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practical management science

Practical Management Science, Revised 3rd Edition Wayne L Winston, S. Christian Albright - Solutions

A homeowner wants to decide whether he should install an electronic heat pump in his home. Given that the cost of installing a new heat pump is fairly large, the homeowner would like to do so only if he can count on being able to recover the initial expense over five consecutive years of cold
City officials in Fort Lauderdale, Florida, are trying to decide whether to evacuate coastal residents in anticipation of a major hurricane that may make landfall near their city within the next 48 hours. Based on previous studies, it is estimated that it will cost approximately$1 million to
An investor has $10,000 in assets and can choose between two different investments. If she invests in the first investment opportunity, there is an 80% chance that she will increase her assets by $590,000 and a 20% chance that she will increase her assets by$190,000. If she invests in the second
Sharp Outfits is trying to decide whether to ship some customer orders now via UPS or wait until after the threat of another UPS strike is over. If Sharp Outfits decides to ship the requested merchandise now and the UPS strike takes place, the company will incur $60,000 in delay and shipping costs.
A publishing company is trying to decide whether to publish a new business law textbook. Based on a careful reading of the latest draft of the manuscript, the publisher’s senior editor in the business textbook division assesses the distribution of possible payoffs earned by publishing this new
A television network earns an average of $1.6 million each season from a hit program and loses an average of $400,000 each season on a program that turns out to be a flop. Of all programs picked up by this network in recent years, 25% turn out to be hits, and 75% turn out to be flops. At a cost of
A manufacturer must decide whether to extend credit to a retailer who would like to open an account with the firm. Past experience with new accounts indicates that 45% are high-risk customers, 35% are moderaterisk customers, and 20% are low-risk customers. If credit is extended, the manufacturer
A city in Ohio is considering replacing its fleet of gasoline-powered automobiles with electric cars. The manufacturer of the electric cars claims that this municipality will experience significant cost savings over the life of the fleet if it chooses to pursue the conversion.If the manufacturer is
A retired partner from Goldman Sachs has 1 million dollars available to invest in particular stocks or bonds. Each investment’s annual rate of return depends on the state of the economy in the coming year.The file P10_69.xlsx contains the distribution of returns for these stocks and bonds as a
A grapefruit farmer in central Florida is trying to decide whether to take protective action to limit damage to his crop in the event that the overnight temperature falls to a level well below freezing. He is concerned that if the temperature falls sufficiently low and he fails to make an effort to
A home appliance company is interested in marketing an innovative new product. The company must decide whether to manufacture this product essentially on its own or employ a subcontractor to manufacture it. The file P10_67.xlsx contains the estimated probability distribution of the cost of
The purchasing agent for a microcomputer manufacturer is currently negotiating a purchase agreement for a particular electronic component with a given supplier.This component is produced in lots of 1000, and the cost of purchasing a lot is $30,000. Unfortunately, past experience indicates that this
Mr. Maloy has just bought a new $30,000 sport utility vehicle. As a reasonably safe driver, he believes that there is only about a 5% chance of being in an accident in the coming year. If he is involved in an accident, the damage to his new vehicle depends on the severity of the accident. The
George Lindsey (1959) looked at box scores of more than 1000 baseball games and found the expected number of runs scored in an inning for each on-base and out situation to be as listed in the file P10_64.xlsx.For example, if a team has a man on first base with one out, it scores 0.5 run on average
The Indiana University basketball team trails by 2 points with 8 seconds to go and has the ball. Should it attempt a 2-point shot or a 3-point shot? Assume that the Indiana shot will end the game and that no foul will occur on the shot. Assume that a 3-point shot has a 30% chance of succeeding, and
Suppose now that the bank’s utility function of profit x (in dollars) is U(x) 1ex150000. Find the strategy that maximizes the bank’s expected utility in this case. How does this optimal strategy compare to the optimal decision with an EMV criterion? Explain any difference in the two optimal
Consider again the bank’s customer loan decision problem in Problem
Suppose now that Techware’s utility function of net revenue x (measured in dollars), earned from the given marketing opportunities, is U(x) 1ex350000.a. Find the course of action that maximizes Techware’s expected utility. How does this optimal decision compare to the optimal decision with
Consider again Techware’s decision problem described in Problem
Anuclear power company is deciding whether to build a nuclear power plant at Diablo Canyon or at Roy Rogers City. The cost of building the power plant is$10 million at Diablo and $20 million at Roy Rogers City. If the company builds at Diablo, however, and an earthquake occurs at Diablo during the
If decision 1 is made, a sure cost of c is incurred. If decision 2 is made, there are two possible outcomes, with costs c1 and c2 and probabilities p and 1 – p. We assume that c1 c c2. The idea is that decision 1, the riskless decision, has a “moderate” cost, whereas decision 2, the risky
Many decision problems have the following simple structure. A decision maker has two possible decisions, 1 and
Pizza King (PK) and Noble Greek (NG) are competitive pizza chains. Pizza King believes there is a 25%chance that NG will charge $6 per pizza, a 50% chance NG will charge $8 per pizza, and a 25%chance that NG will charge $10 per pizza. If PK charges price p1 and NG charges price p2, PK will sell 100
Ford is going to produce a new vehicle, the Pioneer, and wants to determine the amount of annual capacity it should build. Ford’s goal is to maximize the profit from this vehicle over the next 10 years. Each vehicle will sell for $13,000 and incur a variable production cost of $10,000. Building 1
A product manager at Clean & Brite (C&B) seeks to determine whether her company should market a new brand of toothpaste. If this new product succeeds in the marketplace, C&B estimates that it could earn$1,800,000 in future profits from the sale of the new toothpaste. If this new product fails,
Hank is considering placing a bet on the upcoming showdown between the Penn State and Michigan football teams in State College. The winner of this contest will represent the Big Ten Conference in the Rose Bowl on New Year’s Day. Without any additional information, Hank believes that Penn State
FineHair is developing a new product to promote hair growth in cases of male pattern baldness. If FineHair markets the new product and it is successful, the company will earn $500,000 in additional profit. If the marketing of this new product proves to be unsuccessful, the company will lose
A local certified public accountant must decide which of two copying machines to purchase for her expanding business. The cost of purchasing the first machine is $3100, and the cost of maintaining the first machine each year is uncertain. The CPA’s office manager believes that the annual
The senior executives of an oil company are trying to decide whether to drill for oil in a particular field in the Gulf of Mexico. It costs the company $300,000 to drill in the selected field. Company executives believe that if oil is found in this field, its estimated value will be $1,800,000. At
The U.S. government is attempting to determine whether immigrants should be tested for a contagious disease. Let’s assume that the decision will be made on a financial basis. Furthermore, assume that each immigrant who is allowed to enter the United States and has the disease costs the country
A company is deciding whether to market a new product.Assume, for simplicity, that if this product is marketed, there are only two possible outcomes: success or failure. The company assesses that the probabilities of these two outcomes are p and 1 – p, respectively. If the product is marketed,
A customer has approached a bank for a $100,000 1-year loan at a 12% interest rate. If the bank does not approve this loan application, the $100,000 will be invested in bonds that earn a 6% annual return. Without additional information, the bank believes that there is a 4% chance that this customer
The chief executive officer of a firm in a highly competitive industry believes that one of her key employees is providing confidential information to the competition.She is 90% certain that this informer is the vice president of finance, whose contacts have been extremely valuable in obtaining
Suppose now that, at a cost of$90,000, the landowner can request that a soundings test be performed on the site where natural gas is believed to be present. The company that conducts the soundings concedes that 30% of the time the test will indicate that no gas is present when it actually is.When
Consider again the landowner’s decision problem described in Problem
Yearly automobile inspections are required for residents of the state of Pennsylvania. Suppose that 18%of all inspected cars in Pennsylvania have problems that need to be corrected. Unfortunately, Pennsylvania state inspections fail to detect these problems 12% of the time. Consider a car that is
Consider a population of 2000 individuals, 800 of whom are women. Assume that 300 of the women in this population earn at least $60,000 per year, and 200 of the men earn at least $60,000 per yeara. What is the probability that a randomly selected individual from this population earns less than
Suppose that one of your colleagues has $2000 available to invest. Assume that all of this money must be placed in one of three investments: a particular money market fund, a stock, or gold. Each dollar your colleague invests in the money market fund earns a virtually guaranteed 6% annual return.
Suppose that you have sued your employer for damages suffered when you recently slipped and fell on an icy surface that should have been treated by your company’s physical plant department. Specifically, your injury resulting from this accident was sufficiently serious that you, in consultation
Two construction companies are bidding against one another for the right to construct a new community center building in Lewisburg, Pennsylvania. The first construction company, Fine Line Homes, believes that its competitor, Buffalo Valley Construction, will place a bid for this project according
Each day, the manager of a local bookstore must decide how many copies of the community newspaper to order for sale in her shop. She must pay the newspaper’s publisher $0.40 for each copy, and she sells the newspapers to local residents for $0.50 each. Newspapers that are unsold at the end of day
A buyer for a large department store chain must place orders with an athletic shoe manufacturer 6 months prior to the time the shoes will be sold in the department stores. In particular, the buyer must decide on November 1 how many pairs of the manufacturer’s newest model of tennis shoes to order
Consider an investor with $10,000 available to invest.He has the following options regarding the allocation of his available funds: (1) he can invest in a risk-free savings account with a guaranteed 3% annual rate of return; (2) he can invest in a fairly safe stock, where the possible annual rates
Techware Incorporated is considering the introduction of two new software products to the market. In particular, the company has four options regarding these two proposed products: introduce neither product, introduce product 1 only, introduce product 2 only, or introduce both products. Research
A local energy provider offers a landowner $180,000 for the exploration rights to natural gas on a certain site and the option for future development. This option, if exercised, is worth an additional $1,800,000 to the landowner, but this will occur only if natural gas is discovered during the
Carlisle Tire and Rubber, Inc., is considering expanding production to meet potential increases in the demand for one of its tire products. Carlisle’s alternatives are to construct a new plant, expand the existing plant, or do nothing in the short run. The market for this particular tire product
The SweetTooth Candy Company knows it will need 10 tons of sugar 6 months from now to implement its production plans. Jean Dobson, SweetTooth’s purchasing manager, has essentially two options for acquiring the needed sugar. She can either buy the sugar at the going market price when she needs it,
Do the absolute magnitudes of the monetary outcomes matter in the risky venture example? Consider the following two possibilities. In each case, multiply all monetary values in the example by a factor of A. (For example, double them if A 2.) For each part, briefly explain your findings.a.
In the risky venture example, a decision maker with risk tolerance of $1.92 million does not prefer the more risky alternative, in spite of its dominating EMV.Now suppose everything stays the same except for the best monetary outcome of the more risky alternative(the value in cell D14). How much
For the risky venture example, create a line chart that includes three series, that is, three lines (or curves).Each line should show the expected utility of a particular decision for a sequence of possible risk-tolerance values. (You will have to create the data for the chart manually, by changing
The concept behind EVPI is that we purchase perfect information (the envelope), we then open the envelope to see which outcome occurs, and then we make an easy decision. However, we do not get to choose what information the envelope contains. Sometimes a company can pay, not to obtain information,
We related EVPI to the value of an envelope that contains the true ultimate outcome. We can extend this concept to “less than perfect” information. For example, in the Acme problem suppose that we could purchase information that would tell us, with certainty, that one of the following two
These are values where Acme will make the same decision, regardless of the test market results it observes.Skill-Extending Problems
Using trial and error on the prior probabilities in the Acme problem, find values of them that make EVSI equal to
(For example, you couldn’t choose ranges where the probabilities of great and fair are 0.6 and 0.5.)
For the Acme problem, perform the following sensitivity analyses on the three prior probabilities and comment on the results.a. Vary the probability of great in a one-way sensitivity analysis from 0 to 0.6 in increments of 0.1. Do this in such a way that the probabilities of the two other outcomes,
Prior probabilities are often educated guesses at best, so it is worth performing a sensitivity analysis on their values. However, we must make sure that we vary them so that all probabilities are nonnegative and sum to
Explain in general why EVSI is independent of the actual cost of the information. For example, in the Acme problem, EVSI is the same regardless of whether the actual cost of the test market is$100,000, $200,000, or any other value. Then explain how EVSI, together with the actual cost of the
(The idea is that large values of a and/or small values of b make the testing more attractive.) Use PrecisionTree’s two-way sensitivity tool to see whether the optimal decision (test or not test) changes for a reasonable range of values of a andb. Discuss your results.
In deciding whether to perform mandatory drug testing, we claimed that it is difficult to justify such testing under reasonable conditions. Check this yourself in the following questions.a. Drug testing ought to be more attractive if the test is more reliable. Keeping the costs the same as in the
The terms prior and posterior are relative. Assume that the drug test has been performed, and the outcome is positive, which leads to the posterior probabilities in row 20 of Figure 10.29. Now assume there is a second test, probabilistically independent of the first, that can be used as a
Referring to the previous problem, find the same probabilities through the counting argument explained in this section. Start with 100,000 athletes and divide them into the various categories.
In the drug testing, assume there are three possible test results: positive, negative, and inconclusive. For a drug user, the probabilities of these outcomes are 0.65, 0.06, and 0.29. For a nonuser, they are 0.03, 0.72, and 0.25. Use Bayes’ rule to find a table of all posterior probabilities.
Explain in words what information a two-way sensitivity chart, such as the one in Figure 10.28, provides.Demonstrate how you could provide this same information without PrecisionTree’s sensitivity tools, using only data tables. (You can still utilize the tree built with PrecisionTree.)
The tornado chart in Figure 10.25 and the spider chart in Figure 10.26 show basically the same information in slightly different forms. Explain in words exactly what information they provide.
For the SciTools example, after you build the tree as in Figure 10.10 and then run a one-way sensitivity analysis with the dialog box filled in as in Figure 10.23, you obtain three strategy charts. (Try it.) Explain exactly what each of these charts represents. (For this problem, you can ignore the
For the completed decision tree in Figure 10.10, the monetary values in black are those we enter. The monetary values in color are calculated automatically by PrecisionTree. For this particular example, explain exactly how these latter values are calculated (remember the folding-back process) and
In the SciTools example, we saw that there are two equivalent decision tree structures, shown in Figures 10.5 and 10.6. Use PrecisionTree to create the first of these, and verify that it yields the same EMVs and the same optimal decision as the tree we developed in this section.
In a tree built with PrecisionTree, there are two blue values at each end node, and the top one is a probability.Why are so many of these probabilities 0 in the finished tree in Figure 10.10? What do the remaining(positive) probabilities represent?
In the SciTools example, you might argue that there is a continuum of possible low competitor bids (given that there is at least one competing bid), not just four possibilities. In fact, assume the low competitor bid in this case is normally distributed with mean $118,000 and standard deviation
Referring to the previous problem, another possible criterion is called expected regret. Here we calculate the regret for each cell, take a weighted average of these regrets in each row, weighted by the probabilities of the outcomes, and choose the decision with the smallest expected regret.a.
Besides the maximin, maximax, and EMV criteria, there are other possible criteria for making decisions.One possibility involves regret. The idea behind regret is that if we make any decision and then some outcome occurs, we look at that outcome’s column in the payoff table to see how much more we
A decision d is dominated by another decision D if, for every outcome, the payoff from D is better than (or no worse than) the payoff from d.a. Explain why you would never choose a dominated decision, using the maximin criterion; using the maximax criterion; using the EMV criterion.b. Are any of
In the SciTools example, use a two-way data table to see how (or whether) the optimal decision changes as the bid cost and the company’s production cost change simultaneously. Let the bid cost vary from $2000 to$8000 in increments of $1000, and let the production cost vary from $90,000 to
In the SciTools example, suppose that we make two changes: all references to $115,000 change to$110,000, and all references to $125,000 change to$130,000. Rework the EMV calculations and the decision tree. What is the best decision and its corresponding EMV?
For the simple three-decision, three-outcome example, are there any probabilities that make the EMV criterion equivalent to the maximin criterion? Are there any probabilities that make the EMV criterion equivalent to the maximax criterion? Explain.
Using a data table in Excel, perform a sensitivity analysis on the simple three-decision, three-outcome example. Specifically, continue to assume that outcomes O1 and O2 are equally likely, each with probability p. Because the probabilities of all outcomes must sum to 1, the probability of outcome
In the simple three-decision, three-outcome example, we found that decision D3 is the EMV-maximizing decision for the probabilities we used. See whether you can find probabilities that make decision D1 the best.See if you can find probabilities that make decision D2 the best. Qualitatively, how can
In the Indiana MBA program we need to divide a class of 60 students into 10 6-person teams. In the interest of diversity, we have the following goals (listed in descending order of importance):■ At least one woman per team■ At least one member of a minority per team■ At least one student with
You have been hired as a consultant to help design a new airport in northern Indiana that will supplant O’Hare as Chicago’s major airport. Discuss the objectives you consider important in designing and locating the airport.
You have been commissioned to assign 100 remedial education teachers to the 40 schools in the St. Louis School System. What are some objectives you might consider in assigning the teachers to schools?
You are planning to overhaul a hospital computer system. How would you use AHP to determine the type of computer system to install?
You are planning to renovate a hospital. How would you use AHP to help determine what improvements to include in the renovation?
How would you use AHP to determine the greatest sports record of all time? (Many believe it is Joe DiMaggio’s 56-game hitting streak.)
A company is considering buying up to five other businesses. Given knowledge of the company’s view of the trade-off between risk and return, how could trade-off curves be used to determine the companies that should be purchased?
How might you use goal programming to help Congress balance the budget?
At the beginning of the 6-month period, 30 units of product 2 are in inventory.■ During the next 6 months, Wivco has 1000 hours for production available. At the end of the next 6 months, Wivco incurs a 10% holding cost on the value of ending inventory (measured relative to production cost). An
At the beginning of the 6-month period, 60 units of product 1 are in inventory.■ During the next 6 months, at most 175 units of product 2 can be sold on a cash basis, and at most 250 units of product 2 can be sold on a credit basis.It costs $45 to produce each unit of product 2, and each sells
Based on Sartoris and Spruill (1974). Wivco produces two products, which it sells on both a cash and credit basis. Revenues from credit sales will not have been received but are included in determining profit earned during the current 6-month period. Sales during the next 6 months can be made
You are the mayor of Gotham City and you must determine a tax policy for the city. Five types of taxes are used to raise money:■ Property taxes. Let p be the property tax rate.■ A sales tax on all items except food, drugs, and durable goods. Let s be the sales tax rate.■ A sales tax on
At Lummins Engine Corporation, production employees work 10 hours per day, 4 days per week. Each day of the week, at least the following number of employees must be working: Monday through Friday, 7 employees; Saturday and Sunday, 3 employees.Lummins has set the following goals, listed in order of
You are trying to determine which city to live in.New York and Chicago are under consideration. Four objectives will determine your decision: housing cost, cultural opportunities, quality of schools and universities, and crime level. The weight for each objective is in the file P09_39.xlsx. For
A hospital outpatient clinic performs four types of operations. The profit per operation, as well as the minutes of X-ray time and laboratory time used, are given in the file P09_38.xlsx. The clinic has 500 private rooms and 500 intensive care rooms. Type 1 and type 2 operations require a patient
Goal 1 is to minimize the sum of deviations from this requirement.■ Goal 2: For the benchmark jobs referred to in the file P09_37.xlsx, the actual point total for each job should come as close as possible to the point total listed in the table. Goal 2 is to minimize the sum of the absolute
For example, level 2 of factor 1 should earn at least 10 more points than level 1 of factor
A job’s hourly salary equals half its point total. IU has two goals (listed in order of priority) in setting up the points given to each level of each job factor.■ Goal 1: When increasing the level of a factor by 1, the points should increase by at least
Then a job with these requirements has a point total of 10 20 30
Jobs at Indiana University are rated on three factors:■ Factor 1: Complexity of duties■ Factor 2: Education required■ Factor 3: Mental and/or visual demands For each job at IU, the requirement for each factor has been rated on a scale of 1 to 4, with a 4 in factor 1 representing high
Productco produces three products. Each product requires labor, lumber, and paint. The resource requirements, unit price, and variable cost (exclusive of raw materials) for each product are given in the file P09_36.xlsx. At present, 900 labor hours, 1550 gallons of paint, and 1600 board feet of
BeatTrop Foods is trying to choose one of three companies to merge with. Seven factors are important in this decision:■ Factor 1: Contribution to profitability■ Factor 2: Growth potential■ Factor 3: Labor environment ■ Factor 4: R&D ability of company ■ Factor 5: Organizational fit ■

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