a. Construct a decision tree for this problem.
b. Suppose that the decision maker obtains the probabilities P(s1) = .65, P(s2) = .15, and P(s3) = .20. Use the expected value approach to determine the optimal decision.
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21.2 A decision maker faced with four decision alternatives and four states of nature develops the following profit payoff table....The decision maker obtains information that enables the following probabilities assessments: P(s1) = .5, P(s2) = .2, P(s3) = .2, and P(s1) = .1.
a. Use the expected value approach to determine the optimal decision.
b. Now assume that the entries in the payoff table are costs. Use the expected value approach to determine the optimal decision.
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21.3 Hudson Corporation is considering three options for managing its data processing operation:continue with its own staff, hire an outside vendor to do the managing (referred to as outsourcing), or use a combination of its own staff and an outside vendor. The cost of the operation depends on future demand. The annual cost of each option (in thousands of dollars) depends on demand as follows....
a. If the demand probabilities are .2, .5, and .3, which decision alternative will minimize the expected cost of the data processing operation? What is the expected annual cost associated with your recommendation?
b. What is the expected value of perfect information?
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21.4 Myrtle Air Express decided to offer direct service from Cleveland to Myrtle Beach. Management must decide between a full price service using the company’s new fleet of jet aircraft and a discount service using smaller capacity commuter planes. It is clear that the bestchoice depends on the market reaction to the service Myrtle Air offers. Management developed estimates of the contribution to profit for each type of service based upon two possible levels of demand for service to Myrtle Beach: strong and weak. The following table shows the estimated quarterly profits (in thousands of dollars)....
a. What is the decision to be made, what is the chance event, and what is the consequence for this problem? How many decision alternatives are there? How many outcomes are there for the chance event?
b. Suppose that management of Myrtle Air Express believes that the probability of strong demand is .7 and the probability of weak demand is .3. Use the expected value approach to determine an optimal decision.
c. Suppose that the probability of strong demand is .8 and the probability of weak demand is .2. What is the optimal decision using the expected value approach?
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21.5 The distance from Potsdam to larger markets and limited air service have hindered the town in attracting new industry. Air Express, a major overnight delivery service, is considering establishing a regional distribution center in Potsdam. But Air Express will not establish the center unless the length of the runway at the local airport is increased. Anothercandidate for new development is Diagnostic Research, Inc. (DRI), a leading producer of medical testing equipment. DRI is considering building a new manufacturing plant. Increasing the length of the runway is not a requirement for DRI, but the planning commission feels that doing so will help convince DRI to locate their new plant in Potsdam Assuming that the town lengthens the runway, the Potsdam planning commission believes that the probabilities shown in the following table are applicable....For instance, the probability that Air Express will establish a distribution center and DRI will build a plant is .30.The estimated annual revenue to the town, after deducting the cost of lengthening the runway, is as follows:...If the runway expansion project is not conducted, the planning commission assesses the probability DRI will locate their new plant in Potsdam at .6; in this case, the estimated annual revenue to the town will be $450,000. If the runway expansion project is not conducted and DRI does not locate in Potsdam, the annual revenue will be $0 since no cost will have been incurred and no revenues will be forthcoming.
a. What is the decision to be made, what is the chance event, and what is the consequence?
b. Compute the expected annual revenue associated with the decision alternative to lengthen the runway.
c. Compute the expected annual revenue associated with the decision alternative to not lengthen the runway.
d. Should the town elect to lengthen the runway? Explain.
e. Suppose that the probabilities associated with lengthening the runway were as follows:...What effect, if any, would this change in the probabilities have on the recommended decision?
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21.6 Seneca Hill Winery recently purchased land for the purpose of establishing a new vineyard. Management is considering two varieties of white grapes for the new vineyard: Chardonnay and Riesling. The Chardonnay grapes would be used to produce a dry Chardonnay wine, and the Riesling grapes would be used to produce a semi-dry Riesling wine. It takes approximately four years from the time of planting before new grapes can be harvested. This length of time creates a great deal of uncertainty concerning future demand and makes the decision concerning the type of grapes to plant difficult. Three possibilities are being considered: Chardonnay grapes only; Riesling grapes only; and both Chardonnay and Riesling grapes. Seneca management decided that for planning purposes it would be adequate to consider only two demand possibilities for each type of wine: strong or weak. With two possibilities for each type of wine it was necessary to assess four probabilities. With the help of some forecasts in industry publications management made the following probability assessments....Revenue projections show an annual contribution to profit of $20,000 if Seneca Hill plants only Chardonnay grapes and demand is weak for Chardonnay wine, and $70,000 if they plant only Chardonnay grapes and demand is strong for Chardonnay wine. If they plant only Riesling grapes, the annual profit projection is $25,000 if demand is weak for Riesling grapes and $45,000 if demand is strong for Riesling grapes. If Seneca plants both types of grapes, the annual profit projections are shown in the following table....
a. What is the decision to be made, what is the chance event, and what is the consequence? Identify the alternatives for the decisions and the possible outcomes for the chance events.
b. Develop a decision tree.
c. Use the expected value approach to recommend which alternative Seneca Hill Winery should follow in order to maximize expected annual profit.
d. Suppose management is concerned about the probability assessments when demand for Chardonnay wine is strong. Some believe it is likely for Riesling demand to also be strong in this case. Suppose the probability of strong demand for Chardonnayand weak demand for Riesling is .05 and that the probability of strong demand for Chardonnay and strong demand for Riesling is .40. How does this change the recommended decision? Assume that the probabilities when Chardonnay demand is weakare still .05 and .50.
e. Other members of the management team expect the Chardonnay market to become saturated at some point in the future, causing a fall in prices. Suppose that the annual profit projections fall to $50,000 when demand for Chardonnay is strong and only Chardonnay grapes are planted. Using the original probability assessments, determine how this change would affect the optimal decision.
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21.7 The Lake Placid Town Council has 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 significantly; the base-case scenario corresponds to a situation in which Lake Placid continues to attract visitors at currentlevels; and the best-case scenario corresponds to a significant increase in tourism. The consultant has provided probability assessments of .10, .60, and .30 for the worst-case, basecase, and best-case scenarios, respectively.The town council suggested using net cash flow over a five-year planning horizon as the criterion for deciding on the best size. Aconsultant developed the following projections of net cash flow (in thousands of dollars) for a five-year planning horizon. All costs, including the consultant’s fee, are included....
a. What decision should Lake Placid make using the expected value approach?
b. 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?
c. Suppose the probability of the worst-case scenario increases to .2, the probability of the base-case scenario decreases to .5, and the probability of the best-case scenario remains at .3. What effect, if any, would these changes have on the decision recommendation?
d. The consultant suggested that an expenditure of $150,000 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 .4, is it a good investment?
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21.8 Consider a variation of the PDC decision tree shown in Figure 19.5. As before, the company must first decide whether to undertake the market research study. If the market research study is conducted, the outcome will either be favorable (F) or unfavorable (U). However, for this exercise, assume there are only two decision alternatives d1 and d2 and two states of nature s1 and s2. The payoff table showing profit is as follows:...
a. Show the decision tree....
b. Use the following probabilities. What is the optimal decision strategy?
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21.9 A real estate investor has the opportunity to purchase land currently zoned residential. If the county board approves a request to rezone the property as commercial within the next year, the investor will be able to lease the land to a large discount firm that wants to open a new store on the property. However, if the zoning change is not approved, the investor will have to sell the property at a loss. Profits (in thousands of dollars) are shown in the following payoff table....
a. If the probability that the rezoning will be approved is .5, what decision is recommended? What is the expected profit?
b. The investor can purchase an option to buy the land. Under the option, the investor maintains the rights to purchase the land any time during the next three months while learning more about possible resistance to the rezoning proposal from area residents. Probabilities are as follows....What is the optimal decision strategy if the investor uses the option period to learn more about the resistance from area residents before making the purchase decision?
c. If the option will cost the investor an additional $10,000, should the investor purchase the option? Why or why not? What is the maximum that the investor should be willing to pay for the option?
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21.10 Dante Development Corporation is considering bidding on a contract for a new office building complex. Figure 19.9 shows the decision tree prepared by one of Dante’s analysts. At node 1, the company must decide whether to bid on the contract. The cost of preparing the bid is $200,000. The upper branch from node 2 shows that the company has a .8 probability of winning the contract if it submits a bid. If the company wins the bid, it will have to pay $2,000,000 to become a partner in the project. Node 3 shows that the company will then consider doing a market research study to forecast demand for the office units prior to beginning construction. The cost of this study is $150,000. Node 4 is a chance node showing the possible outcomes of the market research study.Nodes 5, 6, and 7 are similar in that they are the decision nodes for Dante to either build the office complex or sell the rights in the project to another developer. The decision to build the complex will result in an income of $5,000,000 if demand is high and $3,000,000 if demand is moderate. If Dante chooses to sell its rights in the project to another developer, incomefrom the sale is estimated to be $3,500,000. The probabilities shown at nodes 4, 8, and 9 are based on the projected outcomes of the market research study.
a. Verify Dante’s profit projections shown at the ending branches of the decision tree by calculating the payoffs of $2,650,000 and $650,000 for first two outcomes.
b. What is the optimal decision strategy for Dante, and what is the expected profit for this project?
c. What would the cost of the market research study have to be before Dante would change its decision about conducting the study?
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21.11 Hale’s TV Productions is considering producing a pilot for a comedy series in the hope of selling it to a major television network. The network may decide to reject the series, but it may also decide to purchase the rights to the series for either one or two years. At this point in time, Hale may either produce the pilot and wait for the network’s decision or transfer the rights for the pilot and series to a competitor for $100,000. Hale’s decision alternatives and profits (in thousands of dollars) are as follows:...The probabilities for the states of nature are P(s1) = .2, P(s2) = .3, and P(s3) = .5. For a consulting fee of $5000, an agency will review the plans for the comedy series and indicate the overall chances of a favorable network reaction to the series. Assume that the agency review will result in a favorable (F) or an unfavorable (U) review and that the following probabilities are relevant....
a. Construct a decision tree for this problem.
b. What is the recommended decision if the agency opinion is not used? What is the expected value?
c. What is the expected value of perfect information?
d. What is Hale’s optimal decision strategy assuming the agency’s information is used?
e. What is the expected value of the agency’s information?
f. Is the agency’s information worth the $5000 fee? What is the maximum that Hale should be willing to pay for the information?
g. What is the recommended decision?
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21.12 Martin’s Service Station is considering entering the snowplowing business for the coming winter season. Martin can purchase either a snowplow blade attachment for the station’s pick-up truck or a new heavy-duty snowplow truck. After analyzing the situation, Martin believes that either alternative would be a profitable investment if the snowfall is heavy. Smaller profits would result if the snowfall is moderate, and losses would result if the snowfall is light. The following profits/losses apply....The probabilities for the states of nature are P(s1) = .4, P(s2) = .3, and P(s3) = .3. Suppose that Martin decides to wait until September before making a final decision. Assessments of the probabilities associated with a normal (N) or unseasonably cold (U) September are as follows:...
a. Construct a decision tree for this problem.
b. What is the recommended decision if Martin does not wait until September? What is the expected value?
c. What is the expected value of perfect information?
d. What is Martin’s optimal decision strategy if the decision is not made until the September weather is determined? What is the expected value of this decision strategy?
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21.13 Lawson’s Department Store faces a buying decision for a seasonal product for which demand can be high, medium, or low. The purchaser for Lawson’s can order 1, 2, or 3 lots of the product before the season begins but cannot reorder later. Profit projections (in thousands of dollars) are shown....
a. If the prior probabilities for the three states of nature are .3, .3, and .4, respectively, what is the recommended order quantity?
b. At each preseason sales meeting, the vice president of sales provides a personal opinion regarding potential demand for this product. Because of the vice president’s enthusiasm and optimistic nature, the predictions of market conditions have always been either “xcellent” (E) or “very good” (V). Probabilities are as follows. What is the optimal decision strategy?
...c. Compute EVPI and EVSI. Discuss whether the firm should consider a consulting expert who could provide independent forecasts of market conditions for the product.
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21.14 Suppose that a decision analysis problem involves three possible states of nature: s1, s2, and s3. The prior probabilities are P(s1) = .2, P(s2) = .5, and P(s3) = .3. The sample information I has associated probabilities P(I|s1) = .1, P(I|s2) = .05, and P(I|s3) = .2. Compute the revised or posterior probabilities: P(s1|I ), P(s2|I ), and P(s3|I ).
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21.15 In the following profit payoff table for a decision problem with two states of nature and three decision alternatives, the prior probabilities for s1 and s2 are P(s1) = .8 and P(s2) = .2....a. What is the optimal decision?
b. Find the EVPI.
c. Suppose that sample information I is obtained, with P(I|s1) = .20 and P(I|s2) = .75. Find the posterior probabilities P(s1|I ) and P(s2|I). Recommend a decision alternative based on these probabilities.
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21.16 To save on expenses, Rona and Jerry agreed to form a carpool for traveling to and from work. Rona preferred to use the somewhat longer but more consistent Queen City Avenue. Although Jerry preferred the quicker expressway, he agreed with Rona that they should take Queen City Avenue if the expressway had a traffic jam. The following payoff table provides the one-way time estimate in minutes for traveling to and from work....Based on their experience with traffic problems, Rona and Jerry agreed on a .15 probability that the expressway would be jammed.In addition, they agreed that weather seemed to affect the traffic conditions on the expressway. Let...The following conditional probabilities apply....
a. Use Bayes’ theorem for probability revision to compute the probability of each weather condition and the conditional probability of the expressway open s1 or jammed s2 given each weather condition.
b. Show the decision tree for this problem.
c. What is the optimal decision strategy, and what is the expected travel time?
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21.17 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)....The state-of-nature probabilities are P(s1) = .35, P(s2) = .35, and P(s3) = .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:...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?
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