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practical management science
Questions and Answers of
Practical Management Science
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
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
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
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
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
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
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%
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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 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.
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
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
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
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
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
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,
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.
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
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.
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,
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
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
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
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
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
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,
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
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
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
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
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
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
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
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
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
(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)
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
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
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,
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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■
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