The following profit payoff table was presented in problem 1. Suppose that they
ID: 3156178 • Letter: T
Question
The following profit payoff table was presented in problem 1. Suppose that they decision maker obtained probability assessments P(s_1)= .65, P(s_2)=.15, P(s_3)=.20.
A. What is the optimal decision strategy if perfect information were available?
B. What is the expected value for the decision strategy developed in part A?
C. Using the expected value approach , what is the recommended decision without perfect information? what is its expected value?
D. What is the expected value for perfect information?
Decision Alternative S_1 S_2 S_3 D_1 250 100 25 D_2 100 100 75Explanation / Answer
In the given problem there are 3 states of nature, S1, S2, S3 and two decision alternatives D1 and D2
a) The perfect information means knowing the best possible option in each state of nature S1, S2, and S3. In the below table those values are underlined. I.e. going with D1 if we know that the state of nature is S1, going with either of D1 or D2 if state of nature is S2 and going ahead with the decision D2 if state of nature is S3.
b) The payoff of perfect information called as EV with PI (Expected value with perfect information)
EV with PI = 192.5
c) The EMV approach is the basically choosing the best possible option between D1 and D2 by looking at the weighted average of D1 and D2 (considering the probabilities as weights)
=250 * 0.65 + 100 * 0.15 + 25 * 0.20
=182.5
= 100 * 0.65 + 100 * 0.15 + 75 *0.20
= 95
Therefor the EMV (Expected monetary value)= Max [E(D1),E(D2)] = 182.5
d) EVPI is the expected value for perfect information that a business concern should be willing to spend. This is calculated by subtracting the expected monetary payoff whithout perfect information i .e EMV from the EV with PI
So, EVPI = EV with PI - EMV
EVPI = 192.5 - 182.5 = 10
ie the business should not spend more than 10 units to get the perfect information
Decision Alternative S_1 S_2 S_3 D_1 250 100 25 D_2 100 100 75Related Questions
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