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Chapter 5 supplement Decision Theory

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## Chapter 5 supplement Decision Theory

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**Chapter 5 supplementDecision Theory**Saba Bahouth – UCO**Quantitative Analysis**Logic Historical Data Marketing Research Scientific Analysis Modeling Problem Decision Qualitative Analysis Emotions Intuition Personal Experience Personal Motivation Rumors The Decision-Making Process Saba Bahouth – UCO**Decision Environments**CERTAINTY: When all parameters (like cost, distance, capacity, time ...) are known. UNCERTAINTY: When it is impossible to assess the probability of possible outcomes. RISK: When there exists a certain probability level associated with possible outcomes. What environment is investing in drilling a new oil well? Saba Bahouth – UCO**Typical Example**A building contractor has to make a decision regarding the capacity of his operation for next year. He has estimated profits (in $1,000) under each of the states of nature he believes might occur, as shown in the table below: Next year’s demand AlternativeLow High Do nothing $50 $60 Expand $20 $80 Subcontract $40 $70 What decisions will he make under different environments and different decision making approaches? Saba Bahouth – UCO**Decision Making Under Certainty**Next year’s demand AlternativeLow High Do nothing $50 $60 Expand $20 $80 Subcontract $40 $70 In this case, we assume that we know, with certainty, the outcome for next year (high or low demand). Therefore, the manager should do nothing if he/she believes that next year's demand will be low, and the manager should expand if he/she believes that next year's demand will be high. Saba Bahouth – UCO**Decisions Under Uncertainty (1/2)**1. MAXIMIN: Determine the worst payoff for each alternative, and then select the best among these worst alternatives. (pessimistic, guaranteed minimum) Next year demand AlternativeLow HighWorst Do nothing $50 $60 50 Expand $20 $80 20 Subcontract $40 $70 40 Therefore select to do nothing. 2. MAXIMAX: Determine the best payoff for each alternative, and then select the best among these best alternatives. (optimistic, greedy) Next year demand AlternativeLow HighBest Do nothing $50 $60 60 Expand $20 $80 80 Subcontract $40 $70 70 Therefore select to expand. Saba Bahouth – UCO**Decisions Under Uncertainty (2/2)**3. Equally Likely (LaPlace): Determine the average payoff for each alternative, and choose the alternative with the best average. Next year demand AlternativeLow HighAverage Do nothing $50 $60 (50+60)/2 = 55 Expand $20 $80 (20+80)/2 = 50 Subcontract $40 $70 (40+70)/2 = 55 Therefore select either to do nothing or to subcontract the work. 4. Minimax Regret: Next year demandRegretsMax. AlternativeLow HighLow HighDo nothing $50 $60 $00 $20 $20 Expand $20 $80 $30 $00 $30Subcontract $40 $70 $10 $10 $10(min.) Therefore select to subcontract the work. Saba Bahouth – UCO**Decision Theory Elements**• A set of possible future conditions exists that will have a bearing on the results of the decision • A list of alternatives for the decision maker to choose from • A known payoff for each alternative under each possible future condition Saba Bahouth – UCO**Decision Making Under Risk (1/2)**1. EXPECTED MONETARY VALUE (EMV): Determine the expected payoff of each alternative, and then select the best alternative. Assume P(low)=.3 and P(high)=.7, the expected monetary value for each alternative is: Next year demand AlternativeLow HighE M VProbability: .3.7 Do nothing $50 $60 .3x50 + .7x60 = 57 Expand $20 $80 .3x20 + .7x80 = 62 Subcontract $40 $70 .3x40 + .7x70 = 61 Therefore select to expand. Saba Bahouth – UCO**Decision Making Under Risk (2/2)**Low .3 Low .3 $50 $50 DECISION TREES: High .7 High .7 $60 $60 Do Nothing Do Nothing $57 Low .3 Low .3 $20 $20 Expand Expand $62 High .7 $80 High .7 $80 Subcontract Subcontract $61 Low .3 Low .3 $40 $40 High .7 High .7 $70 $70 - Branches leaving square nodes represent alternatives. - Branches leaving circular nodes represent outcomes. Saba Bahouth – UCO**Expected Value of Perfect Information (EVPI)**Expected value of perfect information:the difference between the expected payoff under certainty and the expected payoff under risk EVPI = Expected payoff under certainty (EPUC) -Expected payoff under risk (EPUR) Next year demand Alternative Low HighE M V (or EPUR)Probability: .3 .7 Do nothing $50 $60 .3x50 + .7x60 = 57 Expand $20 $80 .3x20 + .7x80 = 62 Subcontract $40 $70 .3x40 + .7x70 = 61 EVPI = Expected payoff under certainty (EPUC) -Expected payoff under risk (EPUR) EVPI = (.3 x 50) + (.7 x 80) -62 EVPI = 9 Saba Bahouth – UCO**Sensitivity Analysis**Probabilities associated with each outcome are estimates. What happens if they were different? Equations: Do nothing: 50 + 10P Expand: 20 + 60P Subcontract: 40 + 30P After solving pairs of equations with two unknown: Do nothing for: 0.00 < P < 0.50 Subcontract for: 0.50 < P < 0.67 Expand for: 0.67 < P < 1.00 80 70 Payoff in case of low demand Payoff in case of high demand 60 Do N. 50 Sub. 40 Exp. 20 0 .50 .67 1.0 Probability of high demand Saba Bahouth – UCO