The following is a payfoff table giving profits for various situations. States o

Question

The following is a payfoff table giving profits for various situations.

                                                                         States of nature                                                                                              Demands

The probabilities for states of nature Low, Medium, and High are 0.25,0.55, and 0.2, respectively. If a perfect forecast of the futue were available, what is the expected valuse of perfect information (EVPI)?

alternatives low medium high alternative 1 80 120 140 alternative 2 90 90 90 alternative 3 50 70 150

Explanation / Answer

EVPI = A - B

A = expected value with perfect information

B = expected value without perfect information

A = 0.25*90 + 0.55*120 + 0.2*150 = 118.5

B = max value in the last column(max value column) = 114

EVPI = 118.5 - 114 = 4.5

low medium high max value alternative1 80 120 140 0.25*80+0.55*120+0.2*140=114 alternative 2 90 90 90 0.25*90+0.55*90+0.2*90=90 alternative3 50 70 150 0.25*50+0.55*70+0.2*150= 81 max value 90 120 150

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