Introduction to Management Science 12th Edition by Bernard Taylor

Exercise 45

In Problem, the Blue Sox general manager has asked a superscout to assign a probability to each of the three states of nature for the pitchers during the next 10 years. The scout estimates there is a.10 probability that these pitchers at this stage of their careers will have no injuries, a.60 probability that they will have a career with the normal number of injuries, and a.30 probability that they will have excessive injuries.
a. Using expected value, determine the best pitcher to sign.
b. Given the following 10-year contract price for each pitcher (in $ millions), which would you recommend signing
c. Suppose that the general manager asked the superscout to determine the probabilities of each state of nature for each individual pitcher, and the results were as follows:
Determine the expected number of wins for each pitcher, and combined with the contract price in part b, indicate which pitcher you would recommend signing.
Problem
The Blue Sox American League baseball team is going to enter the free-agent market over the winter to sign a new starting pitcher. They are considering five prospects who will enter the free-agent market. All five pitchers are in their mid-20s, have been in the major leagues for approximately 5 years, and have been relatively successful. The team's general manager has compiled a lot of information about the pitchers from scouting reports and their playing histories since high school. He has developed a chart projecting how many wins each pitcher will likely have during the next 10 years, given three possible future states of nature: the pitchers will be relatively injury free, they will have a normal career with injuries, or they will have excessive injuries, as shown in the following payoff table:
Determine the best pitcher to sign, using the following decision criteria:
a. Maximax
b. Maximin
c. Equal likelihood
d. Hurwicz ( =.35)