Introduction to Management Science 12th Edition by Bernard Taylor

Exercise 62

In Problem 1, the management of the Oakland Bombers is considering hiring superscout Jerry McGuire to evaluate the team's chances for the coming season. McGuire will evaluate the team, assuming that it will sign one of the four free agents. The team's management has determined the probability that the team will have a losing record with any of the free agents to be.21 by averaging the probabilities of losing for the four free agents in Problem 2. The probability that the team will have a competitive season but not make the playoffs is developed similarly, and it is.35. The probability that the team will make the playoffs is.44. The probability that McGuire will correctly predict that the team will have a losing season is.75, whereas the probability that he will predict a competitive season, given that it has a losing season, is.15, and the probability that he will incorrectly predict a playoff season, given that the team has a losing season, is.10. The probability that he will successfully predict a competitive season is.80, whereas the probability that he will incorrectly predict a losing season, given that the team is competitive, is.10, and the probability that he will incorrectly predict a playoff season, given the team has a competitive season, is.10. The probability that he will correctly predict a playoff season is.85, whereas the probability that he will incorrectly predict a losing season, given that the team makes the playoffs, is.05, and the probability that he will predict a competitive season, given the team makes the playoffs, is.10. Using decision tree analysis and posterior probabilities, determine the decision strategy the team should follow, the expected value of the strategy, and the maximum amount the team should pay for Jerry McGuire's predictions.
Problem 1
The Oakland Bombers professional basketball team just missed making the playoffs last season and believes it needs to sign only one very good free agent to make the playoffs next season. The team is considering four players: Barry Byrd, Rayneal O'Neil, Marvin Johnson, and Michael Gordan. Each player differs according to position, ability, and attractiveness to fans. The payoffs (in $1,000,000s) to the team for each player, based on the contract, profits from attendance, and team product sales for several different season outcomes, are provided in the following table:
Determine the best decision, using the following decision criteria.
a. Maximax
b. Maximin
c. Hurwicz ( =.60)
d. Equal likelihood
Problem 2
In Problem, the Bombers' management has determined the following probabilities of the occurrence of each future season outcome for each player:
Compute the expected value for each player and indicate which player the team should try to sign.
Problem
The Oakland Bombers professional basketball team just missed making the playoffs last season and believes it needs to sign only one very good free agent to make the playoffs next season. The team is considering four players: Barry Byrd, Rayneal O'Neil, Marvin Johnson, and Michael Gordan. Each player differs according to position, ability, and attractiveness to fans. The payoffs (in $1,000,000s) to the team for each player, based on the contract, profits from attendance, and team product sales for several different season outcomes, are provided in the following table:
Determine the best decision, using the following decision criteria.
a. Maximax
b. Maximin
c. Hurwicz ( =.60)
d. Equal likelihood