(2 Marks)

Question 3 (a): 18000 units of an item are required per year. Storage cost is Rs. 0.10 per unit per month. If the cost of placing an order is Rs. 400, find the following:

(i) EOQ
(ii) Number of orders per year
(iii) Cycle period
(iv) Total annual cost if per unit cost is Rs. 2
(2 marks)

(b): A cafeteria with self-service has an arrival rate of 12 per hour. The average time taken by a person to collect and eat his meal is 20 minutes. Assuming that the inter-arrival times are exponentially distributed, how many seats must the cafeteria have to accommodate each customer with 95% probability?
(3 Marks)

Question 4 (a): The following is the pay-off matrix (in rupees) for the two persons zero-sum game:

PLAYER B

PLAYER A

Machine

I II III

I

-3 4 -1

II

3 1 5
II -1 -5 11

Using the Minimax criterion, find the best strategy for each player.
(2 Marks)

(b) Determine which course of action Player B will not use in the following game. Obtain the best strategies for both players and value of the game.

PLAYER B

PLAYER A

 

I II III

I

3 -1 7

II

4 1 -2

(2 Marks)

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