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practical management science
Questions and Answers of
Practical Management Science
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
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
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
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.
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
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
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.
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,
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
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
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
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
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
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
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
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,
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
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
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
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
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
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
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.
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
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
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
Based on Hansen and Wendell (1982). During the month of July, Pittsburgh resident Bill Fly must make four round-trip flights between Pittsburgh and Chicago. The dates of the trips are shown in the
Powerhouse produces capacitors at three locations: Los Angeles, Chicago, and New York. Capacitors are shipped from these locations to public utilities in five regions of the country: northeast (NE),
Delko is considering hiring people for four types of jobs. The company would like to hire the number of people listed in the file P05_62.xlsx for each type of job. Delko can hire four types of
At the beginning of year 1, a new machine must be purchased. The cost of maintaining a machine, depending on its age, is given in the file P05_61.xlsx. The cost of purchasing a machine at the
Suppose it costs $20,000 to purchase a new car. The annual operating cost and resale value of a used car are shown in the file P05_60.xlsx. Assume that you presently have a new car. Determine a
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:
Edsel Motors produces cars in Detroit and Dallas. The Detroit plant can produce up to 8500 cars, and the Dallas plant can produce up to 4000 cars. Producing a car costs $2000 in Detroit and $1800 in
Nash Auto has two plants, two warehouses, and three customers. The plants are in Detroit and Atlanta, the warehouses are in Denver and New York, and the customers are in Los Angeles, Chicago, and
Sunco Oil produces oil at two wells. Well 1 can produce up to 150,000 barrels per day, and well 2 can produce up to 200,000 barrels per day. It is possible to ship oil directly from the wells to
A company manufactures widgets at two factories, one in Memphis and one in Denver. The Memphis factory can produce up to 150 widgets per day, and the Denver factory can produce up to 200 widgets
A company is taking bids on four construction jobs. Three contractors have placed bids on the jobs. Their bids (in thousands of dollars) are given in the file P05_52.xlsx. (A blank indicates that the
Based on Machol (1970). A swimming coach is putting together a relay team for the 400-meter relay. Each swimmer must swim 100 meters of breaststroke, backstroke, butterfly, or freestyle, and each
Five employees are available to perform four jobs. The time it takes each person to perform each job is given in the file P05_50.xlsx. Determine the assignment of employees to jobs that minimizes the
Touche Young has eight auditors. Each can work up to 160 hours during the next month, during which time six projects must be completed. The hours required for each project and the amounts each
The Amorco Oil Company controls two oil fields. Field 1 can produce up to 20 million barrels of oil per day, and field 2 can produce up to 15 million barrels of oil per day. At field 1, it costs
The 7th National Bank has two check-processing sites. Site 1 can process 10,000 checks per day, and site 2 can process 6000 checks per day. The bank processes three types of checks: vendor, salary,
The government is auctioning off oil leases at two sites. At each site, 100,000 acres of land are to be auctioned. Cliff Ewing, Blake Barnes, and Alexis Pickens are bidding for the oil. Government
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_45.xlsx. Each bid
You are trying to help the MCSCC (Monroe County School Corporation) determine the appropriate high school district for each housing development in Bloomington. For each development, you are given the
A truck must travel from New York to Los Angeles. As shown in Figure 5.44, several routes are available. The number associated with each arc is the number of gallons of fuel required by the truck to
The town of Busville has three school districts. The numbers of black students and white students in each district are shown in the file P05_42.xlsx. The Supreme Court requires the schools in
One rather unrealistic assumption in the flight-scheduling model is that a given plane can fly two consecutive flights with no downtime. For example, it could fly flight 5903 that gets into
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
In the flight-scheduling model, use SolverTable to examine the effect of decreasing all net revenues by the same percentage, assuming that the company owns six planes. Let this percentage vary from
We illustrated how a machine replacement problem can be modeled as a shortest path problem. This is probably not the approach most people would think of when they first see a machine replacement
In the VanBuren machine replacement problem, suppose the company starts with a machine that is eight quarters old at the beginning of the first quarter. Modify the model appropriately, keeping in
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, we assumed that the maintenance cost and salvage values are linear functions of age. Suppose instead that the maintenance cost increases by 50% each
Continuing the previous problem, suppose again that all arcs go in both directions, but suppose Maude’s objective is to find the shortest path from node 1 to node 7 (not node 10). Modify the
In Maude’s shortest path problem, suppose all arcs in the current network from higher-numbered nodes to lower-numbered nodes, such as from node 6 to node 5, are disallowed. Modify the spreadsheet
In Maude’s shortest path problem, suppose all arcs in the network are double-arrowed, that is, Maude can travel along each arc (with the same distance) in either direction. Modify the spreadsheet
Expand the RedBrand two-product spreadsheet model so that there are now three products competing for the arc capacity. You can make up the required input data.
In the original RedBrand problem, we assume a constant arc capacity, the same for all allowable arcs. Modify the model so that each arc has its own arc capacity. You can make up the required arc
When we (the authors) originally developed the bus route assignment model, we included an arc capacity constraint: Flow #1. After giving this further thought, we deleted this constraint as being
In the optimal solution to the bus route assignment problem, company 2 is assigned to bus routes 6 and 7. Suppose these two routes are far enough apart that it is infeasible for one company to
In the optimal solution to the machine-to-job assignment problem, jobs 3 and 4 are assigned to different machines. Suppose there is an extra restriction that these jobs must be assigned to the same
In the optimal solution to the machine-to-job assignment problem, jobs 1 and 2 are both assigned to machine 4. Suppose there is an extra restriction that jobs 1 and 2 must be assigned to different
We modeled the bus route assignment problem with the alternative form of the transportation model (as in Figure 5.8). Model it instead with the standard form (as in Figure 5.3). Discuss the pros and
Modify the bus route assignment model, assuming that company 1 decides to place bids on routes 7 and 8 (in addition to its current bids on other routes). The bids on these two routes are $5200 and
In the machine-to-job assignment problem, the current capacities of the machines are 1, 2, 1, 2, and 1. If you could increase one of these capacities by 1, which would you increase? Why?
Modify the machine-to-job assignment model under the assumption that only three of the four jobs must be completed. In other words, one of the four jobs does not have to be assigned to any machine.
One possible solution method for the machine-to-job assignment problem is the following heuristic procedure. Assign the machine to job 1 that completes job 1 quickest. Then assign the machine to job
1. Find the optimal March shipment schedule and its total transportation cost for each of the following:a. Cottonb. Polyesterc. Silk2. The company will be opening a silk-making department in the
In the current blending model, a barrel of any input results in a barrel of output. However, in a real blending problem, there can be losses. Suppose a barrel of input results in only a fraction of a
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
Rylon Corporation manufactures Brute cologne and Chanelle perfume. The raw material needed to manufacture each type of fragrance can be purchased for $60 per pound. Processing 1 pound of raw
A large CPA firm currently has 100 junior staff members and 20 partners. In the long run–say, 20 years from now–the firm would like to consist of 130 junior staff members and 20 partners. During
Based on Rothstein (1973). The Springfield City Police Department employs 30 police officers. Each officer works five days per week. The crime rate fluctuates with the day of the week, so the number
Mondo Motorcycles is determining its production schedule for the next four quarters. Demands for motorcycles are forecasted to be 400 in quarter 1; 700 in quarter 2; 500 in quarter 3; and
The HiTech company produces Blu-Ray disc players. Estimated demands for the next four quarters are 5000, 10,000, 8000, and 2000. At the beginning of quarter 1, HiTech has 60 workers. It costs $2000
An oil company produces gasoline from five inputs. The cost, density, viscosity, and sulfur content, and the number of barrels available of each input are listed in the file P04_78.xlsx. Gasoline
A company produces two products: A and B. Product A sells for $11 per unit and product B sells for $23 per unit. Producing a unit of product A requires two hours on assembly line
Carrington Oil produces gas 1 and gas 2 from two types of crude oil: crude 1 and crude 2. Gas 1 is allowed to contain up to 4% impurities, and gas 2 is allowed to contain up to 3% impurities.
Candy Kane Cosmetics (CKC) produces Leslie Perfume, which requires chemicals and labor. Two production processes are available. Process 1 transforms one unit of labor and two units of chemicals into
Based on Heady and Egbert (1964). Walnut Orchard has two farms that grow wheat and corn. Because of differing soil conditions, there are differences in the yields and costs of growing crops on the
At the beginning of year 1, you have $10,000. Investments A and B are available; their cash flows are shown in the file P04_62.xlsx. Assume that any money not in-vested in A or B earns interest at an
A furniture company manufactures tables and chairs. A table requires 40 board-feet of wood, and a chair requires 30 board-feet of wood. Wood can be purchased at a cost of $1.50 per board-foot,
Hiland’s Appliances stocks laptops, TVs, refrigerators, microwave ovens, and ranges. These products compete for floor space, tie up different amounts of capital, and have different profit margins.
Young MBA Erica Cudahy can invest up to $15,000 in stocks and loans. Each dollar invested in stocks yields $0.10 profit, and each dollar invested in a loan yields $0.15 profit. At least 30% of all
Sunblessed Juice Company sells bags of oranges and cartons of orange juice. Sunblessed grades oranges on a scale of 1 (poor) to 10 (excellent). At present, Sunblessed has 100,000 pounds of grade
You have decided to enter the candy business. You are considering producing two types of candies: Slugger candy and Easy Out candy, both of which consist solely of sugar, nuts, and chocolate. At
NewAge Pharmaceuticals produces the drug NasaMist from four chemicals. Today, the company must produce 1000 pounds of the drug. The three active ingredients in NasaMist are A, B, and C. By weight, at
During each four-hour period, the Smalltown police force requires the following number of on-duty police officers: eight from midnight to 4 a.m.; seven from 4 a.m. to 8 a.m.; six from 8 a.m. to
A bus company believes that it will need the following numbers of bus drivers during each of the next five years: 60 drivers in year 1; 70 drivers in year 2; 50 drivers in year 3; 65 drivers in
You have been commissioned by Indiana University to evaluate the relative efficiency of four degree-granting units: Business, Education, Arts and Sciences, and Health, Physical Education, and
You have been asked to evaluate the efficiency of the Port Charles Police Department. Three precincts are to be evaluated. The inputs and outputs for each precinct are as follows:■ Input 1 = number
The Salem Board of Education wants to evaluate the efficiency of the town’s four elementary schools. The three outputs of the schools are■ Output 1 = average reading score■ Output 2 = average
Pine Valley Bank has three branches. You have been asked to evaluate the efficiency of each. The following inputs and outputs are to be used for the study:■ Input 1 = labor hours used (hundreds per
The pension fund model is streamlined, perhaps too much. It does all of the calculations concerning cash flows in row 20. James decides he would like to break these out into several rows of
In the pension fund model, suppose James has been asked to see how the optimal solution changes if the required payments in years 6 to 15 all increase by the same percentage, where this percentage
In the pension fund model, suppose there is a fourth bond, bond 4. Its unit cost in year 1 is $1020, it returns coupons of $70 in years 2 to 5 and a payment of $1070 in year 6. Modify the model to
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