Unlike the small logistics models presented here, real-world 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 decision variable cells, number of constraints) might such a problem be?
> 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 constraint is, however, that there is a maximum amount of radiat
> 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 thes
> 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. For example, if asset 1 is sold in year 2, the firm receives $20 million. To maintain a regular cas
> To graduate from Southeastern University with a major in operations research (OR), a student must complete at least three math courses, at least three OR courses, and at least two computer courses. Some courses can be used to fulfill more than one requir
> The payback of a project is the number of years it takes before the project’s total cash flow is positive. Payback ignores the time value of money. It is interesting, however, to see how differing assumptions on project growth impact payback. Suppose, fo
> 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. T
> 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. If the space shuttle can carry up to 2000 pounds of items 1 through 3, how many of each item should be taken on the s
> 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. Which items should you bring to Indiana?
> 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 t
> Solve the following modifications of the capital budgeting model. 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 least one of i
> Four projects are available for investment. The projects require the cash flows and yield the net present values (in millions) shown in the file. If $6 million is available now for investment, find the investment plan that maximizes NPV.
> 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: $1.20per foot for a
> A company sells 3-foot, 5-foot, and 9-foot pieces of lumber. The company’s customers demand 25 3-foot boards, 20 5-foot boards, and 15 9-foot boards. The company meets its demands by cutting up 17-foot boards. How can it satisfy its customers’ demands wi
> 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.
> 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 Da
> A software company is considering translating its program into French. Each unit of the program sells for $50 and incurs a variable cost of $10 to produce. Currently, the size of the market for the product is 300,000 units per year, and the English versi
> 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 wher
> 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 servic
> 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
> 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 comp
> 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 s
> Solve Problem 1 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 investment from each group can be selected. b. Find the optimal investm
> 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
> 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
> How hard is it to expand a set-covering model to accommodate new cities? Answer this by modifying the model. Add several cities that must be served: Memphis, Dallas, Tucson, Philadelphia, Cleveland, and Buffalo. You can look up the distances from these c
> Set-covering models such as the original Western model 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.
> Consider a project with the following cash flows: year 1, 2$400; year 2, $200; year 3, $600; year 4, 2$900; year 5, $1000; year 6, $250; year 7, $230. Assume a discount rate of 15% per year. a. Find the project’s NPV if cash flows occur at the ends of th
> In the original Western set-covering model, we assumed that each city must be covered by at least one hub. Suppose that for added flexibility in flight routing, Western requires that each city must be covered by at least two hubs. How do the model and op
> In the original Western set-covering model, 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 these fixed costs can possibly vary across cities. Make up some reasonabl
> 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 s
> 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,
> In the last sheet of the file Fixed Cost Manufacturing Finished.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 altogethe
> 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. What if you instead used a very large value such as 1,0
> Solve the problem 1 using the input data in the file P06_02.xlsx. Data from Problem 1: In the capital budgeting model in Figure 6.5, we supplied the NPV for each investment. Suppose instead that you are given only the streams of cash inflows from each i
> 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?
> 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 t
> 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 product
> Assume the demand for a company’s drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost $16x. Each unit of Wozac is sold for $3. Each
> 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 profita
> 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 Solver to find the new optimal solution. (Is it enough to p
> 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 solution when the amount of available cloth increases from it
> 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. Constrain these quantities to be integers and then run S
> Referring to the previous problem, if it is optimal for the company to produce sweatshirts, use SolverTable to see how much larger the fixed cost of sweatshirt machinery would have to be before the company would not produce any sweatshirts. However, if t
> How difficult is it to expand the Great Threads model to accommodate another type of clothing? Answer by assuming that the company can also produce sweatshirts. The rental cost for sweatshirt equipment is $1100; the variable cost per unit and the selling
> 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 I
> 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 6.5, there are seven investm
> In the capital budgeting model in Figure 6.5, we supplied the NPV for each investment. Suppose instead that you are given only the streams of cash inflows from each investment. This file also shows the cash requirements and the budget. You can assume th
> Modify the original Grand Prix example as follows. Increase the demands at the regions by 200 each, so that total demand is well above total plant capacity. This means that some demands cannot be supplied. Suppose there is a unit penalty cost at each reg
> A bond is currently selling for $1040. It pays the amounts listed in the file at the ends of the next six years. The yield of the bond is the interest rate that would make the NPV of the bond’s payments equal to the bond’s price. Use Excel’s Goal Seek to
> What is the relationship between transportation models and more general logistics models? Explain how these two types of linear optimization models are similar and how they are different.
> “It is essential to constrain all shipments in a transportation problem to have integer values to ensure that the optimal LP solution consists entirely of integer-valued shipments.” Is this statement true or false? Why?
> 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 a network model to help you run your business?
> 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 p
> 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 p
> Kellwood, a company that produces a single product, has three plants and four customers. The three plants will produce 6000, 4000, and 5000 units, respectively, during the next time period. Kellwood has made a commitment to sell 3000 units to customer 1,
> Modify the original Grand Prix example as follows. Increase the demands at the regions by 200 each, so that total demand is well above total plant capacity. However, now interpret these “demands” as “maximum sales,” the most each region can accommodate,
> 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 o
> The yield of a chemical reaction is defined as the ratio (expressed as a percentage) of usable output to the amount of raw material input. Suppose the yield of a chemical reaction depends on the length of time the process is run and the temperature at wh
> 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. Assu
> Based on Ravindran (1971). A library must build shelving to shelve 200 4-inch-high books, 600 8-inchhigh 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 ca
> 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. How should the students be assigned to the four rooms to mini
> 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 th
> 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 600,000 barrels per day. Oil is sent from the fields to a refinery, either in Dallas or in H
> 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.
> 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
> 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
> 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
> 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 incr
> A company manufacturers a product in the United States and sells it in England. The unit cost of manufacturing is $50. The current exchange rate (dollars per pound) is 1.221. The demand function, which indicates how many units the company can sell in Eng
> In the Quality Sweaters model, the range E9:E11 does not have a range name. Open your completed Excel file and name this range Costs. Then look at the formula in cell E12. It does not automatically use the new range name. Modify the formula so that it do
> 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
> 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
> Allied Freight supplies goods to three customers. The company has two warehouses. The warehouse availabilities, the customer requirements, and the unit shipping costs from warehouses to customers are shown in the file. There is a penalty for each unsatis
> 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.
> 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 t
> 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 file P05_64.xlsx. Bill must purchase four round-trip tick
> 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), northwest (NW), midwest (MW), southeast (SE), and south
> 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 eight types of people. Each type is qualified to perform two or more types
> 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 beginning of each year is given in this same file. There is no
> Suppose it costs $30,000 to purchase a new car. The annual operating cost and resale value of a used car are shown in the file. Assume that you presently have a new car. Determine a replacement policy that minimizes your net costs of owning and operating
> Assume that the number of units sold of a product is given by 100 2 0.5P 1 26√A, where P is the price (in dollars) charged for the product and A is the amount spent on advertising (in thousands of dollars). Each unit of the product costs $5 to produce. U
> Here is a problem to challenge your intuition. In the original Grand Prix example, reduce the capacity of plant 2 to 300. Then the total capacity is equal to the total demand. Run Solver on this model. You should find that the optimal solution uses all c
> 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;
> Each year, Data Corporal produces up to 10,000 computers in Boston and up to 6000 computers in Charlotte. There are customers in Los Angeles, New York, and Seattle who must receive 5300, 6700, and 3300 computers, respectively. Producing a computer costs
> 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 Dallas. Cars must be shipped to 12 cities. The costs of
> 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 Philadelphia. Cars are produced at plants, then shipped to
> 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 Sunco’s customers in Los Angeles and New York. Alternativel
> 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 are listed in the file P05_54.xlsx, where a blank means
> 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 per day. The company are shipped by air to customers in Los
> 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 contractor did not bid on the given job.) Contractor 2
> 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 swimmer can swim only one race. The coach believes that ea
> The file gives the annual sales for Microsoft (in millions of dollars) for the years 1984–1993, where 1984 = year 1. a. Fit an exponential curve to these data. b. Assuming you are back in 1993, by what percentage do you estimate that Microsoft has grown
> 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 total time required to perform the four jobs. (A blank
> In the Grand Prix example with varying tax rates, the optimal solution uses all available plant capacity and more than satisfies customer demands. Will this always be the case? Experiment with the unit selling prices and/or tax rates to see whether the c
> 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 auditor can be billed for each project are given in the file
> The Amorco Oil Company controls two oil fields. Field 1 can produce up to 22 million barrels of oil per day, and field 2 can produce up to 19 million barrels of oil per day. At field 1, it costs $42.50 to extract and refine a barrel of oil; at field 2 th
> 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, and personal. The processing cost per check depends on t
> The government is auctioning off oil leases at two sites. At each site, 150,000 acres of land are to be auctioned. Cliff Ewing, Blake Barnes, and Alexis Pickens are bidding for the oil. Government rules statethat no bidder can receive more than 45% of th
> 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 indicates the amount the driver will charge the school system
