Questions and Answers of Practical Management Science

A printing shop receives an average of one order per day. The average length of time required to complete an order is half a day. At any given time, the print shop can work on at most one job.
The file P14_02.xlsx contains five years of monthly data on sales (number of units sold) for a particular company. The company suspects that except for random noise, its sales are growing by a
1. Determine whether you can develop a more accurate estimate of overhead costs.2. Wagner is now preparing a bid for an important order that may involve a considerable amount of repeat business. The
The file P14_03.xlsx contains monthly data on production levels and production costs during a four-year period for a company that produces a single product. Use simple regression on all of the data
Management of a home appliance store wants to understand the growth pattern of the monthly sales of a new technology device over the past two years. The managers have recorded the relevant data in
Do the sales prices of houses in a given community vary systematically with their sizes (as measured in square feet)? Answer this question by estimating a simple regression equation where the sales
The file P14_07.xlsx contains monthly values of the U.S. national debt (in dollars) from 1993 to early 2010. Fit an exponential growth curve to these data. Write a short report to summarize your
The management of a technology company is trying to determine the variable that best explains the variation of employee salaries using a sample of 52 full-time employees; see the file P14_08.xlsx.
We have discussed linear and exponential trend lines. Another popular choice is a power trend line, also called a constant elasticity trend line. This trend line has the form y = axb, and it has the
Sometimes curvature in a scatter plot can be fit adequately (especially to the naked eye) by several trend lines. We discussed the exponential trend line, and the power trend line is discussed in the
Suppose you are an analyst for a company that produces four products, and you are trying to decide how much of each product to produce next month. To model this decision problem, you need the unit
A trucking company wants to predict the yearly maintenance expense (Y) for a truck using the number of miles driven during the year (X1) and the age of the truck (X2, in years) at the beginning of
An antique collector believes that the price received for a particular item increases with its age and with the number of bidders. The file P14_14.xlsx contains data on these three variables for 32
Stock market analysts are continually looking for reliable predictors of stock prices. Consider the problem of modeling the price per share of electric utility stocks (Y). Two variables thought to
Suppose that a regional express delivery service company wants to estimate the cost of shipping a package (Y) as a function of cargo type, where cargo type includes the following possibilities:
The owner of a restaurant in Bloomington, Indiana, has recorded sales data for the past 19 years. He has also recorded data on potentially relevant variables. The data are listed in the file
The file P14_19.xlsxcontains the weekly sales of a particular brand of paper towels at a supermarket for a one-year period.a. Using a span of 3, forecast the sales of this product for the next 10
You have been assigned to forecast the number of aircraft engines ordered each month by Commins Engine Company. At the end of February, the forecast is that 100 engines will be ordered during April.
Simple exponential smoothing with α = 0.3 is being used to forecast sales of digital cameras at Lowland Appliance. Forecasts are made on a monthly basis. After August camera sales are observed, the
A version of simple exponential smoothing can be used to predict the outcome of sporting events. To illustrate, consider pro football. We first assume that all games are played on a neutral field.
Management of a home appliance store would like to understand the growth pattern of the monthly sales of Blu-ray disc players over the past two years. Managers have recorded the relevant data in the
A small computer chip manufacturer wants to forecast monthly ozperating costs as a function of the number of units produced during a month. The company has collected the 16 months of data in the
The file P14_35.xlsx contains the amount of money spent advertising a product (in thousands of dollars) and the number of units sold (in millions) for eight months.a. Assume that the only factor
When potential workers apply for a job that requires extensive manual assembly of small intricate parts, they are initially given three different tests to measure their manual dexterity. The ones who
Callaway Golf is trying to determine how the price of a set of clubs affects the demand for clubs. The file P14_37.xlsx contains the price of a set of clubs (in dollars) and the monthly sales
The file P14_38.xlsx lists the average salary for each Major League Baseball team from 2004 to 2009, along with the number of team wins in each of these years.a. Rearrange the data so that there are
GMC wants to decide whether to retool the Lyra and Libra plants. In addition, GMC wants to determine its production plan at each plant in the coming year. Based on the previous data, formulate a MILP
During 2001, many European markets for mobile phones reached saturation. Because of this, mobile phone operators started to shift their focus from growth and market share to cut-ting costs. One way
1. Using the spreadsheet model from Case 2.1 as a starting point, use Solver to find the optimal set of projects to approve. The solution should maximize the total NPV from the approved projects, and
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
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
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
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
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 Solver Table that captures all decision variable
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
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
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.
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
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
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,
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
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 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, 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
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
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.
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
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
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
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
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
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
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
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).
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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:
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,
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
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
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
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
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
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
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
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
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
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,
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
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
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
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
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

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