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practical management science

Questions and Answers of Practical Management Science

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 120 units of glue 1, at least 150 units of glue 2, and at least
For a week of production, it costs $1000 to set up production line 1 and $2000 to set up production line
Glueco produces three types of glue on two different production lines. Each line can be used by up to seven workers at a time. Workers are paid $500 per week on production line 1 and $900 per week on
A company is considering opening warehouses in four cities: New York, Los Angeles, Chicago, and Atlanta.Each warehouse can ship 100 units per week. The weekly fixed cost of keeping each warehouse
A total of 120 units of raw material are available. If any product 1 is produced, a setup cost of $10 is incurred; if any product 2 is produced, a setup cost of $20 is incurred.a. Determine how to
A manufacturer can sell product 1 at a profit of $2 per unit and product 2 at a profit of $5 per unit. Three units of raw material are needed to manufacture 1 unit of product 1, and 6 units of raw
Because of excessive pollution on the Momiss River, the state of Momiss is going to build some pollution control stations. Three sites (1, 2, and 3) are under consideration. Momiss is interested in
Based on Sonderman and Abrahamson (1985). In treating a brain tumor with radiation, physicians want the maximum amount of radiation possible to bombard the tissue containing the tumors. The
Based on Bean et al. (1987). Boris Milkem’s firm owns six assets. The expected selling price (in millions of dollars) for each asset is given in the file P06_45.xlsx. For example, if asset 1 is
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
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
I am 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 I am considering moving on the truck are given in
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
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.
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? For example, given the solution in Figure 6.28, this
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
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
In the Green Grass shipping model, we assumed that certain inputs (see the range B4:B7 in Figure 6.24) are the same for all plants or plant–customer combinations.Change this so that the unit
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
How hard is it to expand a set-covering model to accommodate new cities? Answer this by modifying the model in Figure 6.18. (See the file LocatingHubs2.xlsx.)Add several cities that must be served:
Set-covering models such as the original Western model in Figure 6.15 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 6.15, 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 original Western set-covering model in Figure 6.15, we assumed that each city must be covered by at least one hub. Suppose that for added flexibility in flight routing, Western requires that
Modify the model appropriately and use Solver to find the optimal solution.
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
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.
In the Great Threads model, we 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.
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
Modify the model as necessary and use Solver to find the new optimal solution.How do you know that the current optimal solution is not optimal for the modified model?
If large minivans are produced, the production level must be from 200 to
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
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 SolverTable that captures all changing cells and
In the optimal solution to the Great Threads model, no pants are produced. Suppose Great Threads has an order for 300 pairs of pants that must be produced.Modify the model appropriately and use
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.
Make up an example, as described in Problem 7, with 20 possible investments. However, do it so the ratios of NPV to cash requirement are in a very tight range, from 3 to 3.2. Then use Solver to find
The models in this chapter are often called combinatorial models because each solution is a combination of the various 0’s and 1’s, and only a finite number of such combinations exist. For the
Does your answer to part a change?Skill-Extending Problems
Suppose in the capital budgeting model in Figure 6.1 that each investment requires $2000 during year 2, and only $5000 is available for investment during year 2.a. Assuming that available money
Expand and then solve the capital budgeting model in Figure 6.1 so that 20 investments are now possible.You can make up the data on cash requirements, NPVs, and the budget, but use the following
As it currently stands, investment 7 in the capital budgeting model in Figure 6.1 has the lowest ratio of NPV to cash requirement, 2.5. Keeping this same ratio, can you change the cash requirement
In the capital budgeting model in Figure 6.1, investment 4 has the largest ratio of NPV to cash requirement, but it is not selected in the optimal solution.How much NPV will be lost if Tatham is
Solve Problem 2 with the extra assumption that the investments can be grouped naturally as follows: 1–4, 5–8, 9–12, 13–16, and 17–20.a. Find the optimal investments when at most one
Solve the previous problem using the input data in the file P06_03.xlsx.
In the capital budgeting model in Figure 6.1, 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
Solve the following modifications of the capital budgeting model in Figure 6.1. (Solve each part independently of the others.)a. Suppose that at most two of projects 1 through 5 can be selected.b.
In the crew-scheduling model in Example 5.7, there are only two cities. Suppose there are more than two cities. Is it possible to modify the network approach appropriately? Discuss how you would do
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),
I 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
Both customers 3 and 4 also want to buy as many of the remaining units as possible. The profit associated with shipping a unit from each plant to each customer is given in the file P05_80.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
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 4 days:day 1, 1500; day 2, 1200; day 3, 1800; day 4,
In the original RedBrand problem (Example 5.4), 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
Based on Ravindran (1971). A library must build shelving to shelve 200 4-inch-high books, 100 8-inchhigh books, and 80 12-inch-high books. Each book is 0.5 inch thick. The library has several ways to
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, 500 long-distance calls must be routed from New York to Los Angeles (L.A.), and 400 calls must be routed from Philadelphia to L.A. On route to L.A. from Philadelphia or New York, calls
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.
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 available
Based on Evans (1984). Currently, State University can store 200 files on hard disk, 100 files in computer memory, and 300 files on tape. Users want to store 300 word-processing files, 100
Let the “cost” of merging an SCI record with a CPS record be ISCI ICPS FSSCI FSCPS where ISCI and ICPS are the incomes from the SCI and CPS records, and FSSCI and FSCPS are the family
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
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.
We 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, we are given the
A truck must travel from New York to Los Angeles. As shown in Figure 5.46, 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_62.xlsx. The Supreme Court requires the schools in
It costs $200 to buy a lawn mower from a lawn supply store. Assume that I can keep a lawn mower for at most 5 years and that the estimated maintenance cost each year of operation is as follows: year
Suppose it costs $10,000 to purchase a new car. The annual operating cost and resale value of a used car are shown in the file P05_59.xlsx. Assume that you presently have a new car. Determine a
Each year, Data Corporal produces up to 400 computers in Boston and up to 300 computers in Raleigh. Los Angeles customers must receive 400 computers, and 300 computers must be supplied to Austin
Fordco produces cars in Detroit and Dallas. The Detroit plant can produce up to 6500 cars, and the Dallas plant can produce up to 6000 cars. Producing a car costs $2000 in Detroit and $1800 in
It costs $10,000 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 50 cars can be shipped from
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
General Ford produces cars in Los Angeles and Detroit and has a warehouse in Atlanta. The company supplies cars to customers in Houston and Tampa.The costs of shipping a car between various points
Widgetco 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 per
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 dash indicates that the
Based on Machol (1970). Doc Councilman 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 three auditors. Each can work up to 160 hours during the next month, during which time three projects must be completed. Project 1 takes 130 hours, project 2 takes 140 hours, and
The Amorco Oil Company controls two oil fields.Field 1 can produce up to 40 million barrels of oil per day, and field 2 can produce up to 50 million barrels of oil per day. At field 1, it costs
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 rules state that no bidder can receive more than 40% of the
The government is auctioning off oil leases at two sites: 1 and
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,
In the crew-scheduling model, there are exactly as many flights departing from Chicago as departing from New York. Suppose more flights are departing from one city than from the other. How would you
Modify the model so that there must be at least 1 hour of downtime between consecutive flights.
One rather unrealistic assumption in the flightscheduling 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 8
In the crew-scheduling problem, suppose that two extra flights are added to the current list. The first leaves Chicago at 11 A.M. and arrives in New York at 2 P.M. The second leaves New York at 6
The required downtime in the crew-scheduling problem is currently assumed to be 1 hour. Suppose we instead require it to be 2 hours. How does the model need to be modified? What is the new optimal
In the crew-scheduling problem, suppose (as in the sensitivity analysis we discussed) that the first Chicago flight, C1, is delayed by 2 hours—that is, its departure and arrival times move up to 8
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 instead that the company imposes no upper
Does the new optimal solution go through node 11?
Assume that Maude’s objective is still to get from node 1 to node
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,
Is it the same as before? Should you have known the answer to this question before making any changes to the original model? Explain.
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
Consider a modification of the original RedBrand problem where there are N plants, M warehouses, and L customers. Assume that the only allowable arcs are from plants to warehouses and from warehouses
In the RedBrand problem with shrinkage, change the assumptions. Now instead of assuming that there is some shrinkage at the warehouses, assume that there is shrinkage in delivery along each route.
How difficult is it to expand the original RedBrand model? Answer this by adding a new plant, two new warehouses, and three new customers, and modify the spreadsheet model appropriately. You can make
In the RedBrand two-product problem, we assumed that the unit shipping costs are the same for both products. Modify the spreadsheet model so that each product has its own unit shipping costs. You can
Continuing the previous problem, make the problem even more general by allowing upper bounds (arc capacities)and lower bounds for the flows on the allowable arcs. Some of the upper bounds can be very

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