Strong | Weak | |
Executive | 960 | -490 |
Discount | 670 | 320 |
The two states of nature are strong and weak demand for air
service.
They will choose to add discount seats to their current service.
The worst case for the executive service is a loss of 490.
The worst case for the discount service is a profit of 320.
Discount has the best worst case, so the conservative approach recommends this
decision.
Deciding on the executive service and encountering the state of nature of a weak demand results in a loss of 490, when there was potential for a profit of 320 for that state of nature. The regret here is 320 - (-490) = 810.
The regret for a discount service under strong demand is only 960-670 = 310.
The greatest regret occurs with the
combination of the executive decision and the weak state of
nature.
EV(executive) = (960)(.7) + (-490)(.3) = 525
EV(discount) = (670)(.7) + (320)(.3) = 565
b) (10 points) Which decision alternative has the highest expected value?The discount service has the highest expected value.
c) (20 points) Consider the estimated quarterly profits for executive class service with weak demand. What would the estimated profits need to be in order to change your answer to part (b) of this question? (I.e. calculate sensitivity to changes in this value.)
EV(executive) = 565
(960)(.7) + x (.3) = 565
.3x = -107
x = -356.666...
The estimated profit for executive service with weak demand would have to be no more of a loss than 356 and 2/3 thousand dollars in order to change the answer to part (b).
Bonus (5 points) Compute the expected value of perfect information (EVPI) for the Alpha Airlines decision.
EVwoPI = 565 (from problem 4.)
EVwPI = (960)(.7) + (320)(.3) = 767
EVPI = | EVwPI - EVwoPI | = 767 - 565 = 203