In: Statistics and Probability
Embassy Publishing Company received a six-chapter manuscript for a new college text- book. The editor of the college division is familiar with the manuscript and estimated a 0.65 probability that the textbook will be successful. If successful, a profit of $600,000 will be realized. If the company decides to publish the textbook and it is unsuccessful, a loss of $200,000 will occur. Before making the decision to accept or reject the manuscript, the editor is consider- ing sending the manuscript out for review. The review cost $5000. A review process provides either a favorable (F) or unfavorable (U) evaluation of the manuscript. Past experience with the review process suggests that probabilities P(F) =0.7 and P(U)= 0.3 apply. Let s1 the textbook is successful, and s2 the textbook is unsuccessful. The editor’s initial probabilities of s1 and s2 will be revised based on whether the review is favorable or unfavorable. The revised probabilities are as follows: P(s1 |F) =0.75 P(s1 |U)= 0.417 P(s2 |F)= 0.25 P(s2 |U)= 0.583
a. Construct a decision tree assuming that the company will first make the decision of whether to send the manuscript out for review and then make the decision to accept or reject the manuscript.
b. Analyze the decision tree to determine the optimal decision strategy for the publish- ing company.
c. What is the expected value of perfect information? What does this EVPI suggest for the company?
A decision tree is a graphical representation of the decision problem that shows the sequential nature of the decision making process. The decision tree is as follows:
(b) The decision tree with the pay-offs is as follows (Review cost is 5000, so I have shown a deduction of 5 beside the "Review" option:
Looking at the decision tree, the optimal strategy would be NOT to go for the review as the Expected Monetary value (EMV) is better in this case (320,000) compared to the case of going for review (315.08)
(c) EVPI = EPC (Expected pay-off under certainty) - EMV
Here, EPC = pay-off if we know for sure the success and failure of the manuscript, i.e, if we know for sure if the manuscript will be a success or failure = 600*0.65 - 200*0.35 = 320
Hence EVPI = 320-320 = 0