Question

non excel solution, please!

6. Suppose that a decision maker faced with four decision alternatives and four states of natuure develops the following profit payoff table. State of Nature Decision Alternative S3 10 14 d1 10 d2 10 10 d3 13 10 8 d4 If the decision maker knows nothing about the probabilities of the four states of nature, what is the recommended decision using the optimistic, conservative, and minimax regret approaches? ANSWERS: 1. D2 2. a) Al b) A2 c) A2 3. Alternative 1 4. A3 Large complex 5. Expected Value - Buy 40, Maximax - Buy 80, Maximin- Buy 20, Minimax - Buy 60. 6. optimistic - D1, conservative - D3, minimax regret - D3

Answer 1

1. optimistic in case of profit we will do maxmin

	S1	S2	S3	S4	max
D1	14	9	10	5	14
D2	11	10	8	7	11
D3	9	10	10	11	11
D4	8	10	11	13	13

as from all the maximums of the decision the minimum is the D2.

2. conservative in case of profit we will do minimax

	S1	S2	S3	S4	min
D1	14	9	10	5	5
D2	11	10	8	7	7
D3	9	10	10	11	9
D4	8	10	11	13	8

as from all the minimum of the decisions, the maximum is the D3.

3. minimax regret approach

in this we will select the max of the column then subtract rest from the max and form a new matrix.

	S1	S2	S3	S4	Max
D1	0	1	1	8	8
D2	3	0	3	6	6
D3	5	0	1	2	5
D4	6	0	0	0	6

now we will find the maximum of all the rows and choose the minimum of them so in this case the decision will be D3 as 5 is minimum.