The following example will illustrate the solution procedure for a decision analysis problem.
T. Bone Puckett, a corporate raider, has acquired a textile company and is contemplating the future of one of its major plants, located in South Carolina. Three alternative decisions are being considered : (1) expand the plant and produce lightweight, durable materials for possible sales to the military, a market with little foreign competition; (2) maintain the status quo at the plant, continuing production of textile goods that are subject to heavy foreign competition; or (3) sell the plant now. If one of the first two alternatives is chosen , the plant will still be sold at the end of a year. The amount of profit that could be earned by selling the plant in a year depends on foreign market conditions, including the status of a trade embargo bill in Congress. The following payoff table describes this decision situation:
State of Nature  

Decision  Good Foreign Competitive Conditions  Poor Foreign Competitive Conditions 
Expand  $ 800,000  $ 500,000 
Maintain status quo  1,300,000  150,000 
Sell now  320,000  320,000 
Determine the best decision by using the following decision criteria:
Maximax
Maximin
Minimax regret
Hurwicz ( a = .3)
Equal likelihood
Assume that it is now possible to estimate a probability of .70 that good foreign competitive conditions will exist and a probability of .30 that poor conditions will exist. Determine the best decision by using expected value and expected opportunity loss.
Compute the expected value of perfect information.
Develop a decision tree, with expected values at the probability nodes.
T. Bone Puckett has hired a consulting firm to provide a report on future political and market situations. The report will be positive (P) or negative (N), indicating either a good (g) or poor (p) future foreign competitive situation. The conditional probability of each report outcome, given each state of nature, is
P (Pg) = .70
P (Ng) = .30
P (Pp) = .20
P (Np) = .80
Determine the posterior probabilities by using Bayes's rule.
Perform a decision tree analysis by using the posterior probability obtained in (e).
Step 1.  (part A): Determine Decisions Without Probabilities
Decision: Maintain status quo.
Decision: Expand.
Decision: Expand.
Decision: Expand.
Decision: Expand.  
Step 2.  (part B): Determine Decisions with EV and EOL
Decision: Maintain status quo.
Decision: Maintain status quo.  
Step 3.  (part C): Compute EVPI
 
Step 4.  (part D): Develop a Decision Tree  
Step 5.  (part E): Determine Posterior Probabilities
 
 
Step 6.  (part F): Perform Decision Tree Analysis with Posterior Probabilities
