Homework SourseThe following is a payfoff table giving profits for various
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 |
Solution
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 |
