HOMEWORK 2 CHALTER 3)MAKEUE The following is a payoff table giving profits for v
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Question
HOMEWORK 2 CHALTER 3)MAKEUE The following is a payoff table giving profits for various situations States of Nature 100 120-1 180 0 14O 120 Alternative 3 Do Nothing The probabilities for states of nature A, B, and C are 0.3, 0.5, and 0.2, respectively a. If the manager of this company is pessimistic, what alternative should he select? b. If the manager of this company is optimistic, what alternative should he select? C. If the coefficient of realism (a) is 0.80, what alternative should be selected (based on the criterion of realism)? d. If the criterion of the opportunity loss (Minimax Regret) is used, what alternative should be selected. Use the payoffs and the probabilities to calculate the expected monetary values (EMV). Based on the EMV, what alternative should the manager select? Calculate the expected value of perfect information (EVPI) (hint: You must calculate the e. f. expected value with perfect information in order to determine the EVPI). Calculate the opportunity loss table and the expected opportunity loss (EOL). Based on EOL criterion, what alternative should be selected? g.Explanation / Answer
a.
Minimum payoffs for alternative 1 is 100.
Minimum payoffs for alternative 2 is 120.
Minimum payoffs for alternative 3 is 50.
Minimum payoffs for do nothing is 0.
Maximum payoff is for alternative 2, so alternative 2 is selected based on pessimistic approach.
b.
Maximum payoffs for alternative 1 is 180.
Maximum payoffs for alternative 2 is 140.
Maximum payoffs for alternative 3 is 200.
Maximum payoffs for do nothing is 0.
Maximum payoff is for alternative 3, so alternative 3 is selected based on optimistic approach.
c.
Coeffcient of realism = 0.8
Weighted Averaege = 0.8 * Best Payoff + (1-0.8) * Worst Payoff
Weighted Average for alternative 1 = 0.8 * 180 + 0.2 * 100 = 164
Weighted Average for alternative 2 = 0.8 * 140 + 0.2 * 120 = 136
Weighted Average for alternative 3 = 0.8 * 200 + 0.2 * 50 = 170
Weighted Average for do nothing = 0.8 * 0 + 0.2 * 0 = 0
Maximum weighted average is for alternative 3, so alternative 3 is selected based on criterion of realism.
d.
Regret = Best Payoff - Payoff received.
The regret table is,
Maximum regret for alternative 1 is 100.
Maximum regret for alternative 2 is 80.
Maximum regret for alternative 3 is 130.
Maximum regret for do nothing is 200.
Minimum regret is for alternative 2, so alternative 2 is selected based on minimax regret approach.
e)
EMV for alternative 1 = 0.3 * 100 + 0.5 * 120 + 0.2 * 180 = 126
EMV for alternative 2 = 0.3 * 120 + 0.5 * 140 + 0.2 * 120 = 130
EMV for alternative 3 = 0.3 * 200 + 0.5 * 100 + 0.2 * 50 = 120
EMV for do nothing = 0.3 * 0 + 0.5 * 0 + 0.2 * 0 = 0
Maximum EMV is for alternative 2, so alternative 2 is selected based on EMV approach.
f)
Maximum EMV is for alternative 2 is 130
So, expected value without perfect information EVwoPI = 130
Expected value with perfect information EVwPI = Sum of maximum payoff for each state * probability
= 0.3 * 200 + 0.5 * 140 + 0.2 * 180 = 166
EVPI = EVwPI - EVwoPI = 166 - 130 = 36
f.
From part (d), the regret table (opportunity loss table) is,
EOL for alternative 1 = 0.3 * 100 + 0.5 * 20 + 0.2 * 0 = 40
EOL for alternative 2 = 0.3 * 80 + 0.5 * 0 + 0.2 * 60 = 36
EOL for alternative 3 = 0.3 * 0 + 0.5 * 40 + 0.2 * 130 = 46
EOL for do nothing = 0.3 * 200 + 0.5 * 140 + 0.2 * 180 = 166
Minimum EOL is for alternative 2, so alternative 2 is selected based on EOL criterion.
Alternatives A B C Alternative 1 100 20 0 Alternative 2 80 0 60 Alternative 3 0 40 130 Do nothing 200 140 180Related Questions
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