2. OPERATION RESEARCH of An operation may be defined as the set of acts required for the achievements of a desired outcomes.
3. DEFNITIONS OF O.R. OPERATION RESEARCH IS SYSTEMATIC, METHOD ORIENTED STUDY OF THE BASIC STRUCTURE, CHARACTERISTICS, FUNCTION & RELATIONSHIP OF AN ORGANISATION TO PROIDE THE EXECUTIVE WITH A SOUND, SCIENTIFIC AND QUANITATIVE BASIS FOR THE DECESION MAKING. ------------------------------BY E.L.ARNOFF & M.J.NETZORG I O.R. IS AN AID FOR THE EXECUTIVE IN MAKING HIS DECISIONS BY PROVIDING HIM WITH THE NEEDED QUANTITATIVE INFORMATION BASED ON THE SCIENTIFIC METHOD OF ANALYSIS ---------------BY C. KITTEL O.R. IS THE APPLICATION OF SCIENTIFIC METHODS TO THE PROBLEM ARISING FROM OPERATIONS INVOLVING INTEGRATED SYSTEMS OF MEN, MACHINE AND MATERIALS. IT NORMALLY UTILIZES THE KNOWLEDGE AND SKILLS OF INTERDISCIPLINARY RESEARCH TEAM TO PROVIDE THE MANAGERS OF SUCH SYSTEMS WITH OPTIMUM OPERATING SOLUTIONS. --------------------BY FABRYCKY & TORGERSEN
12. III. PROCUREMENT: What, when and how to purchase at minimum procurement cost Bidding and replacement policies. IV. MARKETING: Product selection, timing & competitive action Selection of advertising media. Demand forecast and stock level. Customer’s preference for size, colour & packaging of various products. V. FINANCE: Capital requirement, cash flow analysis. Credit policies, credit risks etc. Profit plan of the company. Determination of optimum replacement policies.
13. VI. PERSONNEL: Selection of personnel, determination of retirement age and skills Recruitment of policies & assignments of jobs. VII. RESEARCH AND DEVELOPMENT: Determination of areas of Research and Development Reliability & control of development of projects. Selection of projects & preparation of their budgets.
14. METHODOLOGY OF OR: FORMULATE THE PROBLEM CONSTRUCT A MATHEMATICAL MODEL SOLVE THE MODEL TEST THE MODEL ANALYSE THE RESULT IMPLEMENTATION OF SELECTED STRATEGY
15. DIFFICULTY IN O.R. PROBLEM FORMULATION DATA COLLECTION STUDY BASED ON OBSERVATION OR OLD LAWS TIME FACTOR HUMAN FACTOR
16. DECESION THEORY: DECESION THEORY PROVIDES A RATIONAL APPROACH IN DEALING PROBLEMS CONFRONTED WITH THE PARTIAL , IMPERFECT OR UNCERTAIN FUTURE CONDITION
18. DECESION MAKING ENVIRONMENT: DECESIONS ARE MADE UNDER THREE TYPES OF ENVIRONMENT: D.M.E. CERTAINITY UNCERTAINITY RISK IN THIS , ONLY ONE STATE OF NATURE EXISTS i.e. THERE IS COMPLETE CERTAINITY ABOUT THE FUTURE HERE MORE THAN ONE S.O.N. EXISTS BUT D. MAKER LACKS SUFFICIENT KNOWLEDGE TO ALLOW HIM ASSIGN PROB TO VARIOUS S.O.N. HERE ALSO MORE THAN ONE S.O.N. EXISTS BUT THE D. MAKER HAS SUFFICIENT INFO TO ALLOW HIM ASSIGN PROB TO EACH OF THESE STATES
19. D.M. UNDER UNCERTAINITY: Under condition of uncertainty, the decision maker has knowledge about states of nature that happens but lacks the knowledge about the probabilities of their occurrence. Under conditions of uncertainty, a few decision criterions are available which could be of help to the decision maker. D.M. UNDER UNCERTAINITY Maximax Criterion or Criterion of optimism Maximin Criterion or Criterion of pessimism Minimax Criterion or Regret Criterion Hurwicz Criterion or Criterion of Realism Laplace Criterion or Criterion of Rationality
20. ILLUSTRATION:CONSIDERING A MANUFACTURING COMPANY THAT IS THINKING OF VARIOUS ALTERNATIVES TO INCREASE ITS PRODUCTION TO MEET THE INCREASING MARKET DEMAND. WHICH STRATEGY OR ALTERNATIVE WILL THE CO. EMPLOY ON THE BASIS OF VARIOUS METHODS.
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24. MAXIMUM OF ROW 35,000 70,000 40,000 THIS TABLE SHOWS THAT THE COMPANY WILL MINIMIZE ITS REGRET TO RS 35,000 BY SELECTING ALTERNATIVE- “EXPANSION”
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26. HERE LET α = 0.8 WORKING NOTES: H1 = 0.8 * 50000 + 0.2 * -45000 = 31000 H2 = 0.8 * 70000 + 0.2 * -80000 = 40000 H3 = 0.8 * 30000 + 0.2 * -10000 = 22000 THUS ACCORDING TO HURWICZ CRITERION , COMPANY WILL CHOOSE ALTERNATIVE – “CONSTRUCT” MAX OF ROW MIN OF ROW H -45000 31000 50000 -80000 40000 70,000 -10000 30000 22000
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28. 1250 WORKING NOTES: (E.P.)1 = ¼(50000 + 25000 - 25000 – 45000) = 1250 (E.P.)2 = ¼(70000 + 30000 – 40000 – 80000)= - 5000 (E.P.)3 = ¼(30000 + 15000 – 1000 – 10000 ) = 8500 THUS ACCORDING TO LAPLACE CRITERION , COMPANY WILL CHOOSE ALTERNATIVE – “SUBCONTRACT” - 5000 8500
29. ILLUSTRATION: THE FOLLOWING MATRIX GIVES THE PAYOFF OF DIFFERENT STRATEGIES S1, S2, S3 AGAINST CONDITIONS N1, N2, N3 AND N4. INDICATE THE DECESION TAKEN UNDER THE FOLLOWING APPROACH: OPTIMISTIC PESSIMISTIC REGRET HURWICZ, THE DEGREE OF OPTIMISM BEING 0.7 EQUAL PROBABILITY
30. SOLUTION OPTIMISTIC CRITERION: SO, ACCORDING TO O.C., MAXIMAX PAYOFF IS Rs. 20000 CORRESPONDING TO THE STRATEGY – “S2” AND “S3” . (II) PESSIMISTIC CRITERION: SO, ACCORDING TO P.C., MAXIMIN PAYOFF IS Rs. 0 CORRESPONDING TO THE STRATEGY – “S2” MAX OF ROW 18000 20000 20000 MIN OF ROW - 100 0 - 2000
31. (III) REGRET (SAVAGE CRITERION): THE BEST PAY OFFS FOR EACH STATE OF NATURE N1, N2, N3 & N4 ARE Rs. 20000, Rs. 15000, Rs. 6000 & RS. 18000 RESPECTIVELY. SUBSTRACTING FROM THESE THE PAYOFFS OF CORRESPONDING COLUMN WE GET THE MINIMAX REGRET CORRESPONDS TO STRATEGY “S1”. MAX OF ROW 16000 18000 17000
32. (IV) HURWICZ CRITERION: MAX OF ROW MIN OF ROW 12570 18000 - 100 14000 20000 0 13400 20000 - 2000 HERE = 0.7 WORKING NOTES: H1 = 0.7 *18000 + 0.3 * (- 100) = 12570 H2 = 0.7 * 20000+ 0.3 * 0 = 14000 H3 = 0.7 * 20000 + 0.3 * (- 2000) = 13400 THE MAXIMUM VALUE OF H = Rs. 14000 WHICH CORRESPONDS TO STRATEGY “S2”.
33. (V) EQUAL PROBABILITY CRITERION: WORKING NOTES: (E.P.)1 = ¼(4000 - 100 + 6000 + 18000) = 6975. (E.P.)2 = ¼(20000 + 5000 + 400 + 0 ) = 6350. (E.P.)3 = ¼(20000 + 15000 – 2000 + 1000 ) = 8500. THE MAXIMUM PAYOFF IS Rs. 8500 WHICH CORRESPONDS TO THE STRATEGY – “S3”. EXPECTED PAYOFF 6975 6350 8500
34. DECESION MAKING UNDER RISK: Here more than one state of nature exists and the decision maker has sufficient information to assign probabilities to each of these states. These probabilities could be obtained from the past records or simply the subjective judgment of the decision maker. Under conditions of risk, knowing the probability distribution of the state of nature, the best decision is to select the course of action which has the largest expected pay off value.
35. DECESION MAKING UNDER RISK: Expected Value Criterion or Expected Monetary Value Criterion Expected Opportunity Loss Criterion or Expected Value of Regret Expected Value for Perfect Information Conditional Profit Table Expected Profit Table Conditional Profit Table Conditional Loss table Expected Loss Table Conditional Profit Table with P.I. Expected Profit Table with P.I.
36. ILLUSTRATION A newspaper boy has the following probabilities of selling a magazine: No. of copies sold Probability 10 0.10 11 0.15 12 0.20 13 0.25 14 0.30 Cost of the copy is 30 paisa and sale price is 50 paisa. He cannot return the unsold copies. How many should he order?
42. STEP II: CONSTRUCT CONDITIONAL LOSS TABLE ROW-WISE SUBSTRACTION ROW MAX – OTHER ELEMENTS OF ROW 0 30 90 60 120 20 60 90 30 0 60 30 0 40 20 60 20 0 30 40 0 60 40 20 80
43. STEP III: CONSTRUCT EXPECTED LOSS TABLE: THE OPTIMUM STOCK ACTION IS THE ONE WHICH WILL MINIMIZE EXPECTED OPPORTUNITY LOSS; THIS ACTION CALLS FOR THE STOCKING OF 12 COPIES EACH DAY AT WHICH POINT THERE IS MINIMUM EXPECTED LOSS OF 27.5 PAISE. 0 3 9 6 12 3 9 13.5 4.5 0 12 6 0 8 4 15 5 0 7.5 10 0 18 12 6 24 50 35 27.5 E.O.L. 30 45
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45. EVPI represents the maximum amount of money the decision maker has to pay to get this additional information about the occurrence of various state of nature before a decision has to be made. The procedure to calculate expected value of perfect information is as follows: Construct conditional profit table with perfect information. Construct expected profit table with perfect information. Determine EVPI from relation; EVPI = EPPI – max EMV
47. STEP II: CONSTRUCT EXPECTED PROFIT TABLE WITH PERFECT INFORMATION: 20 200 33 220 48 240 65 260 84 280 EPPI = 250 STEP III: The expected value of perfect information is given by EVPI = EPPI – max EMV = 250 – 222.5 = 27.5 Paise Thus this is the maximum amount which the newsboy willing to pay, per day, for a perfect information. = min E.O.L.
48. illustration Under an employment promotion program, it is proposed to allow sale of newspapers on the buses during off peak hours. The vendor can purchase the newspaper at a special concessional rate of 25 paise per copy against the selling price of 40 paise. Any unsold copies are, however a dead loss. A vendor has estimated the following probability distribution for the no. of copies demanded: How many copies should he ordered so that his expected profit will be maximum? Compute EPPI The vendor is thinking of spending on a small market survey to obtain additional information regarding the demand levels. How much should he be willing to spend on such a survey?