Operations Research (OR) — Winter 2018

Comment on the following statement

OR is the art of winning war without actually fighting it. ii) OR is the art of finding bad answers where worse exists

What is Linear Programming? Explain the basic components of an LP model. Also state its assumptions

Solve the following LP problem using graphical method. Minimize Z = 3 + 212 Subject to constraints 5 + ≥12 + ≥ 612 + 4 ≥12 and , ≥

Atape recorder company manufactures models A, Band C, which have profit contributions per unit of Rs 15, Rs 40 and Rs 60, respectively. The weekly minimum production requirements are 25 units for model A, 130 units for model Band 55 units for model C. Each type of recorder requires a certain amount of time for the manufacturing of the component parts, for assembling and for packing. Specifically, a dozen units of model Arequire 4 hours for manufacturing, 3 hours for assembling and 1 hour for packaging. The corresponding figures for a dozen units of model Bare 2.5, 4 and 2 and for a dozen units of model Care 6, 9 and 4. During the forthcoming week, the company has available 130 hours of manufacturing, 170 hours of assembling and 52 hours of packaging time. Formulate this problem as an LP model so as to maximize the total profit to the company (Do not solve).

Construct the dual of the problem Min = 3 - 2 + z 1 2 Subject to 3 + 5 + 4 ≥ 7,123 6 + + 3 ≥ 4,123 7 - 2 - ≤ 10,123 - 2 + 5 ≥ 3,123 4 + 7 - 2 ≥ 2,123 and , ≥ 0. 1 2, 31

Find the optimal solution of the following transportation problem: Plants Ware houses D1 D2 D3 D4 Supply S1 19 30 50 10 S2 70 30 40 60 9 S3 40 8 70 20 18 Demand 5 8 7

Explain the Hungarian Assignment Method. Is it better than other methods of solving assignment problem? How?

Aconstruction company has requested bids for subcontracts on five different projects. Five companies have responded their bids and are represented below: Bid amounts (‘000 Rs) s Bidders A B C D E Determine the minimum cost assignment of subcontracts to bidders, assuming that each bidder can receive only one contract

What is Simulation? Explain the types of simulation.

In a railway marshalling 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 (the time taken to hump a train) distribution is also exponential with an average of 36 minutes. Calculate the following:

The average number of trains in a queue. (ii) The probability that the queue size exceeds 10. (iii) Expected waiting time in a queue.

What are the three time estimates used in the context of PERT? How are the expected duration of a project and its standard deviation calculated?

(i) For what value of λ, the game with following pay-off matrix is strictly determinable? Player B B1 B2 B3 A1 λ 6 A2 -1 λ -7 A3 -2 4 λ (ii) Define the terms:03 (1) saddle point (2) fair game (3) payoff matrix

What is Replacement? Explain briefly the replacement policies of items whose efficiency deteriorates with time.2

Ten jobs are to be processed on two machines M1 and M2. Determine the optimal sequence and evaluate the total elapsed time, besides the job and machine idle time. The job processing times (in hours) are given below in table. Job processing times in hours Machines J J J J J J J J J J M 8 9 10 4 8 5 6 9 6 71 M 5 3 7 7 6 8 3 7 8 72

What are inventory models? Enumerate various types of inventory models and describe them briefly

Determine the optimal sequence of performing 4 jobs on 5 machines. The matching of each machine is required in the order ABCDE and the process timings as as follows. Jobs Machines A B C D E I 7 5 2 3 9 II 6 6 4 5 III 5 4 5 6 IV 8 3 3 2 Determine a sequence of these jobs that will minimize the total elapsed time T. Also find idle time for all machines.

What is queue? Explain the structure of the queuing system.