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 best choice 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).

$$\begin{matrix} \text{ } & \text{Demand} & \text{for Service}\\ \hline \text{Service} & \text{Strong} & \text{Weak}\\ \text{Full price} & \text{\$960} & \text{-\$490}\\ \text{Discount} & \text{\$670} & \text{\$320}\\ \end{matrix}$$

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?

"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 best choice 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 on 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):

$$\begin{aligned} &\text { Demand for Service }\\ &\begin{array}{lcr} \text { Service } & \text { Strong } & \text { Weak } \\ \text { Full Price } & \$ 960 & -\$ 490 \\ \text { Discount } & \$ 670 & \$ 320 \end{array} \end{aligned}$$

Suppose that management of Myrtle Air Express believes that the probability of strong demand is 0.7 and the probability of weak demand is 0.3. Use the expected value approach to determine an optimal decision."

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 best choice 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

The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature.

$$\begin{matrix} \text{ } & \text{States} & \text{of} & \text{Nature}\\ \hline \text{Decision Alternative} & \text{s1} & \text{s2} & \text{s3}\\ \text{d1} & \text{250} & \text{100} & \text{25}\\ \text{d2} & \text{100} & \text{100} & \text{75}\\ \end{matrix}$$

a. Construct a decision tree for this problem. b. Suppose that the decision maker obtains the probabilities $P \left( s _ { 1 } \right) = .65 , P \left( s _ { 2 } \right) = .15$, and $P \left( s _ { 3 } \right) = .20$

Use the expected value approach to determine the optimal decision.

"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 best choice 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 on 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):

$$\begin{aligned} &\text { Demand for Service }\\ &\begin{array}{lcr} \text { Service } & \text { Strong } & \text { Weak } \\ \text { Full Price } & \$ 960 & -\$ 490 \\ \text { Discount } & \$ 670 & \$ 320 \end{array} \end{aligned}$$

If nothing is known about the probabilities of the chance outcomes, what is the recommended decision using the optimistic, conservative, and minimax regret approaches?"

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.

$$\begin{matrix} \text{ } & \text{ } & \text{Demand}\\ \text{Staffing Options} & \text{High} & \text{Medium} & \text{Low}\\ \text{Own staff} & \text{650} & \text{650} & \text{600}\\ \text{Outside vendor} & \text{900} & \text{600} & \text{300}\\ \text{Combination} & \text{800} & \text{650} & \text{500}\\ \end{matrix}$$

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?

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.

$$\begin{matrix} \text{ } & \text{Riesling} & \text{Demand}\\ \text{Chardonnay Demand} & \text{Weak} & \text{Strong}\\ \text{Weak} & \text{.05} & \text{.50}\\ \text{Strong} & \text{.25} & \text{.20}\\ \end{matrix}$$

Revenue projections show an annual contribution to profit of $20,000 if Seneca Hill only plants Chardonnay grapes and demand is weak for Chardonnay wine, and$70,000 if they only plant Chardonnay grapes and demand is strong for Chardonnay wine. If they only plant 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.

$$\begin{matrix} \text{ } & \text{Riesling} & \text{Demand}\\ \text{Chardonnay Demand} & \text{Weak} & \text{Strong}\\ \text{Weak} & \text{\$22,000} & \text{\$40,000}\\ \text{Strong} & \text{\$26,000} & \text{\$60,000}\\ \end{matrix}$$

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 Chardonnay and 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 weak are 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 Chardonnay grapes only are planted. Using the original probability assessments, determine how this change would affect the optimal decision.

"Investment advisors estimated the stock market returns for four market segments: computers, financial, manufacturing, and pharmaceuticals. Annual return projections vary depending on whether the general economic conditions are improving, stable, or declining. The anticipated annual return percentages for each market segment under each economic condition are as follows:

$$\begin{aligned} &\text { Economic Condition }\\ &\begin{array}{lccc} \text { Market Segment } & \text { Improving } & \text { Stable } & \text { Declining } \\ \text { Computers } & 10 & 2 & -4 \\ \text { Financial } & 8 & 5 & -3 \\ \text { Manufacturing } & 6 & 4 & -2 \\ \text { Pharmaceuticals } & 6 & 5 & -1 \end{array} \end{aligned}$$

At a later date, a revised forecast shows a potential for an improvement in economic conditions. New probabilities are as follows: improving (0.4), stable (0.4), and declining (0.2). What is the preferred market segment for the investor based on these new probabilities? What is the expected return percentage?"

Suppose that management of Myrtle Air Express believes that the probability of strong demand is 0.7 and the probability of weak demand is 0.3 . Use the expected value approach to determine an optimal decision.

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 current levels; 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, base-case, 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. A consultant 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.

$$\begin{matrix} \text{ } & \text{Demand} & \text{Scenario}\\ \text{ } & \text{Worst} & \text{Base} & \text{Best}\\ \text{Center Size} & \text{Case} & \text{Case} & \text{Case}\\ \hline \text{Small} & \text{400} & \text{500} & \text{660}\\ \text{Medium} & \text{-250} & \text{650} & \text{800}\\ \text{Large} & \text{-400} & \text{580} & \text{990}\\ \end{matrix}$$

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 theworst-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?

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. Another candidate 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.

$$\begin{matrix} \text{ } & \text{DRI Plant} & \text{No DRI Plant}\\ \text{Air Express Center} & \text{.30} & \text{.10}\\ \text{No Air Express Center} & \text{.40} & \text{.20}\\ \end{matrix}$$

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:

$$\begin{matrix} \text{ } & \text{DRI Plant} & \text{No DRI Plant}\\ \text{Air Express Center} & \text{\$600,000} & \text{\$150,000}\\ \text{No Air Express Center} & \text{\$250,000} & \text{-\$200,000}\\ \end{matrix}$$

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:

$$\begin{matrix} \text{ } & \text{DRI Plant} & \text{No DRI Plant}\\ \text{Air Express Center} & \text{.40} & \text{.10}\\ \text{No Air Express Center} & \text{.30} & \text{.20}\\ \end{matrix}$$

What effect, if any, would this change in the probabilities have on the recommended decision?

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.

$$\begin{matrix} \text{ } & \text{State} & \text{of Nature}\\ \text{ } & \text{Expressway} & \text{Expressway}\\ \text{ } & \text{Open} & \text{Jammed}\\ \hline \text{Decision Alternative} & \text{s1} & \text{s2}\\ \text{Queen City Avenue, d1} & \text{30} & \text{30}\\ \text{Expressway, d2} & \text{25} & \text{45}\\ \end{matrix}$$

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

$$\begin{aligned} C & = \text { clear } \\ O & = \text { overcast } \\ R & = \text { rain } \end{aligned}$$

The following conditional probabilities apply.

$$\begin{array} { l l l } { P ( C | s _ { 1 } ) = .8 } & { P ( O | s _ { 1 } ) = .2 } & { P ( R | s _ { 1 } ) = .0 } \\ { P ( C | s _ { 2 } ) = .1 } & { P ( O | s _ { 2 } ) = .3 } & P ( R | s _ { 2 } ) = .6 \end{array}$$

a. Use Bayes’ theorem for probability revision to compute the probability of each weather condition and the conditional probability of the expressway open, $s_1$, or jammed, $s_2$, 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?

Alumni donations are an important source of revenue for colleges and universities. If administrators could determine the factors that could lead to increases in the percentage of alumni who make a donation, they might be able to implement policies that could lead to increased revenues. Research shows that students who are more satisfied with their contact with teachers are more likely to graduate. As a result, one might suspect that smaller class sizes and lower student/faculty ratios might lead to a higher percentage of satisfied graduates, which in turn might lead to increases in the percentage of alumni who make a donation. The following table shows data for 48 national universities. The Graduation Rate column is the percentage of students who initially enrolled at the university and graduated. The % of Classes Under 20 column shows the percentages of classes offered with fewer than 20 students. The Student/Faculty Ratio column is the number of students enrolled divided by the total number of faculty. Finally, the Alumni Giving Rate column is the percentage of alumni who made a donation to the university.

Use methods of descriptive statistics to summarize the data.

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 that the probability of strong demand for Chardonnay and weak demand for Riesling is 0.05 and that the probability of strong demand for Chardonnay and strong demand for Riesling is 0.40 . How does this change the recommended decision? Assume that the probabilities when Chardonnay demand is weak are still 0.05 and 0.50 .