Questions and Answers of Practical Management Science

Based on Kelly (1956). You currently have $100. Each week you can invest any amount of money you currently have in a risky investment. With probability 0.4, the amount you invest is tripled (e.g., if
Change the new car simulation from Example 11.4 as follows. It is the same as before for years 1 through 5, including depreciation through year 5. However, the car might sell through year 10. Each
Modify Example 11.8 so that the portfolio now contains 100 shares of stock and one put option on the stock with the same parameters as in the example. You can assume that the price of an option is
A European put option allows an investor to sell a share of stock at the exercise price on the exercise data. For example, if the exercise price is $48, and the stock price is $45 on the exercise
Referring to the retirement example in Example 11.6, rerun the model for a planning horizon of 10 years; 15 years; 25 years. For each, which set of investment weights maximizes the VAR 5% (the 5th
Modify the model from Example 11.6 so that you use only the years 1975 to 2007 of historical data. Run the simulation for the same three sets of investment weights. Comment on whether your results
The simulation output from Example 11.6 indicates that an investment heavy in stocks produces the best results. Would it be better to invest entirely in stocks? Answer this by rerunning the
Run the retirement model from Example 11.6 with a damping factor of 1.0 (instead of 0.98), again using the same three sets of investment weights. Explain in words what it means, in terms of the
In the cash balance model from Example 11.5, is the $250,000 minimum cash balance requirement really “costing” the company very much? Answer this by rerunning the simulation with minimum required
In the cash balance model from Example 11.5, the timing is such that some receipts are delayed by one or two months, and the payments for materials and labor must be made a month in advance. Change
Rerun the new car simulation from Example 11.4, but now use the RISKSIMTABLE function appropriately to simulate discount rates of 5%, 7.5%, 10%, 12.5%, and 15%. Comment on how the outputs change as
Rerun the new car simulation from Example 11.4, but now introduce uncertainty into the fixed development cost. Let it be triangularly distributed with parameters $600 million, $650 million, and $850
In Example 11.3, suppose you want to run five simulations, where the probability of passing inspection is varied from 0.6 to 1.0 in increments of 0.1. Use the RISKSIMTABLE function appropriately to
In Example 11.3, we commented on the 95th percentile on days required and the corresponding date to start production. If the company begins production on this date, then it is 95% sure to complete
In Example 11.2, the gamma distribution was used to model the skewness to the right of the lifetime distribution. Experiment to see whether the triangular distribution could have been used instead.
See how sensitive the results in Example 11.2 are to the following changes. For each part, make the change indicated, run the simulation, and comment on any differences between your outputs and the
Referring to Example 11.1, if the average bid for each competitor stays the same, but their bids exhibit less variability, does Miller’s optimal bid increase or decrease? To study this question,
In Example 11.1, the possible profits vary from negative to positive for each of the 10 possible bids examined.a. For each of these, use @RISK’s RISKTARGET function to find the probability that
If the number of competitors in Example 11.1 doubles, how does the optimal bid change?
1. Starting with the model from Case 2.2, you should replace all of the inputs with probability distributions. Specifically, based on their knowledge of the new product and the market, Jim and
1. You should develop the simulation model just described. Only one @RISK output is required, the total retained impressions. Based on a run of 10 simulations (one for each number of ad agencies
1. Develop a simulation model for 52 weeks of operation at Ebony. Graph the inventory of soap over time. What is the total cost (inventory cost plus production change cost) for the 52 weeks?2. Run
1. Egress management believes that a normal distribution is a reasonable model for the unknown demand in the coming year. What mean and standard deviation should Egress use for the demand
At the beginning of each week, a machine is in one of four conditions: 1 = excellent; 2 = good; 3 5 average; 4 5 bad. The weekly revenue earned by a machine in state 1, 2, 3, or 4 is $100, $90, $50,
United Electric (UE) sells refrigerators for $400 with a one-year warranty. The warranty works as follows. If any part of the refrigerator fails during the first year after purchase, UE replaces the
In the Walton Bookstore example, suppose that Walton receives no money for the first 50 excess calendars returned but receives $2.50 for every calendar after the first 50 returned. Does this change
This is an extension of Case 2.1 from Chapter 2, so you should read that case first. It asks you to develop a spreadsheet model, using a 0-1 variable for each potential project, so that Cliff Erland,
Suppose an investor has the opportunity to buy the following contract, a stock call option, on March 1. The contract allows him to buy 100 shares of ABC stock at the end of March, April, or May at a
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. Your injury was
Two construction companies are bidding against one another for the right to construct a new community center building in Bloomington, Indiana. The first construction company, Fine Line Homes,
A buyer for a large department store chain must place orders with an athletic shoe manufacturer six months prior to the time the shoes will be sold in the department stores. The buyer must decide on
An investor with $10,000 available to invest has the following options: (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
Techware Incorporated is considering the introduction of two new software products to the market. The company has four options regarding these products: introduce neither product, introduce product 1
Starting with the finished version of Example 9.3, change the fixed marketing cost to $4000 (really $4 million) in cell B5, and change the decision criterion to “maximize expected utility,” using
Starting with the finished version of Example 9.2, change the decision criterion to “maximize expected utility,” using an exponential utility function with risk tolerance $5000 (really $5
Starting with the finished version of Example 9.2, change the decision criterion to “maximize expected utility,” using an exponential utility function with risk tolerance $5000 (really $5
You saw in Example 9.4 how Acme prefers to abandon the product when the risk tolerance in cell B12 is $5000 (really $5 million). This is despite the fact that the EMV from continuing with the product
Using the finished version of the file for Example 9.4, use a data table to perform a sensitivity analysis on the risk tolerance. Specifically, let the risk tolerance in cell B12 vary from $10,000 to
The terms prior and posterior are relative. Assume that the test in Figure 9.17 (and in the file Bayes Rule for Disease.xlsx) has been performed, and the outcome is positive, which leads to the
The terms prior and posterior are relative. Assume that the test in Figure 9.17 (and in the file Bayes Rule for Disease.xlsx) has been performed, and the outcome is positive, which leads to the
The model in Example 9.3 has only two market outcomes, good and bad, and two corresponding predictions, good and bad. Modify the decision tree by allowing three outcomes and three predictions, good,
In Example 9.2, a technological failure implies that the game is over—the product must be abandoned. Change the problem so that there are two levels of technological failure, each with probability
If you examine the decision tree in Figure 9.12 (or any other decision trees from PrecisionTree), you will see two numbers (in blue font) to the right of each end node. The bottom number is the
Starting with the finished version of the file for Example 9.3, change the fixed cost in cell B5 to $4000. Then get back into PrecisionTree’s One-Way Sensitivity Analysis dialog box and add three
The finished version of the file for Example 9.3 contains two “Strategy B9” sheets. Explain what each of them indicates and how they differ.
In using Bayes’ rule for the presence of a disease (see Figure 9.17 and the file Bayes Rule for Disease.xlsx), we assumed that there are only two test results, positive or negative. Suppose there
In Example 9.2, use a two-way PrecisionTree sensitivity analysis to examine the changes in both of the two previous problems simultaneously. Let the probability of technological success vary from 0.6
In Example 9.2, the fixed costs are split $4 million for development and $2 million for marketing. Perform a sensitivity analysis where the sum of these two fixed costs remains at $6 million but the
In Example 9.2, Acme’s probability of technological success, 0.8, is evidently large enough to make “continue development” the best decision. How low would this probability have to be to make
Use PrecisionTree to solve problem 7 of the previous section.Problem 7Sometimes a "single-stage" decision can be broken down into a sequence of decisions, with no uncertainty resolved between these
Use PrecisionTree’s Sensitivity Analysis tools to perform the sensitivity analysis requested in problem 5 of the previous section. (Watch the Step 5 video in Figure 9.10 if necessary.)Figure 9.10 A
For the decision problem in Figure 9.1, use data tables to perform the following sensitivity analyses. The goal in each is to see whether decision 1 continues to have the largest EMV. In each part,
The 30 teams in the NBA are each assigned to one of six divisions, where each division has five teams. Suppose the goal is to assign the teams to divisions so that the average distance among teams in
Based on Schrage (1997). The file P08_05.xlsx lists the size of the four main markets for Excel, Word, and the bundle of Excel and Word. (We assume that Microsoft is willing to sell Excel or Word
Modify the function in Example 8.1 so that it becomes f (x) = x sin(x) for 0 ≤ x ≤ 30. (Here, sin(x) is the sine function from trigonometry. You can evaluate it with Excel’s SIN function.) Plot
Consider the sports ratings model in section 7.6. If you were going to use the approach used there to forecast future sports contests, what problems might you encounter early in the season? How might
Consider the sports ratings model in section 7.6. If you were going to give more recent games more weight, how might you determine whether the weight given to a game from k weeks ago should be, say,
You are given that the two nonhypotenuse sides of a right triangle add up to 10 inches. What is the maximum area of the triangle? Can you generalize this result?
Based on Grossman and Hart (1983). A salesperson for Fuller Brush has three options: (1) quit, (2) put forth a low level of effort, or (3) put forth a high level of effort. Suppose for simplicity
Continuing the previous problem, find the portfolio that achieves an expected monthly return of at least 1% and minimizes portfolio variance. Then use SolverTable to sweep out the efficient frontier,
This problem continues using the data from the previous problem. The file P07_40.xlsx includes all of the previous data and contains investment weights in row 3 for creating a portfolio. These
The file P07_39.xlsx contains historical monthly returns for 27 companies. For each company, calculate the estimated mean return and the estimated variance of return. Then calculate the estimated
By the time you are reading this, the 2014 NFL season will have finished, and the results should be available at http://www.pro-football-reference.com/years/ 2014/games.htm. Do whatever it takes to
The file P07_31.xlsx contains scores on all of the regular- season games in the NBA for the 2012–2013 basketball season. Use the same procedure as in Example 7.8 to rate the teams. Then sort the
Carry out the suggestion in Modeling Issue 2. That is, use a weighted sum of squared prediction errors, where the weight on any game played k weeks ago is 0.95k. You can assume that the ratings are
Carry out the suggestion in Modeling Issue 3. That is, find the ratings of the 2013 NFL teams using the sum of absolute prediction errors as the criterion to minimize. Discuss any differences in
The file P07_28.xlsx lists the scores of all NFL games played during the 2008 season. Use this data set to rank the NFL teams from best to worst.
In the solution to the advertising selection model in Example 7.6, we indicated that the women 36 to 55 group is a bottleneck in the sense that the company needs to spend a lot more than it would
The file P06_92.xlsx lists the distances between 21 U.S. cities. You want to locate liver transplant centers in a subset of these 21 cities.a. Suppose you plan to build four liver transplant centers
How hard is it to expand a set-covering model to accommodate new cities? Answer this by modifying the model in Figure 6.25. (See the file Locating Hubs with Distances.xlsx.) Add several cities that
Set-covering models such as the original Western model in Figure 6.22 often have multiple optimal solutions. See how many alternative optimal solutions you can find. Of course, each must use three
In the original Western set-covering model in Figure 6.22, we assumed that each city must be covered by at least one hub. Suppose that for added flexibility in flight routing, Western requires that
In the original Western set-covering model in Figure 6.22, we used the number of hubs as the objective to minimize. Suppose instead that there is a fixed cost of locating a hub in any city, where
In the optimal solution to the Great Threads model, the labor hour and cloth constraints are both binding—the company is using all it has.a. Use SolverTable to see what happens to the optimal
In the Great Threads model, we didn’t constrain the production quantities in row 16 to be integers, arguing that any fractional values could be safely rounded to integers. See whether this is true.
Expand and then solve the capital budgeting model in Figure 6.5 so that 20 investments are now possible. You can make up the data on cash requirements, NPVs, and the budget, but use the following
Solve the previous problem using the input data in the file P06_02.xlsx.Previous problemIn the capital budgeting model in Figure 14.40, we supplied the NPV for each investment. Suppose instead
In the VanBuren machine replacement problem, the company’s current policy is to keep a machine at least four quarters but no more than 12 quarters. Suppose instead that the company imposes no upper
In the VanBuren machine replacement problem, the company’s current policy is to keep a machine at least 4 quarters but no more than 12 quarters. Suppose this policy is instead to keep a machine at
Based on Gaballa and Pearce (1979). Northwest Airlines has determined that it needs the number of ticket agents during each hour of the day listed in the file P04_75.xlsx. Workers work nine-hour
A large U.S. drug company, Pharmco, has 100 million yen coming due in one year. Currently the yen is worth $0.01. Because the value of the yen in U.S. dollars in one year is unknown, the value of
You are playing Serena Williams in tennis, and you have a 42% chance of winning each point.a. Use simulation to estimate the probability you will win a particular game. Note that the first player to
The file P14_52.xlsx contains data on a motel chain’s revenue and advertising.a. Use these data and multiple regression to make predictions of the motel chain’s revenues during the next four
Confederate Express is attempting to determine how its monthly shipping costs depend on the number of units shipped during a month. The file P14_46.xlsx contains the number of units shipped and total
Let Yt be the sales during month t (in thousands of dollars) for a photography studio, and let Pt be the price charged for portraits during month t. The data are in the file P14_39.xlsx.a. Use
A trucking firm must decide at the beginning of the year on the size of its trucking fleet. If on a given day the firm does not have enough trucks, the firm will have to rent trucks from a rental
An exchange curve can be used to display the trade-offs between the average investment in inventory and the annual ordering cost. To illustrate the usefulness of a trade-off curve, suppose that a
A company inventories two items. The relevant data are shown in the file P12_65.xlsx. Determine the optimal inventory policy if no shortages are allowed and if the average investment in inventory is
Based on Riccio et al. (1986). The borough of Staten Island has two sanitation districts. In district 1, street litter piles up at an average rate of 2000 tons per week, and in district 2, it piles
A firm knows that the price of the product it is ordering is going to increase permanently by X dollars. It wants to know how much of the product it should order before the price increase goes into
A newspaper has 500,000 subscribers who pay $4 per month for the paper. It costs the company $200,000 to bill all its customers. Assume that the company can earn interest at a rate of 20% per year on
The penalty cost p used in the shortage model is usually difficult to estimate. As an alternative, a company might use a service-level constraint, such as, “95% of all demand must be met from
Suppose that instead of measuring shortage in terms of cost per shortage per year, a cost of P dollars is incurred for each unit the firm is short. This cost does not depend on the length of time
During each year, CSL Computer Company needs to train 27 service representatives. It costs $12,000 to run a training program, regardless of the number of students being trained. Service reps earn a
Based on Baumol (1952). Money in your savings account earns interest at a 3% annual rate. Each time you go to the bank, you waste 15 minutes in line, and your time is worth $10 per hour. During each
In the basic EOQ model in Example 12.1, suppose that the fixed cost of ordering is $500. Use Solver to find the new optimal order quantity. How does it compare to the optimal order quantity in the
1. What is the optimal number of tokens to hoard?2. What is the present value of the savings over not hoarding at all?3. Suppose that the optimal quantity to hoard is Q. What is the present
If the lead time in Example 12.1 changes from one week to two weeks, how is the optimal policy affected? Does the optimal order quantity change?
In the quantity discount model in Example 12.2, the minimum total annual cost is obtained by ordering enough to achieve the smallest unit purchasing cost. Evidently, the larger unit purchasing costs
In the quantity discount model in Example 12.2, suppose you want to see how the optimal order quantity and the total annual cost vary as the fixed cost of ordering varies. Use SolverTable to perform

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