decision making criterion

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decision making criterion

  1. 1. Operation research <br />GAURAV SONKAR<br />
  2. 2. OPERATION<br />RESEARCH<br />of<br />An operation may be defined as the set of acts required for the achievements of a desired outcomes.<br />
  3. 3. DEFNITIONS OF O.R.<br />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<br />I<br />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<br />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<br />
  4. 4. CHARACTERISTICS OF OR:<br /><ul><li>ITS SYSTEM ORIENTED
  5. 5. USE OF INTERDISCIPLINARY TEAM
  6. 6. APPLICATION OF SCIENTIFIC METHODS
  7. 7. UNCOVERING OF NEW PROBLEMS
  8. 8. IMPROVE THE QUALITY OF DECESIONS
  9. 9. USE OF COMPUTERS
  10. 10. QUANTITATIVE SOLUTION
  11. 11. HUMAN FACTORS</li></li></ul><li>SCOPE OF OPERATION RESEARCH:<br />I. ALLOCATION AND DISTRIBUTION:<br />Optimal allocation of limited resources such as men, machine, and material.<br />Location and size of warehouses, distribution centre, retail depot etc.<br />Distribution policy.<br />II. PRODUCTION AND FACILITY PLANNING:<br />Selection, location and design of production plant.<br />Project scheduling & allocation of resources.<br />Forecasting.<br />Maintenance policy.<br />Scheduling & sequencing.<br />
  12. 12. III. PROCUREMENT: <br />What, when and how to purchase at minimum procurement cost<br />Bidding and replacement policies.<br />IV. MARKETING:<br />Product selection, timing & competitive action<br />Selection of advertising media.<br />Demand forecast and stock level.<br />Customer’s preference for size, colour & packaging of various products. <br />V. FINANCE:<br />Capital requirement, cash flow analysis.<br />Credit policies, credit risks etc.<br />Profit plan of the company.<br />Determination of optimum replacement policies.<br />
  13. 13. VI. PERSONNEL:<br />Selection of personnel, determination of retirement age and skills<br />Recruitment of policies & assignments of jobs.<br /> <br />VII. RESEARCH AND DEVELOPMENT:<br />Determination of areas of Research and Development<br />Reliability & control of development of projects.<br />Selection of projects & preparation of their budgets.<br />
  14. 14. METHODOLOGY OF OR:<br />FORMULATE THE PROBLEM<br />CONSTRUCT A MATHEMATICAL MODEL<br />SOLVE THE MODEL<br />TEST THE MODEL<br />ANALYSE THE RESULT<br />IMPLEMENTATION OF SELECTED STRATEGY<br />
  15. 15. DIFFICULTY IN O.R.<br />PROBLEM FORMULATION<br />DATA COLLECTION<br />STUDY BASED ON OBSERVATION OR OLD LAWS<br />TIME FACTOR<br />HUMAN FACTOR<br />
  16. 16. DECESION THEORY:<br /> DECESION THEORY PROVIDES A RATIONAL APPROACH IN DEALING PROBLEMS CONFRONTED WITH THE PARTIAL , IMPERFECT OR UNCERTAIN FUTURE CONDITION<br />
  17. 17. STEPS IN DECESION THEORY APPROACH:<br />
  18. 18. DECESION MAKING ENVIRONMENT:<br />DECESIONS ARE MADE UNDER THREE TYPES OF ENVIRONMENT:<br />D.M.E.<br />CERTAINITY<br />UNCERTAINITY<br />RISK<br />IN THIS , ONLY ONE STATE OF NATURE EXISTS i.e. THERE IS COMPLETE CERTAINITY ABOUT THE FUTURE<br />HERE MORE THAN ONE S.O.N. EXISTS BUT D. MAKER LACKS SUFFICIENT KNOWLEDGE TO ALLOW HIM ASSIGN PROB TO VARIOUS S.O.N.<br />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<br />
  19. 19. D.M. UNDER UNCERTAINITY:<br />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. <br /> Under conditions of uncertainty, a few decision criterions are available which could be of help to the decision maker.<br />D.M. UNDER UNCERTAINITY<br />Maximax Criterion or Criterion of optimism<br />Maximin Criterion or Criterion of pessimism<br />Minimax Criterion or <br />Regret Criterion<br />Hurwicz Criterion or Criterion of Realism<br />Laplace Criterion or Criterion of Rationality<br />
  20. 20. ILLUSTRATION:CONSIDERING A MANUFACTURING COMPANY THAT IS THINKING OF VARIOUS ALTERNATIVES TO INCREASE ITS PRODUCTION TO MEET THE INCREASING MARKET DEMAND.<br />WHICH STRATEGY OR ALTERNATIVE WILL THE CO. EMPLOY ON THE BASIS OF VARIOUS METHODS.<br />
  21. 21. (I) MAXIMAX CRITERION OR CRITERION OF OPTIMISM:<br /><ul><li>This criterion provides the decision maker with optimistic criterion. The working method is summarizing as follow.</li></ul>Locate the maximum payoff values corresponding to each alternative (or course of action or strategy), then<br />Select an alternative with maximum payoff value.<br />THUS THE MAXIMAX PAYOFF IS Rs. 70,000 CORRESPONDING TO THE ALTERNATIVE “CONSTRUCT”.<br />MAXIMUM <br />OF<br /> ROW<br />50,000<br />70,000<br />30,000<br />
  22. 22. (II) MAXIMIN CRITERION OR CRITERION OF PESSIMISM:<br /><ul><li>This criterion provides the decision maker with pessimistic criterion. The working method is summarizing as follow.</li></ul>Locate the minimum payoff values corresponding to each alternative (or course of action or strategy), then<br /> Select an alternative with maximum payoff value.<br />THUS THE MINIMAX PAYOFF IS Rs. – 10,000 CORRESPONDING TO THE ALTERNATIVE - “SUBCONTRACT”<br />MINIMUM <br />OF<br /> ROW<br />-45,000<br />-80,000<br />-10,000<br />
  23. 23. (III) MINIMAX CRITERION OR MINIMUM REGRET CRITERION: <br /><ul><li>This criterion is also known as opportunity loss decision criterion or minimax regret criterion. The working method is summarizing as follow.</li></ul>Determine the amount of regret corresponding to each alternative for each state of nature. The regret for jthevent corresponding to ithalternative is given by<br />ith regret = (maximum payoff – ith payoff) for the jth event<br /> Determine the maximum regret amount for each alternative. <br />Choose the alternative which corresponds to the minimum of the maximum regrets. <br />
  24. 24. MAXIMUM <br />OF<br /> ROW<br />35,000<br />70,000<br />40,000<br />THIS TABLE SHOWS THAT THE COMPANY WILL MINIMIZE ITS REGRET TO RS 35,000 BY SELECTING ALTERNATIVE- “EXPANSION”<br />
  25. 25. (IV) Hurwicz Criterion or Criterion of Realism:<br /><ul><li>Also called weighted average criterion, it is a compromise between the maximax (optimistic) and minimax (pessimistic) decision criterion. This concept allows the decision maker to take into account both maximum and minimum for each alternative and assign them weights according to his degree of optimism (or pessimism). The working method is summarizing as follow:</li></ul>Choose an appropriate degree of optimism, α so that (1-α) represents degree of pessimism.<br />Determine the maximum as well as minimum of each alternative and obtain<br />P = α. Maximum + (1-α). Minimum<br /> for each alternative.<br />Choose the alternative that yields the maximum value of P. <br />
  26. 26. HERE LET α = 0.8<br />WORKING NOTES:<br />H1 = 0.8 * 50000 + 0.2 * -45000 = 31000<br />H2 = 0.8 * 70000 + 0.2 * -80000 = 40000<br />H3 = 0.8 * 30000 + 0.2 * -10000 = 22000<br />THUS ACCORDING TO HURWICZ CRITERION , COMPANY WILL CHOOSE ALTERNATIVE – “CONSTRUCT”<br />MAX<br />OF<br /> ROW<br />MIN <br />OF<br /> ROW<br />H<br />-45000<br />31000<br />50000<br />-80000<br />40000<br />70,000<br />-10000<br />30000<br />22000<br />
  27. 27. (V) Laplace Criterion or Criterion of Rationality: <br /><ul><li>Also known as equal probabilities criterion or criterion of rationality. Since the probability of states of nature are not known, it is assumed that all states of nature will occur with equal probability, i.e. assign an equal probability. The working method is summarizing as follow:</li></ul>Determine expected value for each alternative; if n denotes the number of events and P’s denote the payoffs, then expected value is given by 1n[P1+P2+….+Pn]<br />Choose the alternative that yields the maximum value of P.<br />
  28. 28. 1250<br />WORKING NOTES:<br />(E.P.)1 = ¼(50000 + 25000 - 25000 – 45000) = 1250<br />(E.P.)2 = ¼(70000 + 30000 – 40000 – 80000)= - 5000<br />(E.P.)3 = ¼(30000 + 15000 – 1000 – 10000 ) = 8500<br />THUS ACCORDING TO LAPLACE CRITERION , COMPANY WILL CHOOSE ALTERNATIVE – “SUBCONTRACT”<br />- 5000<br />8500<br />
  29. 29. ILLUSTRATION: THE FOLLOWING MATRIX GIVES THE PAYOFF OF DIFFERENT STRATEGIES S1, S2, S3 AGAINST CONDITIONS N1, N2, N3 AND N4.<br />INDICATE THE DECESION TAKEN UNDER THE FOLLOWING APPROACH:<br />OPTIMISTIC<br />PESSIMISTIC<br />REGRET<br />HURWICZ, THE DEGREE OF OPTIMISM BEING 0.7<br />EQUAL PROBABILITY<br />
  30. 30. SOLUTION<br />OPTIMISTIC CRITERION:<br />SO, ACCORDING TO O.C., MAXIMAX PAYOFF IS Rs. 20000 CORRESPONDING TO THE STRATEGY – “S2” AND “S3” .<br />(II) PESSIMISTIC CRITERION:<br />SO, ACCORDING TO P.C., MAXIMIN PAYOFF IS Rs. 0 CORRESPONDING TO THE STRATEGY – “S2”<br />MAX <br />OF <br />ROW<br />18000<br />20000<br />20000<br />MIN<br />OF <br />ROW<br />- 100<br />0<br />- 2000<br />
  31. 31. (III) REGRET (SAVAGE CRITERION): <br />THE BEST PAY OFFS FOR EACH STATE OF NATURE N1, N2, N3 & N4 ARE Rs. 20000, Rs. 15000, Rs. 6000 & RS. 18000 RESPECTIVELY.<br />SUBSTRACTING FROM THESE THE PAYOFFS OF CORRESPONDING COLUMN WE GET<br />THE MINIMAX REGRET CORRESPONDS TO STRATEGY “S1”.<br />MAX <br />OF <br />ROW<br />16000<br />18000<br />17000<br />
  32. 32. (IV) HURWICZ CRITERION:<br />MAX <br />OF <br />ROW<br />MIN<br />OF <br />ROW<br />12570<br />18000<br />- 100<br />14000<br />20000<br />0<br />13400<br />20000<br />- 2000<br />HERE  = 0.7 <br />WORKING NOTES:<br /> H1 = 0.7 *18000 + 0.3 * (- 100) = 12570<br />H2 = 0.7 * 20000+ 0.3 * 0 = 14000<br />H3 = 0.7 * 20000 + 0.3 * (- 2000) = 13400<br />THE MAXIMUM VALUE OF H = Rs. 14000 WHICH CORRESPONDS TO STRATEGY “S2”.<br />
  33. 33. (V) EQUAL PROBABILITY CRITERION:<br />WORKING NOTES:<br />(E.P.)1 = ¼(4000 - 100 + 6000 + 18000) = 6975.<br />(E.P.)2 = ¼(20000 + 5000 + 400 + 0 ) = 6350.<br />(E.P.)3 = ¼(20000 + 15000 – 2000 + 1000 ) = 8500.<br />THE MAXIMUM PAYOFF IS Rs. 8500 WHICH CORRESPONDS TO THE STRATEGY – “S3”.<br />EXPECTED PAYOFF<br />6975<br />6350<br />8500<br />
  34. 34. DECESION MAKING UNDER RISK:<br />Here more than one state of nature exists and the decision maker has sufficient information to assign probabilities to each of these states. <br />These probabilities could be obtained from the past records or simply the subjective judgment of the decision maker. <br />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.<br />
  35. 35. DECESION MAKING UNDER RISK:<br />Expected Value Criterion <br />or <br />Expected Monetary Value Criterion<br />Expected Opportunity Loss Criterion<br /> or <br />Expected Value of Regret <br />Expected Value for Perfect Information<br />Conditional Profit Table<br />Expected Profit Table<br />Conditional Profit Table<br />Conditional Loss table<br />Expected Loss Table <br />Conditional Profit Table with P.I.<br />Expected Profit Table with P.I. <br />
  36. 36. ILLUSTRATION<br />A newspaper boy has the following probabilities of selling a magazine:<br /> No. of copies sold Probability<br /> 10 0.10<br /> 11 0.15<br /> 12 0.20<br /> 13 0.25<br /> 14 0.30<br />Cost of the copy is 30 paisa and sale price is 50 paisa. He cannot return the unsold copies. How many should he order?<br />
  37. 37. Expected Value Criterion:<br /><ul><li>The expected monetary value for a given course of action is the weighted sum of possible payoffs for each alternative. It is obtained by summing the payoffs for each course of action multiplied by the probabilities associated with state of nature. It consists of following steps:</li></ul>Construct a payoff table listing the alternative decisions and the various state of nature. Enter the conditional profit for each decision event combination along with the associated probabilities. (Construct Conditional profit table).<br /> Calculate the EMV for each decision alternative by multiplying the conditional profits by assigned probabilities and adding the resulting conditional values. (Construct expected profit table).<br />Select the alternative that yields the highest EMV.<br />
  38. 38. SOLUTION<br />Cost Price = 30 paisa.<br />Selling Price = 50 paisa.<br />Profit = Selling price – Cost price = 20 paisa.<br />STEP I : CONSTRUCT CONDITIONAL PROFIT TABLE<br />Profit * S.P. = 20 S.P. ;When D ≥ S<br />Conditional<br /> Profit<br />=<br />S.P. * D – C.P. * S = 50D – 30S; When D < S<br />110<br />200<br />140<br />80<br />170<br />200<br />160<br />130<br />190<br />220<br />180<br />210<br />240<br />200<br />220<br />240<br />260<br />200<br />230<br />220<br />280<br />220<br />240<br />260<br />200<br />
  39. 39. STEP II: CONSTRUCT EXPECTED PROFIT TABLE:<br />17<br />20<br />14<br />11<br />8<br />30<br />33<br />28.5<br />24<br />19.5<br />40<br />44<br />48<br />42<br />36<br />50<br />65<br />55<br />60<br />57.5<br />78<br />66<br />60<br />72<br />84<br />TOTAL EXPECTED<br /> PROFIT<br />222.5<br />220<br />200<br />205<br />215<br />THE NEWS BOY MUST, THEREFORE, ORDER 12 COPIES TO EARN THE HIGHEST POSSIBLE AVERAGE DAILY PROFIT OF 222.5 PAISE<br />
  40. 40. EXPECTED OPPORTUNITY LOSS CRITERION:<br /><ul><li>EOL represents the amount by which maximum possible profit will be reduced under various possible stock actions. The course of action that minimizes these losses or reductions is the optimal decision alternative. The procedure to calculate expected opportunity losses is as follows: </li></ul>Prepare the conditional profit table for each decision-event combination and write associated probabilities. (Construct Conditional profit table). <br />For each event, determine the conditional opportunity loss (COL) by subtracting the payoff from the maximum payoff for that event. (Construct Conditional loss table).<br />Calculate the expected opportunity loss for each decision alternative by multiplying the COL’s by the associated probabilities and then adding the values. (Construct Expected loss table).<br />Select the alternative that yields the lowest EOL.<br />
  41. 41. SOLUTION<br />Cost Price = 30 paisa.<br />Selling Price = 50 paisa.<br />Profit = Selling price – Cost price = 20 paisa.<br />STEP I : CONSTRUCT CONDITIONAL PROFIT TABLE<br />Profit * S.P. = 20 S.P. ;When D ≥ S<br />Conditional<br /> Profit<br />=<br />S.P. * D – C.P. * S = 50D – 30S; When D < S<br />110<br />200<br />140<br />80<br />170<br />200<br />160<br />130<br />190<br />220<br />180<br />210<br />240<br />200<br />220<br />240<br />260<br />200<br />230<br />220<br />280<br />220<br />240<br />260<br />200<br />
  42. 42. STEP II: CONSTRUCT CONDITIONAL LOSS TABLE<br />ROW-WISE SUBSTRACTION<br />ROW MAX – OTHER ELEMENTS OF ROW<br />0<br />30<br />90<br />60<br />120<br />20<br />60<br />90<br />30<br />0<br />60<br />30<br />0<br />40<br />20<br />60<br />20<br />0<br />30<br />40<br />0<br />60<br />40<br />20<br />80<br />
  43. 43. STEP III: CONSTRUCT EXPECTED LOSS TABLE:<br />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.<br />0<br />3<br />9<br />6<br />12<br />3<br />9<br />13.5<br />4.5<br />0<br />12<br />6<br />0<br />8<br />4<br />15<br />5<br />0<br />7.5<br />10<br />0<br />18<br />12<br />6<br />24<br />50<br />35<br />27.5<br />E.O.L.<br />30<br />45<br />
  44. 44. Expected Value for Perfect Information:<br /><ul><li>Perfect Information means complete and accurate information about the future demand and that remove all the uncertainty for future.
  45. 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: </li></ul>Construct conditional profit table with perfect information.<br />Construct expected profit table with perfect information.<br />Determine EVPI from relation; <br />EVPI = EPPI – max EMV<br />
  46. 46. SOLUTION<br />Cost Price = 30 paisa.<br />Selling Price = 50 paisa.<br />Profit = Selling price – Cost price = 20 paisa. STEP I : CONSTRUCT CONDITIONAL PROFIT TABLE<br />200<br />220<br />240<br />260<br />280<br />
  47. 47. STEP II: CONSTRUCT EXPECTED PROFIT TABLE WITH PERFECT INFORMATION:<br />20<br />200<br />33<br />220<br />48<br />240<br />65<br />260<br />84<br />280<br />EPPI = 250<br />STEP III: The expected value of perfect information is <br />given by<br />EVPI = EPPI – max EMV<br />= 250 – 222.5<br />= 27.5 Paise <br />Thus this is the maximum amount which the newsboy<br /> willing to pay, per day, for a perfect information.<br />= min E.O.L.<br />
  48. 48. illustration<br />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:<br />How many copies should he ordered so that his expected profit will be maximum?<br />Compute EPPI<br />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?<br />
  49. 49. SOLUTION<br />(a) CALCULATION OF EXPECTED PROFIT:<br />Cost Price = 25 paisa.<br />Selling Price = 40 paisa.<br />Profit = Selling price – Cost price = 40 – 25 = 15 paisa.<br />STEP I : CONSTRUCT CONDITIONAL PROFIT TABLE:<br />150<br />225<br />175<br />100<br />125<br />200<br />225<br />190<br />140<br />165<br />215<br />240<br />180<br />205<br />230<br />255<br />225<br />240<br />255<br />220<br />270<br />225<br />245<br />240<br />260<br />285<br />240<br />255<br />270<br />225<br />300<br />285<br />240<br />255<br />270<br />225<br />

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