Question

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Q19) A manager has developed a payoff table that indicates the profits associated with a set of alternatives under two possible states of nature.(20 Marks)

Alt S1 S2

1. 10 2

2 -2 8

3 8. 5

1. a) If the manager uses maximax as the decision criterion, which of the alternatives should shechoose?

2. b) If the manager uses maximin as the decision criterion, which of the alternatives should she choose?

3. c) If the manager uses minimax regret as the decision criterion, which of the alternatives would she choose?

4. d) Use Hurwicz criteria to select the best decision. Assume alpha=0.3

5. e) Use the expected value criterion to select the best alternative. Assume that the probability of S2 isequal to 0.4.

Answer 1

a)

Alt	S1	S2	Max
1	10	2	10
2	-2	8	8
3	8	5	8

Best Alternative is 1.

b)

Alt	S1	S2	Min
1	10	2	2
2	-2	8	-2
3	8	5	5

Best Alternative is 3.

c)

Alt	S1	S2
1	10	2
2	-2	8
3	8	5
	Regret Table
Alt	S1	S2	Max
1	0	2	2
2	12	8	12
3	2	5	5

Best Alternative is 1.

d)

Alt	S1	S2	Payoff
1	10	2	4.4
2	-2	8	1
3	8	5	5.9

Best Alternative is 3.

e)

Alt	S1	S2	Expected Payoff
1	10	2	6.8
2	-2	8	2
3	8	5	6.8
Probability	0.6	0.4

Since 1 & 3 has the equal expected payoff, hence either of them cam be selected.