JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD MCA 2019 OPERATIONS RESEARCH Previous Question Paper (April/May - 2019 - R17)

Solve following problems using Big – M method. Minimize 60X1 + 80X2. Constraints: 20X1+30X2 ≥ 900; 40X1+30X2 ≥ 1200; X1, X2 ≥ 0.

A company has three production facilities S1, S2 and S3 with production capacity of 7, 9 and 18 units (in 100s) per week of a product, respectively. These units are to be shipped to four warehouses D1, D2, D3 and D4 with requirement of 5, 6, 7 and 14 units (in 100s) per week, respectively. Formulate this transportation problem as an LP model to minimize the total transportation cost.

There are five jobs, each of which must go through the two machines A and B in the order AB. Processing times are given below for Jobs 1, 2, 3, 4, 5. Time for A: 5, 1, 9, 3, 10; Time for B: 2, 6, 7, 8, 4. Determine a sequence for five jobs that will minimize the elapsed time T.

A milk plant is considering replacement of a machine whose cost price is Rs. 12,200 and the scrap value Rs. 200. The running (maintenance and operating) costs in Rs. for years 1 through 8 are: 200, 500, 800, 1200, 1800, 2500, 3200, 4000. When should the machine be replaced?

In a railway marshaling yard, goods trains arrive at a rate of 30 trains per day. Assuming that the inter arrival time follows an exponential distribution and the service time distribution is also exponential with an average of 36 minutes. Calculate: a) The average no. of trains in the queue, b) The probability that the queue size exceeds 10. If the input of trains increases to an average 33 per day, what will be change in (a) and (b).

A mechanic services 4 machines. For each machine, the mean time between service requirements is 10 hours and is assumed to be from an exponential distributions. The repair time tends to follow the same distribution with a mean of two hours. When a machine is down for repairs the time lost has a value of Rs.20 per hour. The mechanic costs Rs.50 per day. Find: a) What are the expected no. of machines in operation? b) What is the expected down time cost per day? c) Would it be desirable to provide two mechanics each to service only two machines?

The annual demand of 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: a) Economic order quantity, b) No. of orders per year, c) Time between two consecutive orders, d) The optimal cost.

Consider the following data: Unit cost = Rs.100, Order cost = Rs.160, Inventory carrying cost = Rs.20, Back order cost (Stock out cost) = Rs.10, Annual demand = 1000 units. Compute the following: a) Minimum cost order quantity, b) Time between orders, c) Minimum number of back orders, d) Maximum inventory level, e) Overall annual cost.

Find the saddle point (or points) and hence solve the game for Player A (A1, A2, A3) and Player B (B1, B2, B3) with values: A1(15, 2, 3), A2(6, 5, 7), A3(-7, 4, 0).

What is Dynamic programming and what sort of problems can be solved by it? State and establish Bellman’s principle of optimality.