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MS11 SM14 REDUCED

# MS11 SM14 REDUCED - Chapter 14 Decision Analysis Learning...

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Chapter 14 Decision Analysis Learning Objectives 1. Learn how to describe a problem situation in terms of decisions to be made, chance events and consequences. 2. Be able to analyze a simple decision analysis problem from both a payoff table and decision tree point of view. 3. Be able to develop a risk profile and interpret its meaning. 4. Be able to use sensitivity analysis to study how changes in problem inputs affect or alter the recommended decision. 5. Be able to determine the potential value of additional information. 6. Learn how new information and revised probability values can be used in the decision analysis approach to problem solving. 7. Understand what a decision strategy is. 8. Learn how to evaluate the contribution and efficiency of additional decision making information. 9. Be able to use a Bayesian approach to computing revised probabilities. 10. Know what is meant by utility. 11. Understand why utility could be preferred to monetary value in some situations. 12. Be able to use expected utility to select a decision alternative. 13. Be able to use TreePlan software for decision analysis problems. 14. Understand the following terms: decision alternatives decision strategy chance events risk profile states of nature sensitivity analysis influence diagram prior probabilities payoff table posterior probabilities decision tree expected value of sample information (EVSI) optimistic approach efficiency of sample information conservative approach Bayesian revision minimax regret approach utility opportunity loss or regret lottery expected value approach expected utility expected value of perfect information (EVPI) Solutions: 14 - 1

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Chapter 14 1. a. s 1 s 3 s 2 s 1 s 3 s 2 d 1 d 2 250 100 25 100 100 75 b. Decision Maximum Profit Minimum Profit d 1 250 25 d 2 100 75 Optimistic approach: select d 1 Conservative approach: select d 2 Regret or opportunity loss table: s 1 s 2 s 3 d 1 0 0 50 d 2 150 0 0 Maximum Regret: 50 for d 1 and 150 for d 2 ; select d 1 2. a. Decision Maximum Profit Minimum Profit d 1 14 5 d 2 11 7 d 3 11 9 d 4 13 8 Optimistic approach: select d 1 Conservative approach: select d 3 Regret or Opportunity Loss Table with the Maximum Regret s 1 s 2 s 3 s 4 Maximum Regret 14 - 2
Decision Analysis d 1 0 1 1 8 8 d 2 3 0 3 6 6 d 3 5 0 1 2 5 d 4 6 0 0 0 6 Minimax regret approach: select d 3 b. The choice of which approach to use is up to the decision maker. Since different approaches can result in different recommendations, the most appropriate approach should be selected before analyzing the problem. c. Decision Minimum Cost Maximum Cost d 1 5 14 d 2 7 11 d 3 9 11 d 4 8 13 Optimistic approach: select d 1 Conservative approach: select d 2 or d 3 Regret or Opportunity Loss Table s 1 s 2 s 3 s 4 Maximum Regret d 1 6 0 2 0 6 d 2 3 1 0 2 3 d 3 1 1 2 6 6 d 4 0 1 3 8 8 Minimax regret approach: select d 2 3. a. The decision to be made is to choose the best plant size. There are 2 alternatives to choose from: a small plant or a large plant.

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