# Chapter 5 supplement Decision Theory - PowerPoint PPT Presentation

Chapter 5 supplement Decision Theory

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Chapter 5 supplement Decision Theory

## Chapter 5 supplement Decision Theory

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1. Chapter 5 supplementDecision Theory Saba Bahouth – UCO

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. Saba Bahouth – UCO

13. 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