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Chapter 5 supplement Decision Theory Saba Bahouth – UCO 1 The Decision-Making Process Quantitative Analysis Problem Logic Historical Data Marketing Research Scientific Analysis Modeling Decision Qualitative Analysis Emotions Intuition Personal Experience Personal Motivation Rumors Saba Bahouth – UCO 2 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 3 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: Alternative Do nothing Expand Subcontract Next year’s demand Low High $50 $60 $20 $80 $40 $70 What decisions will he make under different environments and different decision making approaches? Saba Bahouth – UCO 4 Decision Making Under Certainty Alternative Do nothing Expand Subcontract Next year’s demand Low High $50 $60 $20 $80 $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 5 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 Alternative Low High Worst 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 Alternative Low High Do nothing $50 $60 Expand $20 $80 Subcontract $40 $70 Therefore select to expand. Saba Bahouth – UCO Best 60 80 70 6 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 Alternative Low High Average 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: Alternative Do nothing Expand Subcontract Next year demand Low High $50 $60 $20 $80 $40 $70 Regrets Low High $00 $20 $30 $00 $10 $10 Max. $20 $30 $10 (min.) Therefore select to subcontract the work. Saba Bahouth – UCO 7 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 8 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 Low High Alternative Probability: Do nothing Expand Subcontract Therefore select to expand. .3 .7 $50 $20 $40 $60 $80 $70 Saba Bahouth – UCO EMV .3x50 + .7x60 = 57 .3x20 + .7x80 = 62 .3x40 + .7x70 = 61 9 Decision Making Under Risk (2/2) DECISION TREES: Low .3 $50 Low .3 $50 High .7 $60 High .7 $60 Low .3 $20 High .7 $80 Low .3 $40 High .7 $70 $57 Low .3 $20 Expand Expand $62 High .7 $80 Low .3 $40 High .7 $70 $61 - Branches leaving square nodes represent alternatives. - Branches leaving circular nodes represent outcomes. Saba Bahouth – UCO 10 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) Alternative Probability: Do nothing Expand Subcontract Next year demand Low High .3 .7 $50 $60 $20 $80 $40 $70 E M V (or EPUR) .3x50 + .7x60 = 57 .3x20 + .7x80 = 62 .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 11 Saba Bahouth – UCO 12 Sensitivity Analysis 80 70 60 Do N. 50 Sub. 40 Exp. Payoff in case of high demand Payoff in case of low demand Probabilities associated with each outcome are estimates. What happens if they were different? Equations: Do nothing: Expand: Subcontract: 50 + 10P 20 + 60P 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 20 0 .50 .67 Probability of high demand 1.0 Saba Bahouth – UCO 13