MS - 51 Operations Research

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ASSIGNMENT

Course Code                                                 :                                          MS - 51

Course Title                                                  :                                          Operations Research

Assignment Code                                        :                                          MS-51/TMA/SEM - I /2016

Coverage                                                       :                                          All Blocks

Note: Attempt all the questions and submit this assignment on or before 30th April, 2016 to the coordinator of your study centre.

Question. 1. Define Operations Research. Also, give a brief historical background of Operations Research.

Answer: Operations research, or operational research in British usage, is a discipline that deals with the application of advanced analytical methods to help make better decisions. Further, the term 'operational analysis' is used in the British (and some British Commonwealth) military, as an intrinsic part of capability development, management and assurance. In particular, operational analysis forms part of the Combined Operational Effectiveness

Question. 2. ABC Company is engaged in manufacturing five brands of packed snacks. It is having five manufacturing set ups, each capable of manufacturing any of its brands one at a time. The cost to make a brand on these set ups vary according to the following table:

	S1	S2	S3	S4	S5
B1	4	6	7	5	11
B2	7	3	6	9	5
B3	8	5	4	6	9
B4	9	12	7	11	10
B5	7	5	9	8	11

Assuming five set ups are S1 ,S2, S3, S4, and S5 and five brands are B1, B2, B3, B4 and B5, find the optimum assignment of products on these set ups resulting in the minimum cost.

Answer: Step 1: Subtract the lowest element of each row from the respective row, we get the following total opportunity matrix.

	S1	S2	S3	S4	S5
B1	0	2	3	1	7
B2	4	0	3	6	2

Question. 3. What is goal programming? State clearly its assumptions. Identify the major differences between linear programming & goal programming.

Answer: Goal programming is a branch of multi-objective optimization, which in turn is a branch of multi-criteria decision analysis (MCDA). This is an optimization programme. It can be thought of as an extension or generalisation of linear programming to handle multiple, normally conflicting objective measures. Each of these measures is given a goal or target value to be achieved. Unwanted deviations from this set of target values are then minimised in an achievement function. This can be a vector or a weighted sum dependent on the goal

Question. 4. A company has determined from its analysis of production and accounting data that, for a part number KC-438, the annual demand is equal to 10,000 units, the cost to purchase the item is Rs 36 per order, and the holding cost is Rs 2/unit/year.

(a) What should the economic order quantity be?

(b) What is the number of days’ supply per optimum order? (Assume 300 working days in a year)

Answer: (a) We know that we want to sell 10,000 units over the course of the year, but we don't know whether to order them all once, or split up our orders into smaller quantities to save on the cost of holding inventory. (Apparently the unit cost of buying each unit is the same either way, so we're ignoring it.)

Since our revenue won't change, we maximize profit by minimizing cost.

Question. 5. “Game theory provides a systematic quantitative approach for analyzing competitive situations in which the competitors make use of logical process and techniques in order to determine an optimal strategy for winning”. Comment.

Answer: Game theory resolves this conflicting situation of business and military operations. This important technique of operation research provides a basis for determining under specified conditions, the particular strategy that will result in maximum gain or minimum loss. Thus game theory may be defined as a body of knowledge that deals the decision making of two or more rational opponents in the condition of conflict and competition.

Assumptions:

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