Chapter 20, Problem 13PS

The Islander Fishing Company purchases clams for $\text{\$1}\text{.50}$ per pound from fishermen and sells them to various restaurants for $\text{\$2}\text{.50}$ per pound. Any clams not sold to the restaurants by the end of the week can be sold to a local soup company for $\text{\$0}\text{.50}$ per pound. The company can purchase 500, 1,000 or 2,000 pounds. The probabilities of various levels of demand are as follows:

a. For each possible purchase level (500, 1,000, or 2,000 pounds). compute the profit (or loss) for each level of demand.

b. Determine the optimal action based on the maximax criterion.

c. Determine the optimal action based on the maximax criterion.

d. Using the expected monetary value (EMV) criterion, determine the optimal number of pounds of clams the company should purchase from the fishermen. Discuss.

e. Compute the standard deviation for each possible purchase level.

f. Compute the expected opportunity loss (EOL) for purchasing 500, 1,000, and 2,000 pounds of clams.

g. Explain the meaning of the expected value of perfect information (EVPI) in this problem.

h. Compute the coefficient of variation for purchasing 500, 1,000, and 2,000 pounds of clams. Discuss.

i. Compute the return-to-risk ratio (RTRR) for purchasing 500, 1,000, and 2,000 pounds of clams. Discuss.

j. Based on (d) and (1). would you choose to purchase 500, 1,000, or 2,000 pounds of claims? Why?

k. Compare the results of (d), (f), (h), and (i) and explain any differences.

l. Suppose that clams can be sold to restaurants for $\text{\$3}$ per pound. Repeat (a) through (i) with this selling price for clams and compare the results with those in (k).

m. What would he the effect on the results in (a) through (k) if the probability of the demand for 500, 1,000, and 2,000 clams were 0.4, 0.4, and 0.2, respectively?