decision making criterion

Operation research GAURAV SONKAR

OPERATION RESEARCH of An operation may be defined as the set of acts required for the achievements of a desired outcomes.

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

CHARACTERISTICS OF OR: ,[object Object]

APPLICATION OF SCIENTIFIC METHODS

IMPROVE THE QUALITY OF DECESIONS

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.

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.

METHODOLOGY OF OR: FORMULATE THE PROBLEM CONSTRUCT A MATHEMATICAL MODEL SOLVE THE MODEL TEST THE MODEL ANALYSE THE RESULT IMPLEMENTATION OF SELECTED STRATEGY

DIFFICULTY IN O.R. PROBLEM FORMULATION DATA COLLECTION STUDY BASED ON OBSERVATION OR OLD LAWS TIME FACTOR HUMAN FACTOR

DECESION THEORY: DECESION THEORY PROVIDES A RATIONAL APPROACH IN DEALING PROBLEMS CONFRONTED WITH THE PARTIAL , IMPERFECT OR UNCERTAIN FUTURE CONDITION

STEPS IN DECESION THEORY APPROACH:

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

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

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.

(I) MAXIMAX CRITERION OR CRITERION OF OPTIMISM: ,[object Object],Locate the maximum payoff values corresponding to each alternative (or course of action or strategy), then Select an alternative with maximum payoff value. THUS THE MAXIMAX PAYOFF IS Rs. 70,000 CORRESPONDING TO THE ALTERNATIVE “CONSTRUCT”. MAXIMUM OF ROW 50,000 70,000 30,000

(II) MAXIMIN CRITERION OR CRITERION OF PESSIMISM: ,[object Object],Locate the minimum payoff values corresponding to each alternative (or course of action or strategy), then Select an alternative with maximum payoff value. THUS THE MINIMAX PAYOFF IS Rs. – 10,000 CORRESPONDING TO THE ALTERNATIVE - “SUBCONTRACT” MINIMUM OF ROW -45,000 -80,000 -10,000

(III) MINIMAX CRITERION OR MINIMUM REGRET CRITERION: ,[object Object],Determine the amount of regret corresponding to each alternative for each state of nature. The regret for jthevent corresponding to ithalternative is given by ith regret = (maximum payoff – ith payoff) for the jth event Determine the maximum regret amount for each alternative. Choose the alternative which corresponds to the minimum of the maximum regrets.

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”

(IV) Hurwicz Criterion or Criterion of Realism: ,[object Object],Choose an appropriate degree of optimism, α so that (1-α) represents degree of pessimism. Determine the maximum as well as minimum of each alternative and obtain P = α. Maximum + (1-α). Minimum for each alternative. Choose the alternative that yields the maximum value of P.

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

(V) Laplace Criterion or Criterion of Rationality: ,[object Object],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 1[P1+P2+….+Pn] Choose the alternative that yields the maximum value of P.

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

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

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

(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

(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”.

(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

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.

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.

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?

Expected Value Criterion: ,[object Object],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). 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). Select the alternative that yields the highest EMV.

SOLUTION Cost Price = 30 paisa. Selling Price = 50 paisa. Profit = Selling price – Cost price = 20 paisa. STEP I : CONSTRUCT CONDITIONAL PROFIT TABLE Profit * S.P. = 20 S.P. ;When D ≥ S Conditional Profit = S.P. * D – C.P. * S = 50D – 30S; When D < S 110 200 140 80 170 200 160 130 190 220 180 210 240 200 220 240 260 200 230 220 280 220 240 260 200

STEP II: CONSTRUCT EXPECTED PROFIT TABLE: 17 20 14 11 8 30 33 28.5 24 19.5 40 44 48 42 36 50 65 55 60 57.5 78 66 60 72 84 TOTAL EXPECTED PROFIT 222.5 220 200 205 215 THE NEWS BOY MUST, THEREFORE, ORDER 12 COPIES TO EARN THE HIGHEST POSSIBLE AVERAGE DAILY PROFIT OF 222.5 PAISE

EXPECTED OPPORTUNITY LOSS CRITERION: ,[object Object],Prepare the conditional profit table for each decision-event combination and write associated probabilities. (Construct Conditional profit table). For each event, determine the conditional opportunity loss (COL) by subtracting the payoff from the maximum payoff for that event. (Construct Conditional loss table). 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). Select the alternative that yields the lowest EOL.

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

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