Problem
JR Davidson recently started a practice in Landscape Design and is considering the purchase of an automated drafting system. JR can purchase a system with three possible drafting capacities. The payoffs for having any of these systems depend on the demand for drafting services over the next few years. The costs for each system are shown as follows along with JR's assessment of the probabilities that demand will match the capacity of each one:
Total Cost Probability Small system $10,0000.4 Medium system $14,0000.3 Large system $20,0000.3 Working at capacity, each system would generate net cash flow at a yearly rate of 50 percent of its total cost. If a system is chosen that is smaller than demand, it would work at capacity. If a system is chosen that is larger than demand, revenue from the system would be limited by demand. For convenience, JR has initially decided to count cash flow for three years, without discounting. For example, if JR chooses the Medium system and demand is Small, then the profit is calculated as follows:
Profit=30.5×10,000-14,000=$1,000
I. What is the best decision under the maximax criterion?
II. What is the best decision under the maximin criterion?
III. What is the best decision under the minimax regret criterion?
IV. What is the best decision under the expected payoff criterion?1
Reviewing the analysis, JR decides that the assumption of a 3-year horizon is too restrictive. Instead, it makes more sense to treat the horizon as uncertain, with the following probability distribution:
Two years of cash flow has 0.4 probability.
Three years of cash flow has 0.4 probability.
Four years of cash flow has 0.2 probability.Now, what is the best decision under the expected payoff criterion?"