For the question #4 in Homework # 1, we developed the following decision table f

Question

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. Which equipment should be selected based on the minimax regret criterion? The probabilities for the market have been determined tobe60%for favorable market and 40% for unfavorable market. Which equipment should be selected to maximize the expected profit the operation? What is the expected value of perfect information in this situation? Which equipment would minimize the expected opportunity loss? 1

Explanation / Answer

Ans A:

Bellow are the possible returns, identifying the Best return for different States of nature. This will help identifying the regret:

Worst regret is the worst possible loss for choosing an equipment by not choosing the best choice. Regret is calculated by the Best Return - return for the Choosen Equipment. Worst return is the max value of the Regret for different states of nature.

Thus, the below worst regret table is consructed:

Clearly the worst regret is minimized for Oiler J, with worst regret of 110000 (units). ..... (Answer)

Ans B:

Expected profits for different choices are as below:

Hence Sub 100 should be choosen to maximize expected return, with expected return of 118000 (units) ........ (Ans)

Ans C: To find expected value of perfect information,we need to first identify highest possible return for each State of Nature, this is termed as EV|PI (Expected Value given Perfect Information) and calculated as:

Max return (Favourale)*Probability(Favourable) + Max return (Unfavourale)*Probability(Unfavourale)

And Expected Value of perfect informatiuon is calculated as EV|PI - max(Expected Return)

= 178000 - 118000 = 60000 (units) --------------------(ANS)

Conceptually Expected Value of perfect informatiuon is nothing but the extra revenue we could make over EMV if we knew the outcome in advance,

Ans D: Expected opportunity loss = Expected value of the Regrets = p(Favourable)*(Regret for Favourable) + p(Unfavourable)*(Regret for Unfavourable). Below table calculates that using the regret table above (Ans A).

Hence, Sub100 has minimum EOL value 60000. (Ans).

Alternative Favourable Unfavourable Sub100 310000 -170000 Oiler J 270000 -130000 Texan 80000 -20000 Best Return 310000 -20000

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