Problem 3. Consider the following decision table, which Joe Blackburn has develo

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Question

Problem 3.

Consider the following decision table, which Joe Blackburn has developed for Vanderbilt Enterprises

(2) What is the maximax decision?

(3) What is the Laplace decision?

(4) What is the minimax regret decision?

(5) If the probability of the three states of natures are: P(Low) = 0.4, P(Medium) = 0.2, P(High) = 0.4, then which alternative has the highest EMV?

(6) With the probabilities given in (5), calculate the EVPI.

States of Nature High S60 $70 $70 $70 $80 Altematives Low $40 385 $60 S65 S70 Medium $100 S60 $70 S75 $65

1) Maximin Decision:

Maximin = 65,

Decision: D and E

Maximax = 100

Decision: A

3) Laplace Criteria:

For A: 1/3 * (40+100+60) = 66.667

For B: 1/3 * (85+60+70) = 71.667

For C: 1/3 * (60+70+70) = 66.667

For D: 1/3 * (65+75+70) = 70

For E: 1/3 * (70+65+80) = 71.6667

Decision: B and E

Regret:

Minimax Regret = 10

Decision : C and D

5) EMV:

On the basis of expected monetary value, the best choice is the B as this maximises his EMV.

6) EVwPI = 0.4*85 + 0.2*100 + 0.4*80 = 86

EVPI = EMwV - EVwoPI = 86 - 74 = 12

Maximin Criteria Low Medium High Minimum A 40 100 60 40 B 85 60 70 60 C 60 70 70 60 D 65 75 70 65 E 70 65 80 65

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