The following profit payoff table shows profit for a decision analysis problem w

ID: 2748014 • Letter: T

Question

The following profit payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature:

The probabilities for the states of nature are P(s1) = 0.45, P(s2) = 0.25 and P(s3) = 0.3.

What is the optimal decision strategy if perfect information were available?

answer:

What is the expected value for the decision strategy developed in part (a)???????????? If required, round your answer to one decimal place.

Using the expected value approach, what is the recommended decision without perfect information?

Answer:

d1

What is its expected value????????????? If required, round your answer to one decimal place.

What is the expected value of perfect information?????????????? If required, round your answer to one decimal place.

State of Nature Decision Alternative S1 S2 S3 d1 250 100 100 d2 200 100 150

a) Optimal decision strategy if perfect information were available is already answered by you:

b) Expected value of decision strategy developed in part a:

0.45*(S1d1) + 0.25*(S2d1) + 0.3*(S3d2).......(S2d1 = S2d2)

= 0.45*250 + 0.25*100 + 0.3*150 = 182.5

c) Without perfect info:

Lets compute for both d1 & d2

For d1: 0.45*250 + 0.25*100 + 0.3*100 = 167.5

For d2: 0.45*200 + 0.25*100 + 0.3*150 = 160

Hence d1

d) Expected value as calculated above: 167.5

e) EVPI = EV|PI - EMV = 182.5 - 167.5 = 15

S1 : d1 S2 : d1 or d2 S3 : d2

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