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MB0048 OPERATIONS RESEARCH

1 Discuss the various stages involved in the methodology of Operations Research. Briefly explain the techniques and tools of Operations Research.

Answer: OR Methodology The basic dominant characteristic feature of operations research is that it employs mathematical representations or models to analyse problems. This distinct approach represents an adaptation of the scientific methodology used by the physical sciences. The scientific method translates a real given problem into a mathematical representation which is solved and retransformed into the original context.

2 a. Explain the steps involved in linear programming problem formulation. Discuss in brief the advantages of linear programming.

Answer: Mathematical Formulation of LPP: The procedure for mathematical formulation of a linear programming problem consists of the following major steps:

b. Alpha Limited produces & sells two different products under the brand names black & white. The profit per unit on these products in Rs. 50 & Rs. 40 respectively. Both the products employ the same manufacturing process which has a fixed total capacity of 50,000 man-hours. As per the estimates of the marketing research department of Alpha Limited, there is a market demand for maximum 8,000 units of Black & 10,000 units of white. Subject to the overall demand, the products can be sold in any possible combination. If it takes 3 hours to produce one unit of black & 2 hours to produce one unit of white, formulate the model of linear programming.

3 a. What is degeneracy in transportation problem? How it can be resolved?

Answer: Degeneracy in transportation problem It is shown that a basic solution to an m-origin, n destination; transportation problem can have at the most m+n-1 positive basic variables (non-zero), otherwise the basic solution degenerates. It follows that whenever the number of basic cells is less than m + n – 1, the transportation problem is a degenerate one. The degeneracy can develop in two ways:

b. Solve the following transportation problem using Vogel’s approximation method.

Factories Distribution Centres Supply

C1 C2 C3 C4

F1 3 2 7 6 50

F2 7 5 2 3 60

F3 2 5 4 5 25

Requirements 60 40 20 15

Answer: b)

4 a. Explain the steps in Hungarian method. Differentiate between Transportation and

Assignment problem.

Answer: Hungarian method algorithm is based on the concept of opportunity cost and is more efficient in solving assignment problems. The following steps are adopted to solve an AP using the Hungarian method algorithm.

b. Find the optimal assignment of four jobs and four machines when the cost of

assignment is given by the following table:

J1 J2 J3 J4

M1 10 9 8 7

M2 3 4 5 6

M3 2 1 1 2

M4 4 3 5 6

5 Define Simulation. Explain the Simulation procedure. Discuss the use of Simulation

with an example.

Answer: Simulation is a numerical technique for conducting experiments that involve certain types of mathematical and logical relationships necessary to describe the behaviour and structure of a complex real world system over an extended period of time.

6 Explain the following:

a. Integer programming model

b. PERT and CPM

Answer: PERTSome key points of PERT are as follows:

c. Operating Characteristics of a Queuing System

Answer: A queuing model has the following operating characteristics which enables us to understand and efficiently manage a queue:

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