Assignment: Decision Analysis
1. The Lake Placid Town Council decided to build a new community center to be used for conventions, concerts, and other public events, but considerable controversy surrounds the appropriate size. Many influential citizens want a large center that would be a showcase for the area. But the mayor feels that if demand does not support such a center, the community will lose a large amount of money. To provide structure for the decision process, the council narrowed the building alternatives to three sizes: small, medium, and large. Everybody agreed that the critical factor in choosing the best size is the number of people who will want to use the new facility. A regional planning consultant provided demand estimates under three scenarios: worst case, base case, and best case. The worst-case scenario corresponds to a situation in which tourism drops substantially; the base-case scenario corresponds to a situation in which Lake Placid continues to attract visitors at current levels; and the best-case scenario corresponds to a substantial increase in tourism. The consultant has provided probability assessments of 0.20, 0.55, and 0.25 for the worst-case, base-case, and best-case scenarios, respectively.
The town council suggested using net cash flow over a 5-year planning horizon as the criterion for deciding on the best size. The following projections of net cash flow (in thousands of dollars) for a 5- year planning horizon have been developed. All costs, including the consultant's fee, have been included. [5 points]
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Demand Scenario
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Center Size
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Worst Case
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Base Case
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Best Case
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Small
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400
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550
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700
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Medium
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-200
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600
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800
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Large
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-400
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650
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1000
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a. If nothing is known about the probabilities of the three scenarios, what is the recommended decision using the optimistic, conservative, and minimax regret approaches? Considering probability assessments provided by the consultant, what decision should Lake Placid make using the expected value approach?
b. Construct risk profiles for the medium and large alternatives. Given the mayor's concern over the possibility of losing money and the result of part (a), which alternative would you recommend?
c. Compute the expected value of perfect information. Do you think it would be worth trying to obtain additional information concerning which scenario is likely to occur?
d. Suppose the probability of the worst-case scenario increases to 0.3, the probability of the base-case scenario decreases to 0.45, and the probability of the best-case scenario remains at 0.25. What effect, if any, would these changes have on the decision recommendation?
e. The consultant has suggested that an expenditure of $120,000 on a promotional campaign over the planning horizon will effectively reduce the probability of the worst-case scenario to zero. If the campaign can be expected to also increase the probability of the best-case scenario to 0.4, is it a good investment?
2. The Gorman Manufacturing Company must decide whether to manufacture a component part at its Milan, Michigan, plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit (in thousands of dollars).
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State of Nature
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Low Demand
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Medium Demand
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High Demand
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Decision Alternative
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s1
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s2
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s3
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Manufacture, d1
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-30
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35
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100
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Purchase, d2
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10
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40
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70
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The state-of-nature probabilities are P(s1) = 0.30, P(s2) = 0.40, and P(s3) = 0.30.
a. Use a decision tree to recommend a decision.
b. Use EVPI to determine whether Gorman should attempt to obtain a better estimate of demand.
c. A test market study of the potential demand for the product is expected to report either a favorable (F) or unfavorable (U) condition. The relevant conditional probabilities are as follows:
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P(F | s1) = 0.15
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P(U | s1) = 0.85
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P(F | s2) = 0.35
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P(U | s2) = 0.65
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P(F | s3) = 0.70
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P(U | s3) = 0.30
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What is the probability that the market research report will be favorable?
d. What is Gorman's optimal decision strategy?
e. What is the expected value of the market research information?
f. What is the efficiency of the information?