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practical management science

Practical Management Science 5th Edition Wayne L. Winston, Christian Albright - Solutions

In the capital budgeting model in Figure 6.5, investment 4 is tied for the largest ROI, but it is not selected in the optimal solution. How much NPV will be lost if Tatham is forced to select investment 4? Answer by solving a suitably modified model.Figure 6.5: Capital Budgeting Model Н G. 1
Change the capital budgeting model in Figure 6.5 so that 80% of each cost in row 5 is incurred right now, at the beginning of year 1, and the other 20% is incurred a year from now, at the beginning of year 2. You can assume that the NPVs don’t change. The available budget in year 1 is $11.5
Make up an example, as described in the previous problem, with 20 possible investments. However, do it so the ROIs are in a very tight range, such as from 12% to 13%. Then use Solver to find the optimal solution when the Solver Integer Optimality setting is 5%, and record the solution. Next, solve
In the Dorian production model, the optimal solution calls for the minimum number of compact cars and midsize minivans to be produced, but for more than the minimum number of large minivans to be produced. If the large minivans are evidently that profit-able, why doesn’t Dorian discontinue making
As the Dorian production model is currently stated, each vehicle type has a minimum production level; if this type is produced at all, its production quantity must be at least this minimum. Suppose that for large minivans, there is also a maximum production level of 400. If large minivans are
The optimal solution to the Dorian production model appears to be sensitive to the model inputs. For each of the following inputs, create a one-way Solver Table that captures all decision variable cells and the objective cell as outputs. You can choose the ranges of these inputs to make the results
If Solver could handle IF functions correctly, how would you use them in the Dorian production example to create an arguably more natural model—without binary variables? Run Solver on your modified model. Do you get the correct solution? (You will have to use the GRG Nonlinear method.)
In the Dorian production model, suppose that the production quantity of compact cars must either be less than or equal to 100 (a small batch) or greater than or equal to 1000 (a large batch). The same statements hold for the other vehicle types as well, except that the small and large batch limits
Suppose in the Dorian production model that no minimum production limits are placed on the individual vehicle types. However, minimum production limits are placed on all cars and on all minivans. Specifically, if Dorian produces any cars, regardless of size, it must produce at least 1500 cars
In the United Copiers service center model, we assumed that the potential locations of service centers are the same as existing customer locations. Change the model so that the customer locations are the ones given, but the only potential service center locations are in Memphis, Houston, Cleveland,
In the United Copiers service center model, we used total distance traveled as the objective to minimize. Suppose in addition that there is an annual fixed cost of locating a service center in any city, where this fixed cost can vary across cities. There is also a cost per mile of traveling. Modify
In the Green Grass shipping model, we assumed that certain inputs are the same for all plants or plant–customer combinations. Change this so that the unit production cost, the monthly fixed cost, and the monthly capacity can vary by plant, and the unit shipping cost can vary by plant–customer
In the optimal solution to the Green Grass shipping model, the Miami customer’s order is not satisfied. Suppose that Green Grass decides, as a matter of policy, to satisfy each customer’s order (at the customer’s bid price). How much profit will the company lose from this policy decision?
In the Green Grass shipping model, use SolverTable to perform a sensitivity analysis on the fixed cost of opening a plant, letting it vary over some reasonable range that extends below and above the current value of $60,000. Keep track of enough outputs so that you can see the effect on the plants
In the United Copiers service center model, we assumed that a customer is serviced totally by a single service center. Suppose a customer can be serviced partly by multiple service centers. For example, the customer in Denver could get half of its service from Dallas and the other half from San
In the Green Grass shipping model, we assumed that the plants are already built, so that in each month, the only decision is whether to open particular plants (at a monthly fixed cost). Consider instead a general location-shipping model of this type where the plants are not yet built. The company
In the Green Grass shipping model, we currently assume that if a customer’s order is satisfied, it must be satisfied from a single plant. Suppose instead that it can be satisfied from more than one plant. For example, if the company decides to satisfy Dallas’s order, it could ship part of this
In the cutting stock example, we minimized the total number of rolls cut. Do you get the same solution if you minimize the total inches of waste? Solve the problem with this objective.
Woodco sells 3-foot, 5-foot, and 9-foot pieces of lumber. Woodco’s customers demand 25 3-foot boards, 20 5-foot boards, and 15 9-foot boards. Woodco meets its demands by cutting up 17-foot boards. How can it satisfy its customers’ demands with the least amount of waste? Assume that all boards
The Mayfree Appliance Company requires sheet metal for its appliances. The company can purchase long coils of sheet metal in two different widths: 65 inches and 40 inches. The company must purchase the coils by linear foot of length: $1.20 per foot for a 64-inch coil and $1.00 per foot for a
Four projects are available for investment. The projects require the cash flows and yield the net present values (in millions) shown in the file P06_39.xlsx. If $6 million is available now for investment, find the investment plan that maximizes NPV.
You are given a group of possible investment projects for your company’s capital. For each project, you are given the NPV the project would add to the firm, as well as the cash outflow required by each project during each year. Given the information in the file P06_40.xlsx, determine the
You are moving from New Jersey to Indiana and have rented a truck that can haul up to 1100 cubic feet of furniture. The volume and value of each item you are considering moving on the truck are given in the file P06_41.xlsx. Which items should you bring to Indiana?
NASA must determine how many of three types of objects to bring on board the space shuttle. The weight and benefit of each of the items are given in the file P06_42.xlsx. If the space shuttle can carry up to 2600 pounds of items 1 through 3, how many of each item should be taken on the space
Coach Night is trying to choose the starting lineup for the basketball team. The team consists of seven players who have been rated on a scale of 1 (poor) to 3 (excellent) according to their ball handling, shooting, rebounding, and defensive abilities. The positions that each player is allowed to
To graduate from Southeastern University with a major in operations research (OR), a student must complete at least two math courses, at least two OR courses, and at least two computer courses. Some courses can be used to fulfill more than one requirement: Calculus can fulfill the math requirement;
The Cubs are trying to determine which of the following free-agent pitchers should be signed: Rick Sutcliffe (RS), Bruce Sutter (BS), Dennis Eckersley (DE), Steve Trout (ST), or Tim Stoddard (TS). (Feel free to substitute your own set of players for these “old” guys.) The cost of signing each
Because of excessive pollution on the Momiss River, the state of Momiss is going to build some pollution control stations. Three sites are under consideration. Momiss is interested in controlling the pollution levels of two pollutants. The state legislature requires that at least 80,000 tons of
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 2. A total of 15,000 units of raw
A company is considering opening warehouses in four cities: New York, Los Angeles, Chicago, and Atlanta. Each warehouse can ship 10,000 units per week. The weekly fixed cost of keeping each warehouse open is $40,000 for New York, $50,000 for Los Angeles, $30,000 for Chicago, and $25,000 for
The TightBond company 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 2. For a week of production, it costs $5000 to set up production line 1
Avion 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
A product can be produced on four different machines. Each machine has a fixed setup cost, variable production cost per unit processed, and a production capacity, given in the file P06_53.xlsx. A total of 2000 units of the product must be produced. Determine how to minimize the total cost.
Consider the Pigskin example (Example 3.3) from Chapter 3. 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
McPherson Publishers is considering publishing five textbooks. The maximum number of copies of each textbook that can be sold, the variable cost of producing each textbook, the selling price of each textbook, and the fixed cost of a production run for each book are given in the file P06_55.xlsx.
Toshovo Computer owns four production plants at which computer workstations are produced. The company can sell up to 20,000 computers per year at a price of $3500 per computer. For each plant, the production capacity, the production cost per computer, and the fixed cost of operating a plant for a
Eastinghouse sells air conditioners. The annual demand for air conditioners in each region of the country is as follows: East, 100,000; South, 150,000; Midwest, 110,000; and West, 90,000. Eastinghouse is considering building its air conditioners in four different cities: New York, Atlanta, Chicago,
During the next five periods, the demands listed in the file P06_58.xlsx must be met on time. At the beginning of period 1, the inventory level is 0. During each period when production occurs, a setup cost of $2500 and a per-unit production cost of $20 are incurred. At the end of each period, a
At a machine tool plant, five jobs must be completed each day. The time it takes to do each job depends on the machine used to do the job. If a machine is used at all, a setup time is required. The relevant times (in minutes) are given in the file P06_59.xlsx.a. Determine how to minimize the sum of
Bertallo Classic 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
Eight jobs need to be completed. Each job can be completed on any of six machines, and each machine can complete any number of jobs. If a machine is assigned to at least one job, the setup time listed in the file P06_62.xlsx is required. (All times are in hours.) The time required for each machine
Based on Walker (1974). The Smalltown Fire Department currently has seven conventional ladder companies and seven alarm boxes. The two closest ladder companies to each alarm box are listed in the file P06_63.xlsx. The town council wants to maximize the number of conventional ladder companies that
State University must purchase 1100 computers from three vendors. Vendor 1 charges $500 per computer plus a total delivery charge of $5000. Vendor 2 charges $350 per computer plus a total delivery charge of $4000. Vendor 3 charges $250 per computer plus a total delivery charge of $6000. Vendor 1
At Blair General Hospital, six types of surgical operations are performed. The types of operations each surgeon is qualified to perform (indicated by an X) are listed in the file P06_65.xlsx. Suppose that surgeons 1 and 2 dislike each other and cannot be on duty at the same time. Determine the
Spencer Electric ships 12,000 capacitors per month to its customers. The capacitors can be produced at three different plants. The production capacity, fixed monthly cost of operation, and variable cost of producing a capacitor at each plant are given in the file P06_66.xlsx. The fixed cost for a
Based on Liggett (1973). A court decision has stated that the enrollment of each high school in Metropolis must be at least 20% black. The numbers of black students and white students in each of the city’s five school districts are listed in the file P06_67.xlsx. The distance (in miles) that a
Based on Westerberg, Bjorklund, and Hultman (1977). Newcor’s steel mill has received an order for 150 tons of steel. The steel must be 5% carbon and 5% molybdenum by weight. The steel is manufactured by combining three types of metal: steel ingots, scrap steel, and alloys. Four individual steel
Based on Boykin (1985). Thompson Chemicals produces 359 million pounds of the chemical maleic anhydride annually. A total of four reactors are available to produce maleic anhydride. Each reactor can be run on one of three settings. The cost (in thousands of dollars) and pounds produced (in
Based on Zangwill (1992). Murray Manufacturing runs a day shift and a night shift. Regardless of the number of units produced, the only production cost during a shift is a setup cost. It costs $8000 to run the day shift and $4500 to run the night shift. Demand for the next two days is as follows:
Based on Fitzsimmons and Allen (1983). The State of Texas frequently audits companies doing business in Texas. Because these companies often have headquarters located outside the state, auditors must be sent to out-of-state locations. Each year, auditors must make 500 trips to cities in the
Suppose you own 11 bronze coins worth a total of $150, 11 silver coins worth a total of $160, and 11 gold coins worth a total of $170. Develop a linear integer model to find a combination of coins worth exactly $110.
Cousin Bruzie of radio station WABC schedules radio commercials in 60-second blocks. This hour, the station has sold time for commercials of 15, 16, 20, 25, 30, 35, 40, and 50 seconds. Determine the minimum number of 60-second blocks of commercials that must be scheduled to fit in all the current
Based on Bean et al. (1988). Simon’s Mall has 10,000 square feet of space to rent and wants to deter-mine the types of stores that should occupy the mall. The minimum number and maximum number of each type of store (along with the square footage of each type) are given in the file P06_74.xlsx.
Indiana University’s Business School has two rooms that seat 50 students, one room that seats 100 students, and one room that seats 150 students. Classes are held five hours a day. At present, the four types of requests for rooms are listed in the file P06_75.xlsx. The business school must decide
Based on Efroymson and Ray (1966). Stonecutters is a new bakery chain that sells bread to customers throughout the state of Indiana. Stonecutters is considering building bakeries in three locations: Evansville, Indianapolis, and South Bend. Each bakery can bake up to 900,000 loaves of bread each
On Monday morning, you have $3000 in cash on hand. For the next seven days, the following cash requirements must be met: Monday, $5000; Tuesday, $6000; Wednesday, $9000; Thursday, $2000; Friday, $7000; Saturday, $2000; Sunday, $3000. At the beginning of each day, you must decide how much money (if
Based on Eaton et al. (1985). The city of Springfield 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,
Arthur Ross, Inc., must complete many corporate tax returns during the period February 15 to April 15. This year, the company must begin and complete the five jobs shown in the file P06_79.xlsx during this eight-week period. Arthur Ross employs four full-time accountants who normally work 40 hours
Based on Muckstadt and Wilson (1968). PSI believes it will need the amounts of generating capacity (in millions of kwh) shown in the file P06_80.xlsx during the next five years. The company has a choice of building (and then operating) power plants with the capacities (in millions of kwh) and costs
Newsome Construction is considering erecting three office buildings. The time (in years) required to complete each of them and the number of workers required to be on the job at all times are shown in the file P06_81.xlsx. After a building is completed, it brings in the following amount of rent per
Four trucks are available to deliver milk to five grocery stores. The capacity and daily operating cost of each truck are shown in the file P06_82xlsx. The demand of each grocery store can be supplied by only one truck, but a truck can deliver to more than one grocery. The daily demands of each
A county is going to build two hospitals. There are nine cities in which the hospitals can be built. The number of hospital visits per year made by people in each city and the x-y coordinates of each city are listed in the file P06_83.xlsx. The county’s goal is to minimize the total distance that
It is currently the beginning of year 1. Gotham City is trying to sell municipal bonds to support improvements in recreational facilities and highways. The face values of the bonds and the due dates at which principal comes due are listed in the file P06_84.xlsx. (The due dates are the beginnings
Based on Spencer et al. (1990). When you lease 800 phone numbers from AT&T for telemarketing, AT&T uses an optimization model to tell you where you should locate calling centers to minimize your operating costs over a 10-year horizon. To illustrate the model, suppose you are considering
State University is scheduling 24 sections of a large computer skills course in the Fall semester. There are eight time slots for these sections, four on Monday/ Wednesday (MW) and four on Tuesday/Thursday (TR). In each time slot, three sections are scheduled. These are shown in the file
Hoosier Power needs to determine a capacity expansion plan to meet Bloomington’s power needs for the next 20 years. The current capacity is 5000 kwh. The demand for the current year is 4000 kwh, and demand is expected to increase by 1000 kwh in each succeeding year. At the beginning of each year,
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 can-not contain both GUR and TSP. The percentage
Sam is in his final year of college and is trying to schedule his courses for the year. He has narrowed his search to 16 courses, each of which is offered in at least one time slot (out of a possible five time slots) in each semester. The file P06_89.xlsx lists the courses and when they are
A medical supply company has customers in eight cities. It is trying to decide how many salespeople it needs to service these customers. Each salesperson needs to be located in one of the eight cities and needs to be assigned to a subset of the customers. For example, the company might base a
You are scheduling company interviews at the annual university career fair. Five interview rooms are avail-able. Interviews are conducted from 9 am to 5 pm. Each company wants all of its interviews conducted in a single room. The time preferences for the companies are listed in the file
This problem is based on Motorola’s online method for choosing suppliers. Suppose Motorola solicits bids from five suppliers for eight products. The list price for each product and the quantity of each product that Motorola needs to purchase during the next year are listed in the file
Specialty Software is considering 10 projects. The years each project will be developed, the number of programmers needed each year for each project, and the revenue (exclusive of labor costs) from each project are listed in the file P06_94.xlsx. For example, project 1, if undertaken, will require
You are moving away from Bloomington and need to load a truck. The items that will go on the truck must all be packed in boxes. The size (in cubic feet) of each item and each available box are listed in the file P06_95.xlsx. For example, the first item requires 87 cubic feet, and the first box can
Based on McBride and Zufryden (1988). A company is trying to determine which of five possible products to include in its product line. The fixed cost of producing each product and the unit profit for each product are listed in the file P06_96.xlsx. There are five customer segments. The number of
Suppose that you want to divide a state containing 12 cities into five congressional districts. How might you use IP to assign cities to districts?
An insurance company has hired you to determine the number of sales divisions into which the country should be divided. Each division will need a president, a vice president, and a divisional staff. The time needed to call on a client will depend on the distance of the salesperson from the client.
Ten different types of brownies are sold. You are thinking of developing a new brownie for sale. Brownies are rated on the basis of five qualities: price, chocolate flavor, chewiness, sweetness, and ease of preparation. You want to group the 10 brownies on the market into three clusters. Each
Telco, a national telemarketing firm, usually picks a number of sites around the country from which it makes its calls. As a service, AD&D’s telecommunication marketing department wants to help Telco choose the number and location of its sites. How can IP be used to approach this problem?
Solve the following modifications of the capital budgeting model in Figure 6.5. (Solve each part independently of the others.)a. Suppose that at most two of projects 3, 5, and 6 can be selected.b. Suppose that if investment 5 is selected, then investment 1 must also be selected.c. Suppose that at
How difficult is it to add nodes and arcs to an existing shortest path model? Answer by adding a new node, node 11, to Maude’s network. Assume that node 11 is at the top of the network, geographically, with double-arrowed arcs joining it to nodes 2, 5, and 7 with distances 45, 22, and 10. Assume
You have been assigned to ensure that each high school in the Indianapolis area is racially balanced. Explain how you would use a network model to help attain this goal.
You want to start a campus business to match compatible male and female students for dating. How would you use the models in this chapter to help you run your business?
A company produces several products at several different plants. The products are then shipped to two warehouses for storage and are finally shipped to one of many customers. How would you use a network flow model to help the company reduce its production and distribution costs? Pay particular
You have put four valuable paintings up for sale. Four customers are bidding for the paintings. Customer 1 is willing to buy two paintings, but each other customer is willing to purchase at most one painting. The prices that each customer is willing to pay are given in the file P05_81.xlsx.
Kellwood, a company that produces a single product, has three plants and four customers. The three plants will produce 3000, 5000, and 5000 units, respectively, during the next time period. Kellwood has made a commitment to sell 4000 units to customer 1, 3000 units to customer 2, and at least 3000
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, 600. After being used, a napkin can be cleaned by one of two methods: fast service or slow
In the original RedBrand problem, suppose that the company could add up to 100 tons of capacity, in increments of 10 tons, to any single plant. Use SolverTable to determine the yearly savings in cost from having extra capacity at the various plants. Assume that the capacity will cost $28,000 per
Based on Ravindran (1971). A library must build shelving to shelve 200 4-inch-high books, 600 8-inch-high books, and 500 12-inch-high books. Each book is 0.5 inch thick. The library has several ways to store the books. For example, an 8-inch-high shelf can be built to store all books of height less
Eight students need to be assigned to four dorm rooms at Faber College. Based on incompatibility measurements, the cost incurred for any pair of students rooming together is shown in the file P05_76.xlsx. How should the students be assigned to the four rooms to minimize the total amount of
At present, 40,000 long-distance calls must be routed from New York to Los Angeles (L.A.), and 30,000 calls must be routed from Philadelphia to L.A. On route to L.A. from Philadelphia or New York, calls are sent through Indianapolis or Cleveland, then through Dallas or Denver, and finally to L.A.
Ewing Oil has oil fields in San Diego and Los Angeles. The San Diego field can produce up to 500,000 barrels per day, and the Los Angeles field can produce up to 400,000 barrels per day. Oil is sent from the fields to a refinery, either in Dallas or in Houston. (Assume that each refinery has
Rework the previous problem under the assumption that Galveston has a refinery capacity of 150,000 barrels per day and Mobile has a refinery capacity of 180,000 barrels per day.Data from Previous Problem:In Problem 55, assume that before being shipped to Los Angeles or New York, all oil produced at
In Problem 55, assume that before being shipped to Los Angeles or New York, all oil produced at the wells must be refined at either Galveston or Mobile. To refine 1000 barrels of oil costs $5780 at Mobile and $6250 at Galveston. Assuming that both Mobile and Galveston have infinite refinery
Bloomington has two hospitals. Hospital 1 has four ambulances, and hospital 2 has two ambulances. Ambulance service is deemed adequate if there is only a 10% chance that no ambulance will be available when an ambulance call is received by a hospital. The average length of an ambulance service call
There are 15 jobs that must be done by 10 employees. Each job must be done by a single employee, and each employee can do at most two jobs. The times (in minutes) for the employees to do the jobs are listed in the file P05_70.xlsx, where blanks indicate disallowed assignments.a. Assuming that not
Based on Glover and Klingman (1977). The government has many computer files that must be merged frequently. For example, consider the Survey of Current Income (SCI) and the Consumer Price Service (CPS) files, which keep track of family income and family size. The breakdown of records in each file
Referring to the previous problem, suppose that Allied Freight can purchase and ship extra units to either warehouse for a total cost of $100 per unit and that all customer demand must be met. Determine how to minimize the sum of purchasing and shipping costs.Data from Previous Problem:Allied
Allied Freight supplies goods to three customers, who each require 30 units. The company has two ware-houses. In warehouse 1, 40 units are available, and in warehouse 2, 30 units are available. The costs of shipping one unit from each warehouse to each customer are shown in the file P05_67.xlsx.
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
Three professors must be assigned to teach six sections of finance. Each professor must teach two sections of finance, and each has ranked the six time periods during which finance is taught, as shown in the file P05_65.xlsx. A ranking of 10 means that the professor wants to teach at that time, and

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