1. For the question #4 in Homework #1, we developed the following decision table
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Question
1. For the question #4 in Homework #1, we developed the following decision table for Ken who is the owner of OilCo. Answer the following questions based on this problem. States of Nature Alternatives Favorable Unfavorable Sub100 290,000 -150,000 Oiler J 340,000 -190,000 Texan 90,000 -10,000 a) Which equipment should be selected based on the minimax regret criterion? The probabilities for the market have been determined to be 40% for favorable market and 60% for unfavorable market. b) Which equipment should be selected to maximize the expected profit of the operation? c) What is the expected value of perfect information in this situation? d) Which equipment would minimize the expected opportunity loss?
Explanation / Answer
Payoff matrix is,
a)
The regret table is,
Regret = Best Payoff for each state of nature - Payoff received
Maximum regret for Sub100 = 140,000
Maximum regret for Oiler = 180,000
Maximum regret for Texan = 250,000
Minimum of these three is for Sub100.
So, Sub100 should be selected based on the minimax regret criterion.
b)
Expected profit for Sub100 = 0.4 * 290,000 + 0.6 * -150,000 = 26,000
Expected profit for Oiler = 0.4 * 340,000 + 0.6 * -190,000 = 22,000
Expected profit for Texan = 0.4 * 90,000 + 0.6 * -10,000 = 30,000
Maximum expected profit is for Texan.
So, Texan should be selected to maximize the expected profit of the operation.
(c)
Expected value of perfect information, EVPI = EVwPI - EVwoPI
where EVwPI is Expected value with perfect information
and EVwoPI is Expected value without perfect information
EVwoPI is the maximum expected profit. So, EVwoPI = 30,000
EVwPI is sum of product of probabilities of each state of nature with the maximum payoff.
EVwPI = 0.4 * 340,000 + 0.6 * -10,000 = 130,000
EVPI = EVwPI - EVwoPI = 130,000 - 30,000 = 100,000
So, the expected value of perfect information in this situation is 100,000
d)
Expected opportunity loss is sum of probabilities with regrets for each state of nature
Expected opportunity loss for Sub100 = 0.4 * 50,000 + 0.6 * 140,000 = 104,000
Expected opportunity loss for Oiler = 0.4 * 0 + 0.6 * 180,000 = 108,000
Expected opportunity loss for Texan = 0.4 * 250,000 + 0.6 * 0 = 100,000
Minimum expected opportunity loss is for Texan.
So, Texan would minimize the expected opportunity loss.
Alternative States of Nature Favorable Unfavorable Sub100 290,000 -150,000 Oiler 340,000 -190,000 Texan 90,000 -10,000Related Questions
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