Question

Problem 13-14 (Algorithmic) The followng profit payoff table shows profit for a decision analysis problem vwith two decision alternatives and three states of nature: State of Nature Decision Alternative SS2 53 di 250 100 100 200 100 150 The probabilities for the states of nature are PO)-0.45. Prs)·О.25 and Prn)-03. a. What is the optimal decision strategy if perfect information was available? 51 : 53 i b. What is the expected value for the decision strategy developed in part (a)? If required, round your answer to one decimal place. e. Using the expected value approach, what is the recommended decision wethout perfect information? What is its expected value? If required. round your answer to one decimal place. d. What is the expected value of perfect information? If required. round your answer to one decimal place.

Answer 1

a. Since its a profit problem,we take the maximum payoff decision alternative for a given state of nature.

So, optimal decision strategy if perfect information was available is :

S1 :d1

S2: d1 or d2

S3: d2

b. Expected value with perfect information =P(s1) *pay off in d1+P(s2) *Pay off in d1 or d2 +P(s3)*Pay off in d2

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

=182.5

c. Using the treeplan plugin for excel,we draw the decision tree as shown below :

The recommended decision without perfect information : d1

VN 0 QR 0.45 s1 250 250 250 0.25 d1 S2 100 00 100 0167.5 0.3 53 100 00 100 167 0.45 s1 200 200 0.25 S2 d2 100 0160 100 100 0.3 53 150150

The expected value without perfect information(from the decision tree)=EVwoPI=167.5

d.Expected value of perfect information =Expected value with perfect information-Expected value without perfect information

EVPI=EVwPI-EVwoPI

=182.5-167.5=$15

Expected value of perfect information = 15