# Operation Research

**Topics:**Operations research, Optimization, Linear programming

**Pages:**12 (2390 words)

**Published:**February 26, 2014

Master of Business Administration- MBA Semester 2

MB0048 – Operations Research - 4 Credits

(Book ID: B1631)

(Roll no: 1305009661)

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

Ans: 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. OR methodology consists of five steps. They are defining the problem, constructing the model, solving the model, validating the model, and implementing the result. Definition: The first and the most important step in the OR approach of problem solving is to define the problem. Construction: based on the problem definition, you need to identify and select the most appropriate model to represent the system. Solution: After deciding on an appropriate model, you need to develop a solution for the model and interpret the solution in the context of the given problem. Validation: A model is a representation of a system, however, the optimal solution must work towards improving the system’s performance. Implementation: You need to apply the optimal solution obtained from the model to the system and note the improvement in the performance of the system. Techniques and tools of operation research:

Linear programming: You can use linear programming to find a solution for optimising a given objective. The objective may be to maximize profit or to minimize cost. Inventory control methods: The production, purchasing, and material managers are always confronted with questions, such as when To buy, and how much to keep in stock. Goal programming: In linear programming , you take a single objective function and consider all other factors as constraints. Queuing model: The queuing theory is based on the concept of probability. There is no maximization or minimization of an objective function. Transportation model: The transportation model is an important class of linear programs. The supply at each source and the demand at each destination are known. In additional to the above, there are tools such as the sequence model, the assignment model, and network analysis, which you will learn in detail in the later units. Q.2: a. Explain the steps involved in linear programming problem formulation. Discuss in brief the advantages of linear programming.

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.

Ans: (A)The steps involved in the formation of linear programming problem are as follows: Step 1

Identify the Decision Variables of interest to the decision maker and express them as x1, x2, x3……… Step 2

Ascertain the Objective of the decision maker whether he wants to minimize or to maximize. Step 3

Ascertain the cost (in case of minimization problem) or the profit (in case of maximization problem) per unit of each of the decision variables. Step 4

Ascertain the constraints representing the maximum availability or minimum commitment or equality and represent them as less than or equal to (≤) type inequality or greater than or equal to (≥) type inequality or 'equal to' (=) type equality respectively. Step 5

Put non-negativity restriction as under:

xj ≥ 0; j = 1, 2 ….n (non-negativity restriction) Step 6

Now...

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