Chapter 5S: Decision Theory
A small building contractor has recently experienced two successive years in which work
opportunities exceeded the firm's capacity. The contractor must now make a decision on
capacity for next year. Estimated profits under each of the two possible states of nature are
as shown in the table below. Which alternative should be selected if the decision criterion is
d. Minimax regret?
. Suppose after a certain amount of discussion, the contractor is able to
subjectively assess the probabilities of low and high demand:
(low) 5 .3 and
(high) 5 .7.
a. Determine the expected profit of each alternative. Which alternative is best? Why?
b. Analyze the problem using a decision tree. Show the expected profit of each alternative
on the tree.
c. Compute the expected value of perfect information. How could the contractor use this
. Construct a graph that will enable you to perform sensitivity
analysis on the problem. Over what range of
(high) would the alternative of doing nothing
be best? Expand? Subcontract?
A firm that plans to expand its product line must decide whether to build a small or a large
facility to produce the new products. If it builds a small facility and demand is low, the net
present value after deducting for building costs will be $400,000. If demand is high, the firm
can either maintain the small facility or expand it. Expansion would have a net present value
of $450,000, and maintaining the small facility would have a net present value of $50,000.
If a large facility is built and demand is high, the estimated net present value is $800,000. If
demand turns out to be low, the net present value will be −$10,000.
The probability that demand will be high is estimated to be .60, and the probability of low
demand is estimated to be .40.
a. Analyze using a tree diagram.
c. Determine the range over which each alternative would be best in terms of the value of
Determine the course of action that has the highest expected payoff for this decision tree.
The lease of Theme Park, Inc., is about to expire. Management must decide whether to
renew the lease for another 10 years or to relocate near the site of a proposed motel. The
town planning board is currently debating the merits of granting approval to the motel. A
consultant has estimated the net present value of Theme Park's two alternatives under each
state of nature as shown on the following page.
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