## Wednesday, 30 April 2014

### MB0048- OPERATIONS RESEARCH

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ASSIGNMENT

 DRIVE SPRING 2014 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.

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

Answer : 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 given problem into a mathematical representation which is solved and retransformed into the

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:

A problem consists of a linear function of variable called objective function subject to set of linear equation or inequalities called constraints, are known as linear programming problem.
In LP model the various parameters namely the objective function coefficients, R.H.S, coefficients of the constraints and resource values are certainly known and their value do not change with time. Thus the profit or cost per unit of product, availability of labour and material, market demand is known with certainty

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

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. 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:
Case 1 - The degeneracy develops while

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. Determine the entering variable

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.

b. Find the optimal assignment of four jobs and four machines when the cost of assignment is given by the following table:

Computation/Solution to the problem: Applying Hungarian method

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, project management, energy, manufacturing, engineering, research and development, insurance, oil & gas, transportation, and the environment.

Monte Carlo simulation furnishes the decision-maker with a range of possible outcomes and the probabilities they will occur for

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 number of cars waiting for shipment in the company and average number of empty space in the truck. Random Numbers 82, 54, 50, 96, 85, 34, 30, 02, 64, 47.  5 +5 = 10 marks(200 - 250 words each)

 Production Rate Probability Cum. Probability Random Numbers 147 0.05 0.05 00-04 148 0.10 0.15 05-14

6 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 strategy for one player, no matter how that player's opponents may play. Many simple games can be solved using dominance. The opposite, intransitivity, occurs in games where one strategy may be better or worse than another strategy for one player, depending on how the player's opponents may play.

Terminology

b. Describe the Constituents of a Queuing System.

Answer : Characteristics of a queuing system that impact its performance, for example, queuing requirements of a restaurant will depend upon factors like:
·         How do customers arrive in the restaurant? Are customer arrivals more during lunch and dinnertime (a regular restaurant)? Or is the customer traffic more uniformly distributed (a cafe)?
·         How much time do customers spend in the restaurant? Do customers typically leave the restaurant in a fixed amount of time? Does the customer service time vary with the type of customer?
·

c. Differentiate between PERT and CPM

Answer : Project management is an important part of every business enterprise. Whenever a new product or service is launched; when embarking on a marketing campaign; or when organizing any new projects; project management is needed to make everything organized and successful.

As all projects consume resources such as materials, time, people, and money; starting one would entail an effective project management team and the right techniques to accomplish them, especially those projects that are very
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