MB0048- OPERATIONS RESEARCH

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ASSIGNMENT

DRIVE	SPRING 2015
PROGRAM	MBADS/ MBAFLEX/ MBAHCSN3/ MBAN2/ PGDBAN2
SUBJECT CODE & NAME	MB0048- OPERATIONS RESEARCH
SEMESTER	2
BK ID	B1631
CREDITS	4
MARKS	60

Note: Answer all questions. Kindly note that answers for 10 marks questions should be approximately of 400 words. Each question is followed by evaluation scheme.

Q1. Discuss the methodology of Operations Research. Explain in brief the phases of Operations Research.

Answer : The basic dominant characteristic feature of operations research is that it employs mathematical representations or models to analyse problems

Steps in the OR methodology

As shown in figure 1.3, OR methodology consists of five steps. They are - defining the problem...................................

2a. Explain the graphical method of solving Linear Programming Problem.

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

b. A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper in a week. There are 160 production hours in awake. It requires 0.20 and 0.40 hours to produce a ton of grade X and Y papers. The mill earns a profit of Rs. 200 and Rs. 500 per ton of grade X and Y paper

respectively. Formulate this as a Linear Programming Problem.

Answer : Objective function is to maximize the profit

Thus Max. Z=200X₁+500X₂

Constraints 1.Raw materials

         2. Production hour.............................

Q 3 a. Explain how to solve the degeneracy in transportation problems.

Answer : 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. The degeneracy can develop in two ways:

Case 1 - The degeneracy develops while determining an initial assignment via any one of the initial assignment methods discussed earlier. To resolve degeneracy, you must augment the positive variables by as

b.  Explain the procedure of MODI method of finding solution through optimality test.                                                                                                       

Answer : Transportation Algorithm for Minimization Problem (MODI Method)

After evaluating an initial basic feasible solution to a transportation problem, the next question is how to get the optimum solution. The basic techniques are illustrated as follows:

1. Determine the net evaluations for the non–basic variables (empty cells)

2. ------------------------------------

Q.4 a. Explain the steps involved in Hungarian method of solving Assignment problems.

Answer : Steps in Hungarian method

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.

Step 1: Prepare row ruled matrix by selecting the minimum values for each row and subtract it from the other elements of the row.

Step 2:

b. Find an optimal solution to an assignment problem with the following cost matrix:

Answer : The solution is as follows.

First, the minimum element in each row is subtracted from all the elements in that row.

This gives the following reduced-cost matrix..............

Since both the machines M2 and M4 have a zero cost corresponding to job J1 only, a  feasible assignment using

Q5.a. Explain the Monte Carlo Simulation.

Answer: Monte Carlo simulation is a computerized mathematical technique that allows people to account for risk in quantitative analysis and decision making. The technique is used by professionals in such widely disparate fields as finance,

b. A Company produces 150 cars. But the production rate varies with the distribution.

Production Rate	Probability
147	0.05
148	0.10
149	0.15
150	0.20
151	0.30
152	0.15
153	0.05

At present the track will hold 150 cars. Using the following random numbers determine the average ……...............

Q6 a. Explain the dominance principle in game theory.

Answer : In game ..theory, strategic dominance (commonly called simply dominance) occurs when one strategy is better than another

Terminology

When a player tries to choose the "best" strategy among a multitude of options, that player may compare two strategies A and B to see which one is better. The result of the comparison is one of:

B dominates A: choosing B always gives as good as or a better outcome than choosing A.

There are 2 possibilities:

B strictly dominates A:

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