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Optimal Selection

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DECISION THEORY & DECISION TREES(Decision making under risk) Janet Kim, president Kim Manufacturing, Inc., is considering whether or not to build more manufacturing plants in Wisconsin. She has developed the following pay-off table for her decision: Payoff in dollars Alternative Build large plant Build small plant Don’t build Market probabilities Favorable Market 400,000 80,000 0 0.4 Unfavorable Market -300,000 -10,000 0 0.6

(a) Use the expected monetary value approach to determine the decision that Kim should make. (b) Use the expected opportunity loss (regret) approach to determine the decision that Kim should make. (c) What is the expected value of perfect information? Class Example 2 (Decision making under uncertainty) Even though independent gas stations have been having a difficult time, Susan Solomon has been thinking about starting her own independent gasoline station. Susan’s problem is to decide how large her station should be. The annual returns depend on both the size of her station and a number of market factors related to the oil industry and demand for gasoline. After a careful analysis Susan has developed the following table: Size of gas station Small Medium Large Very large Payoff in dollars Good Market 50,000 80,000 100,000 300,000 Fair Market 20,000 30,000 30,000 25,000 Poor Market -10,000 -20,000 -40,000 -160,000

(a) What is the Maximax (optimistic) decision? (b) What is the Maximin (pessimistic) decision? (c) What is the criterion of realism decision? Use α = 0.8. (d) What is the equally likely decision?

(e) What is the minimax regret decision? Class Example 3 (Decision trees) A group of medical professionals is considering the construction of a private clinic. If the medical demand is high (that is, there is favorable market for the clinic), the doctors would realize a net profit of $100,000. If the market is not favorable, they could

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