Question

The table shows both the prospective profits and losses for a company (in thousands of dollars), depending on what decision is made and what state of nature occurs. Use the information to determine what the company should do. State the decision number and its value. Do all calculations within the spaces provided.

           

	States of Nature
	Pr = 0.30	Pr = 0.40	Pr = 0.30
Decision	s1	s2	s3
d1	30	80	-30
d2	100	30	-40
d3	-80	-10	120
d4	20	20	20

1. if a Maximin strategy is used.
2. if a Maximax strategy is used.
3. if Minimax Regret is the strategy.
4. if Equal Likelihood is the strategy.
5. What is the EVPI?

	States of Nature
	Pr = 0.30	Pr = 0.40	Pr = 0.30
Decision	s1	s2	s3
d1
d2
d3
d4

Answer 1

a. Maximin:

In maximin we choose the worst (lowest) for each decision and then take the best (maximum) from those lowest values.

Decision	S1	S2	S3	Worst
D1	30	80	-30	-30
D2	100	30	-40	-40
D3	-80	-10	120	-80
D4	20	20	20	20

The best among the worsts is -30 (for D1)

Hence, D1 is the decision.

b. Maximax:

In Maximax we choose the best (max) for each decision and then take the best (max) from those max values.

Decision	S1	S2	S3	Best
D1	30	80	-30	80
D2	100	30	-40	100
D3	-80	-10	120	120
D4	20	20	20	20

The best among these bests is 120 (for D3)

Hence, D3 is the decision.

c. Minimax Regret:

First we will find the regret table. For the regret table, we will take the Best payoff for a State and the regret for that state each decision is the best payoff – the payoff of that cell.

Then we take the best for each decision and the worst among those best to make a decision.

The Regret table is:

Decision	S1	S2	S3	Best
D1	70	0	150	150
D2	0	50	160	160
D3	180	90	0	180
D4	80	60	100	100

The worst is 100 (for D4)

Hence, D4 is the decision

d. Equal Likelihood:

In equal likelihood we will take the average of payoff for each decision. The best among those averages will then be chosen.

Decision	S1	S2	S3	Average
D1	30	80	-30	26.67
D2	100	30	-40	30
D3	-80	-10	120	10
D4	20	20	20	20

Best among the average is 30 (for D2)

Hence, D2 is chosen.

e. EVPI:

We know that EVPI = EVwPI – EVwoPI

EVwoPI = best EMV

Finding EMV:

Decision	S1	S2	S3	EMV
Probability	0.3	0.4	0.3
D1	30	80	-30	32
D2	100	30	-40	30
D3	-80	-10	120	8
D4	20	20	20	20

Best EMV = 32

For EVwPI, we will select the best for each state, and then find the EMV for that best state value.

For S1, best payoff = 100

For S2, best payoff = 80

For S3, best payoff = 120

Hence, EVwPI = 100*0.3 + 80*0.4 + 120*0.3 = 98

Hence, EVPI = EVwPI – EVwoPI = 98 – 32 = 66

Answer is: 66

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