Exercises Decision Making MisSue Consider this set of data: Low (15%) High (35%)

Question

Exercises Decision Making MisSue Consider this set of data: Low (15%) High (35%) 250k 350k 400k 150k Med (50%) 55k 100k 300k 25k Solution 5k Make product A Make product B Make product C Make product D 50k -200k 10k Make decision under certainty Use certainty, MaxiMax, MiniMax 1. Make Decisions under Uncertainty Use Laplace and Least Regret 2. Make Decisions under Risk Use the decision EVM (weighted average) and opportunity loss 3. 4. Determine the value for perfect information Calculate the value of perfect information of this problem

Explanation / Answer

1) Make decision under certainty

Maximax - in this criterion, we find the Maximum payoff of each decision alternative and then select the alternative, whose Maximum payoff is the Maximum of all.

Max of payoff of product A = MAX(250k, 55k, 5k) = 250k

Max of payoff of product B = MAX(350k, 100k, -50k) = 350k

Max of payoff of product C = MAX(400k, 300k, -200k) = 400k

Max of payoff of product D = MAX(150k, 25k, 10k) = 150k

Maximum out of the above is 400k. Therefore, best decision is Make Product C

___________

Maximin - in this criterion, we find the Minimum payoff of each decision alternative and then select the alternative, whose Minimum payoff is the Maximum of all.

Min of payoff of product A = MIN(250k, 55k, 5k) = 5k

Min of payoff of product B = MIN(350k, 100k, -50k) = -50k

Min of payoff of product C = MIN(400k, 300k, -200k) = -200k

Min of payoff of product D = MIN(150k, 25k, 10k) = 10k

Maximum out of the above is 10k. Therefore, best decision is Make Product D

2) Make decision under Uncertainty

Laplace (Equal likelihood) - find the average payoff (under the three demand states) of each decision alternative and then select the decision alternative whose average payoff is the Maximum of all.

Average of payoff of product A = AVERAGE(250k, 55k, 5k) = 103.3k

Average of payoff of product B = AVERAGE(350k, 100k, -50k) = 133.3k

Average of payoff of product C = AVERAGE(400k, 300k, -200k) = 166.7k

Average of payoff of product D = AVERAGE(150k, 25k, 10k) = 61.7k

Maximum out of the above is 166.7k. Therefore, best decision is Make Product C

Least regret - in this criterion, we find the Maximum Regret of each decision alternative and then select the alternative, whose Maximum regret is the Minimum of all. Regret for each decision under each state of nature is calculated in a separate table. It is calculated by subtracting the maximum payoff under each state of nature out of the three decision alternatives - payoff for particular state of nature for the particular decision alternative. For example, regret for decision Make Product C for High Demand = MAX(250,350,400,150) - 400 = 400-400 = 0

Regret table is as follows (values of $ 1000)

Mnimum value out of the above is 200k. Therefore best decision is Make Product B

3) Make decisions under Risk

EMV of Make Product A = .35*250+.5*55+.15*5 = 115.75k

EMV of Make Product B = .35*350+.5*100+.15*(-50) = 165k

EMV of Make Product C = .35*400+.5*300+.15*(-200) = 260k

EMV of Make Product D = .35*150+.5*25+.15*10 = 66.5k

Maximum out of the above is 260k, therefore best decision is Make Product C

4) Value of Perfect Information

Expected Value with Perfect Information (EVwPI) = Max payoff for High demand * Probability of high demand + Max payoff for Med demand * Probability of Med demand + Max payoff for Low demand * Probability of Low demand

= 400*.35 + 300*.5 + 10*.15

= 291.5k

Expected Value of Perfect Information = EVwPI - EMVmax = 291.5 - 260 = 31.5k

High Med Low Max Make Product A 150 245 5 245 Make Product B 50 200 60 200 Make Product C 0 0 210 210 Make Product D 250 275 0 275

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