CH_05S_10th_Edition

CH_05S_10th_Edition - Decision Theory CHAPTER 5S DECISION...

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Decision Theory CHAPTER 5S DECISION THEORY PROBLEMS P1. Here is a payoff matrix; parentheses designate a loss. The probabilities of the states of nature, P(1) and P(2), are unknown. States of Nature Alternatives 1 2 A B C $500 700 (300) $300 100 600 a. Which alternative should be selected under the maximax criterion? b. Which alternative should be selected under the maximin criterion? c. Which alternative should be selected under the Laplace criterion? d. What is the opportunity loss table? e. Which alternative should be selected under the minimax regret criterion? P2. Refer to Problem 1. Construct the sensitivity graph, as shown on p. 207 of your textbook. a. For what range of values of P(2) is alternative A preferred? a. For what range of values of P(2) is alternative B preferred? b. For what range of values of P(2) is alternative C preferred? 1
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Chapter 5 Supplement P3. Fall has come, and the department manager of the Purple Pentagon Discount Store must decide how many snow blowers to order for the winter season. He believes there is an association between the weather and the demand for snow blowers: a winter with heavy snow should produce a high demand, and a winter with light snow should produce a low demand. However, if he guesses wrong and orders a large number of snow blowers when the weather turns out to have light snow, he will suffer a loss. Here is his payoff matrix. States of Nature Alternatives Heavy snow Medium snow Light snow Large Order Medium Order Small Order $5,000 2,000 500 $1,000 3,000 500 $(4,000) (2,000) 1,000 a. Which alternative should be selected under the maximax criterion? b. Which alternative should be selected under the maximin criterion? c. Which alternative should be selected under the Laplace criterion? d. What is the opportunity loss table? e. Which alternative should be selected under the minimax regret criterion? P4. Refer to Problem 3. Suppose that the following probabilities are available regarding the snowfall next winter: P(heavy snow) = .10 P(medium snow) = .50 P(light snow) = .40 a. Which alternative should be selected under the expected value criterion? b. What is the value of the EVPI? c.
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CH_05S_10th_Edition - Decision Theory CHAPTER 5S DECISION...

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