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practical management science

Practical Management Science 4th Edition Wayne L. Winston, S. Christian Albright - Solutions

A Wall Street firm is trying to package nine mortgages for sale. The sizes of the mortgages (in thousands of dollars) are listed in the file P08_32.xlsx. To be sold, each package must consist of at least $1,000,000 in mortgages. What is the largest number of packages that can be created?
Music radio WABC has commercials of the following lengths (in seconds): 15, 15, 20, 25, 30, 35, 40, 57.The commercials must be assigned to 60-second breaks. What is the fewest number of breaks that are needed to air all of the commercials?
The goal is to build a quantitative model to explain the variation in quarterly revenue. A reasonable model is as follows:Predicted Sales abQuarter#cQ1dQ2eQ3 wherea, b,c, d, and e are parameters to estimate.a. Find the values ofa, b,c, d, and e that best fit this model.b. What does your model say
The file P08_30.xlsx contains quarterly revenue for Nike for the years 1991 to 1998. It also contains quarterly “indicator” variables Q1, Q2, and Q3. Here Q1 is 1 for the first quarter of a fiscal year(July–September) and 0 otherwise. Q2 and Q3 are defined similarly for the second and third
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 the divisions is minimized. In other words, the goal is to make the assignments so that teams within
The data from Problem 20, plus the setup times, are listed in the file P08_22.xlsx. Use Evolutionary Solver to find an optimal sequence of jobs.
Repeat Problem 20, but now assume there is a setup time for changing from any job to another job, and this setup time can depend on the jobs. For example, the setup time when changing from job 2 to job 4 can be different from the setup time when changing from job 3 to job
The traveling salesperson problem is notoriously difficult when the number of cities is even of moderate size. The file P08_21.xlsx contains two sheets, one with a distance matrix for a 30-city problem and the other with a distance matrix for a 45-city problem. See whether Evolutionary Solver can
The term churn is common in marketing. It means that a customer switches loyalty to another company. The file P08_19.xlsx contains data on over 3000 customers of a cell phone provider. Columns B through N provide information about the account and usage of each customer, and column O indicates
Continuing the previous problem, determine the portfolio that minimizes the chance that you will lose money during any month, subject to a lower bound constraint on your expected monthly return. (The lower bound will depend on your data. It must not be above the largest average return of your
Visit http://biz.yahoo.com/r/. Under Research Tools, click on Historical Quotes, and then download the monthly returns on at least four stocks for the preceding 60 months. Use this data to determine the portfolio that maximizes the chance of beating the S&P 500 for these years. (Note that the
Which curve provides the better fit? (Hint: You need to use reasonable bounds for the parameters for each curve. For example, L 14.5 is reasonable.)
Sales of a product over time often follow an S-shaped curve. Two functions that yield S-shaped curves are the Pearl (or logistic) curve Y 1 L aebt and the Gompertz curve Y Lebekt Here, Y is annual sales, t is time (in years), L is the upper limit on sales, anda, b, and k are parameters to
Report what you find. Then try Evolutionary Solver. Does it find the correct solution?
(Here, sin(x) is the sine function from trigonometry. You can evaluate it with Excel’s SIN function.) Plot a lot of points from 0 to 30 to see what the graph of this function looks like. Then use GRG Nonlinear Solver to find its maximum. Try the following starting points (and don’t use the
Plot a lot of points from 1 to 7 to see what the graph of this function looks like. Then use GRG Nonlinear Solver to find its maximum. Try the following starting points (and don’t use the Multistart option): 1, 3, 5, 6, and 6.9. Report what you find. Then try Evolutionary Solver. Does it find the
Modify the function in Example 8.1 so that it becomes f (x) (x1)(x2)(x3)(x4)(x5)(x6)(x7)for 1 x
For the aggregate planning example (Example 4.3 in Chapter 4), is it likely that the cost per worker of changing the size of the workforce during a month would be constant (as we assumed)? How could an NLP model account for a situation in which the cost per worker of changing the size of the
For the oil blending example (Example 4.4 in Chapter 4), discuss where you think the assumptions of a linear model are most likely to break down. How might an NLP model look in this situation?
For the product mix examples (Examples 3.1 and 3.2 in Chapter 3), discuss where you think the assumptions of a linear model are most likely to break down.How might an NLP model look in this situation?
J&J has given you $12 million to spend on advertising Huggys diapers during the next 12 months. At the beginning of January, Huggys has a 30% market share.During any month, 10% of the people who purchase Huggys defect to brand X, and a fraction 0.2a12 of customers who usually buy brand X switch to
A firm is planning to spend $75,000 on advertising. It costs $3000 per minute to advertise on television and$1000 per minute to advertise on radio. If the firm buys x minutes of television advertising and y minutes of radio advertising, its revenue in thousands of dollars is given by 0.3x2 0.4y2
Each plant can produce up to 500 units. Each unit produced can be sold for $10. At most 800 widgets can be sold.Determine how Widgetco can maximize its profit.
It costs 125x12 dollars to produce x units at plant 1 and 235x13 dollars to produce x units at plant
Repeat the previous problem, but analyze GE instead of Microsoft.
Given the data in the file Stock Beta.xlsx, estimate the beta (and alpha) for Microsoft (MSFT). Do this for each criterion and each period of time to obtain a table analogous to that in the top right of Figure 7.41. What do you conclude about Microsoft?
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 correlations between the companies’ returns. Note that “return” here means monthly return. (Hint:
The stocks in Example 7.9 are all positively correlated.What happens when they are negatively correlated?Answer for each of the following scenarios. In each case, two of the three correlations are the negatives of their original values. Discuss the differences between the optimal portfolios in
The method for rating teams in Example 7.8 is based on actual and predicted point spreads. This method can be biased if some teams run up the score in a few games. An alternative possibility is to base the ratings only on wins and losses. For each game, you observe whether the home team wins. Then
By the time you are reading this, the 2010–2011 NBA season will have finished, and the results should be available at http://www.basketball-reference.com/leagues/NBA_2010_games.html. Perform a Web query from the Data ribbon to import the scores.(Paste this URL into the Address box and then click
By the time you are reading this, the 2010 NFL season will have finished, and the results should be available at http://www.pro-football-reference.com/years/2010/games.htm. Perform a Web query from the Data ribbon to import the scores. (Paste this URL into the Address box and then click on the
The file P07_31.xlsx contains scores on all of the regular-season games in the NBA for the 2009–2010 basketball season. Use the same procedure as in Example 7.8 to rate the teams. Then sort the teams based on the ratings. Do these ratings appear to be approximately correct? (You might recall that
Keep track of the changing cells and the target cell.Skill-Extending Problem
In Example 7.5, we implied that each of the five observations was from one period of time, such as a particular week. Suppose instead that each is an average over several weeks. For example, the 4.7 million exposures corresponding to one ad might really be an average over 15 different weeks where
In estimating the advertising response function in Example 7.5, we indicated that the sum of squared prediction errors or RMSE could be used as the objective, and we used RMSE. Try using the sum of squared prediction errors instead. Does Solver find the same solution as in the example? Try running
In the peak-load pricing model in Example 7.4, the demand functions have positive and negative coefficients of prices. The negative coefficients indicate that as the price of a product increases, demand for that product decreases. The positive coefficients indicate that as the price of a product
In the peak-load pricing model in Example 7.4, we assumed that the capacity level is a decision variable.Assume now that capacity has already been set at 30 kwh. (Note that the cost of capacity is now a sunk cost, so it is irrelevant to the decision problem.)Change the model appropriately and run
In Example 7.1, two points on the demand curve were given (see Figure 7.10).a. Suppose three additional points are estimated by Madison: (1) demand of 460 when price is $65,(2) demand of 355 when price is $75, and(3) demand of 275 when price is $85. With these new points and the original two
Determine which products the company should produce to maximize its profit, assuming that it will produce exactly enough to meet customer demand. (Hint: Use a binary changing cell for each product and a binary changing cell for each customer segment-product combination. To ensure that a customer
Based on Angel et al. (2003). A fertilizer company is trying to determine the cheapest fertilizer mix that provides desired amounts of nutrients. The mix is made by combining the following fertilizers: SSA, SPO, GUR, TSP, KCI, FERT, and SPF. The mix cannot contain both GUR and TSP. The percentage
This year, the company must begin and complete the five jobs shown in the file P06_79.xlsx during this eightweek period. Arthur Ross employs four full-time accountants who normally work 40 hours per week. If necessary, however, they can work up to 20 hours of overtime per week for which they are
Based on Eaton et al. (1985). Gotham City has been divided into eight districts. The time (in minutes) it takes an ambulance to travel from one district to another is shown in the file P06_78.xlsx. The population of each district (in thousands) is as follows: district 1, 40; district 2, 30;
Heinsco produces tomato sauce at five different plants.The tomato sauce is then shipped to one of three warehouses, where it is stored until it is shipped to one of the company’s four customers. The following inputs for the problem are given in the file P06_61.xlsx:■ The plant capacities (in
Find Pigskin’s optimal production policy if, in addition to the given production and holding costs, there is a fixed cost of $50,000 during any month in which there is positive production. Assume now that storage capacity is 20,000 footballs.
Fruit Computer produces two types of computers: Pear computers and Apricot computers. The relevant data are given in the file P06_52.xlsx. The equipment cost is a fixed cost that is incurred if any of this type of computer is produced. A total of 2000 chips and 1500 hours of labor are available.a.
During a week on a production line, each worker produces the number of units of glue shown in the file P06_51.xlsx. Each week, at least 800 units of glue 1, at least 750 units of glue 2, and at least 100 units of glue 3 must be produced. Determine how to minimize the total cost of meeting weekly
For a week of production, it costs $5000 to set up production line 1 and $4000 to set up production line
Glueco produces three types of glue on two different production lines. Each line can be used by up to 20 workers at a time. Workers are paid $500 per week on production line 1 and $900 per week on production line
A total of 15,000 units of raw material are available. If any product 1 is produced, a setup cost of $20,000 is incurred; if any product 2 is produced, a setup cost of$35,000 is incurred.a. Determine how to maximize the manufacturer’s profit.b. If either of the products is not produced in the
A manufacturer can sell product 1 at a profit of $20 per unit and product 2 at a profit of $40 per unit. Three units of raw material are needed to manufacture one unit of product 1, and six units of raw material are needed to manufacture one unit of product
Set-covering models such as the original Western model in Figure 6.18 often have multiple optimal solutions. See how many alternative optimal solutions you can find. Of course, each must use three hubs because this is optimal. (Hint: Use various initial values in the changing cells and then run
In the last sheet of the file Fixed Cost Manufacturing.xlsx, we illustrated one way to model the Great Threads problem with IF functions that didn’t work. Try a slightly different approach here. Eliminate the binary variables in row 14 altogether, and eliminate the upper bounds in row 18 and the
In the Great Threads model, you found an upper bound on production of any clothing type by calculating the amount that could be produced if all of the resources were devoted to this clothing type.a. What if you instead used a very large value such as 1,000,000 for this upper bound? Try it and see
Make up an example, as described in Problem 8, with 20 possible investments. However, do it so the ratios of NPV to cash requirement are in a very tight range, from 3.0 to 3.2. Then use Solver to find the optimal 306 Chapter 6 Optimization Models with Integer Variables solution when the Solver
The models in this chapter are often called combinatorial models because each solution is a combination of the various 0–1 values, and only a finite number of such combinations exist. For the capital budgeting model in Figure 6.4, there are seven investments, so there are 27 128 possible
Expand and then solve the capital budgeting model in Figure 6.4 so that 20 investments are now possible.You can make up the data on cash requirements, NPVs, and the budget, but use the following guidelines:■ The cash requirements and NPVs for the various investments can vary widely, but the ratio
Does your answer to part a change?
Solve the previous problem using the input data in the file P06_02.xlsx.
In the capital budgeting model in Figure 6.4, we supplied the NPV for each investment. Suppose instead that you are given only the streams of cash inflows from each investment shown in the file P06_01.xlsx.This file also shows the cash requirements and the budget. You can assume that (1) all cash
Unlike the small logistics models presented here, realworld logistics problems can be huge. Imagine the global problem a company like FedEx faces each day.Describe as well as you can the types of decisions and constraints it has. How large (number of changing cells, number of constraints) might
Based on Denardo et al. (1988). Three fires have just broken out in New York. Fires 1 and 2 each require two fire engines, and fire 3 requires three fire engines.The “cost” of responding to each fire depends on the time at which the fire engines arrive. Let tij be the time in minutes when the
After being used, a napkin can be cleaned by one of two methods: fast service or slow service. Fast service costs 50 cents per napkin, and a napkin cleaned via fast service is available for use the day after it is last used. Slow service costs 30 cents per napkin, and these napkins can be reused
Based on Jacobs (1954). The Carter Caterer Company must have the following number of clean napkins available at the beginning of each of the next four days: day 1, 1500; day 2, 1200; day 3, 1800; day 4,
A school system has 16 bus drivers that must cover 12 bus routes. Each driver can cover at most one route.The driver’s bids for the various routes are listed in the file P05_66.xlsx. Each bid indicates the amount the driver will charge the school system to drive that route. How should the drivers
It costs $300 to buy a lawn mower from a lawn supply store. Assume that you can keep a lawn mower for at most five years and that the estimated maintenance cost each year of operation is as follows: year 1, $90;year 2, $135; year 3, $175; year 4, $200; year 5, $250.You have just purchased a new
It costs $8,000 to produce a car at each plant. The costs of shipping a car between various cities are listed in the file P05_56.xlsx. Assume that during a week, at most 75 cars can be shipped from a warehouse to any particular city. Determine how to meet Nash’s weekly demands at minimum cost.
Modify the model so that there must be at least one hour of downtime between consecutive flights.
In the flight-scheduling model, use SolverTable to examine the effect of increasing both the fixed cost per plane and the overnight cost by the same percentage, assuming that the company owns eight planes. Let this percentage vary from 0% to 50% in increments of 10%. Discuss the changes that occur
The required downtime in the crew-scheduling problem is currently assumed to be one hour. Suppose instead that it is required to be two hours. How does the model need to be modified? What is the new optimal solution?
In the crew-scheduling problem, suppose (as in the sensitivity analysis we discussed) that the first Chicago flight, C1, is delayed by two hours—that is, its departure and arrival times move up to 8 A.M. and 10 A.M., respectively. How does the model need to be modified? What is the new optimal
Suppose there is an extra restriction that jobs 1 and 2 must be assigned to different machines.Change the model to accommodate this restriction and find the new optimal solution.
Continuing the previous problem (with capacity 300 at plant 2), suppose you want to see how much extra capacity and extra demand you can add to plant 1 and region 2 (the same amount to each) before the total shipping cost stops decreasing and starts increasing.Use SolverTable appropriately to find
Explain why extra capacity can be valuable even though the company already has more total capacity than it requires.
In the original Grand Prix example, the total capacity of the three plants is 1550, well above the total customer demand. Would it help to have 100 more units of capacity at plant 1? What is the most Grand Prix would be willing to pay for this extra capacity? Answer the same questions for plant 2
Explain why it is problematic to include a constraint such as the following in an LP model for a blending problem:Total octane in gasoline 1 blend Barrels of gasoline 1 blended daily Ú 10
The worker scheduling model in this chapter was purposely made small (only seven changing cells).What would make a similar problem for a company like McDonald’s much harder? What types of constraints would be required? How many changing cells (approximately) might there be?
Based on Dobson and Kalish (1988). Chandler Enterprises produces two competing products, A and B. The company wants to sell these products to two groups of customers. The values each customer places on a unit of A and B are shown in the file P04_123.xlsx. Each customer will buy either product A or
Each processed unit of raw material 2 yields one unit of A and two units of B. The unit prices for the products are A, $5; B, $4; C, $25. The quality levels of each product are A, 8; B, 7; C, 6.The average quality level of the units sold must be at least
Each processed unit of raw material 1 yields two units of A and three units of B. It costs $3 to purchase and process a unit of raw material
It costs $6 to purchase and process one unit of raw material
Bexter Labs produces three products: A, B, and C.Bexter can sell up to 2000 units of product A, up to 2500 units of product B, and up to 800 units of product C. Each unit of product C uses two units of A and three units of B and incurs $5 in processing costs.Products A and B are produced from
Each process 2 run yields 1 ounce of product B and 0.8 ounce of liquid waste. Process 2 incurs $8 in costs. Chemco can dispose of liquid waste in the Port Charles River or use the waste to produce product C or product D. Government regulations limit the amount of waste Chemco is allowed to dump
Each pound of raw material can yield 2 ounces of input 1, requiring 2 hours of processing time and incurring $2 in processing costs.Each pound of raw material can yield 3 ounces of input 2, requiring 2 hours of processing time and incurring $4 in processing costs. Two production processes are
The output from running process 3 for an hour is two barrels of gas 3.Each month, 4000 barrels of crude 1, at $45 per barrel, and 7000 barrels of crude 2, at $55 per barrel, can be purchased. All gas produced can be sold at the following per-barrel prices: gas 1, $85; gas 2, $90;gas 3, $95.
Running process 3 for an hour costs $14 and requires two barrels of crude 2 and three barrels of gas
The output from running process 2 for an hour is three barrels of gas
Running process 2 for an hour costs$30 and requires one barrel of crude 1 and three barrels of crude
The output from running process 1 for an hour is two barrels of gas 1 and one barrel of gas
Sunco Oil has three different processes that can be used to manufacture various types of gasoline. Each process involves blending oils in the company’s catalytic cracker. Running process 1 for an hour costs$20 and requires two barrels of crude oil 1 and three barrels of crude oil
Assume the per-ton cost of holding either product in inventory for one month is $5.a. Determine a minimum cost production schedule for the next four months.b. There is an important aspect of this situation that cannot be modeled by linear programming. What is it? (Hint: If Owens makes product 1 and
A cost of$2000 is incurred each time a new machine is purchased, and a cost of $1000 is incurred if a machine is retired from service. At the end of each month, Owens would like to have at least 50 tons of each product in inventory. At the beginning of month 1, Owens has five machines on line 1 and
Owens-Wheat uses two production lines to produce three types of fiberglass mat. The demand requirements(in tons) for each of the next four months are shown in the file P04_115.xlsx. If it were dedicated entirely to the production of one product, a line 1 machine could produce either 20 tons of type
The production line employees at Grummins Engine work four days a week, 10 hours a day. Each day of the week, the following minimum numbers of line employees are needed: Monday through Friday, 70 employees; Saturday and Sunday, 30 employees.Grummins employs 110 line employees. Determine how to
Based on Smith (1965). Silicon Valley Corporation(Silvco) manufactures transistors. An important aspect of the manufacture of transistors is the melting of the element germanium (a major component of a transistor) in a furnace. Unfortunately, the melting process yields germanium of highly variable
Air conditioners can be produced in either New York or Los Angeles. It takes 1.5 hours of skilled labor to produce an air conditioner in Los Angeles, and it takes 2 hours in New York. It costs $400 to produce an air conditioner in Los Angeles, and it costs $350 in New York. During each month, each
During the next three months, a heating and cooling company must meet (on time) the following demands for air conditioners: month 1, 300; month 2, 400;month 3,
Each processed unit of raw material 2 yields one unit of A and two units of B. The unit prices for the products are A, $5; B, $4; C, $25. The quality levels of each product are: A, 8; B, 7; C, 6.The average quality level of the units sold must be at least
Each processed unit of raw material 1 yields two units of A and three units of B. It costs $3 to purchase and process a unit of raw material
It costs $6 to purchase and process one unit of raw material
Bexter Labs produces three products: A, B, and C.Bexter can sell up to 3000 units of product A, up to 2000 units of product B, and up to 2000 units of product C. Each unit of product C uses two units of A and three units of B and incurs $5 in processing costs.Products A and B are produced from

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