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practical management science

Questions and Answers of Practical Management Science

Stockco fills orders for three products for a local warehouse.Stockco must determine how many of each product should be ordered at the beginning of the current month. This month, 400 units of product
The Pine Valley Board of Education must hire teachers for the coming school year. The types of teachers and the salaries that must be paid are given in the file P09_33.xlsx. For example, 20 teachers
Based on Lin et al. (1984). You have been hired by Arthur Ross to determine which of the following accounts receivable methods should be used in an audit of the Keating Five and Dime Store: analytic
A consumer is trying to determine which type of frozen dinner to eat. She considers three attributes to be important: taste, nutritional value, and price. Nutritional value is considered to be
You are trying to determine which of two secretarial candidates (John or Sharon) to hire. The three objectives that are important to your decision are personality, typing ability, and intelligence.
You are trying to determine which MBA program to attend. You have been accepted at two schools: Indiana and Northwestern. You have chosen three attributes to use in helping you make your decision:
In determining where to invest your money, two objectives, expected rate of return and degree of risk, are considered to be equally important. Two investments(1 and 2) have the pairwise comparison
You are ready to select your mate for life and have determined that physical attractiveness, intelligence, and personality are key factors in selecting a satisfactory mate. Your pairwise comparison
Your company is about to purchase a new PC. Three objectives are important in determining which computer you should purchase: cost, user friendliness, and software availability. The pairwise
Each professor’s annual salary increase is determined by his or her performance in three areas: teaching, research, and service to the university. The administration has assessed the pairwise
Referring to the portfolio optimization example from Chapter 7 (see Example 7.9), we constructed the efficient frontier by minimizing portfolio variance, with a lower bound constraint on the expected
In the capital budgeting example from Chapter 6 (see Example 6.1), we maximized NPV for a given budget.Now find a trade-off curve for NPV versus budget.Specifically, minimize the amount invested,
GMCO produces three types of cars: compact, medium, and large. The variable cost per car and production capacity (per year) for each type of car are given in the file P09_22.xlsx. The annual demand
If a company spends a on advertising (measured in thousands of dollars) and charges a price of p dollars per unit, then it can sell 1000 10p 20a12 units of the product. The cost per unit of
Plantco produces three products. Three workers work for Plantco, and the company must determine which product(s) each worker should produce. The number of units each worker would produce if he or she
Widgetco produces two types of widgets. Each widget is made of steel and aluminum and is assembled with skilled labor. The resources used and the per-unit profit contribution (ignoring cost of
Based on Vasko et al. (1987). Bethlehem Steel can fill orders using five different types of steel molds. Up to three different molds of each type can be purchased.Each individual mold can be used to
Based on Klingman and Phillips (1984). The Marines need to fill three types of jobs in two cities (Los Angeles and Chicago). The numbers of jobs of each type that must be filled in each city are
The HAL computer must determine which of eight research and development (R&D) projects to undertake.For each project, four quantities are of interest:(1) the net present value (NPV, in millions of
A new president has just been elected and has set the following economic goals (listed from highest to lowest priority):■ Goal 1: Balance the budget (this means revenues are at least as large as
A small aerospace company is considering eight projects:■ Project 1: Develop an automated test facility.■ Project 2: Bar code all inventory and machinery.■ Project 3: Introduce a CAD/CAM
The amounts of available land (in thousands of square feet) at sites 2 through 5 are given in the file P09_13.xlsx. The cost of building each facility (in thousands of dollars), the annual
Other facilities can be built at sites 2 through
Based on Taylor and Keown (1984). Gotham City is trying to determine the type and location of recreational facilities to build during the next decade. Four types of facilities are under
Lucy’s Music Store at present employs 5 full-time employees and 3 part-time employees. The normal workload is 40 hours per week for full-time employees and 20 hours per week for part-time
Globots can be produced by regular-time labor or by overtime labor. Production capacity (number of globots) and production costs during the next 4 quarters are shown in the file P09_11.xlsx. Wivco
During the next 4 quarters, Wivco faces the following demands for globots: quarter 1, 13; quarter 2, 14;quarter 3, 12; quarter 4,
Based on Lee and Moore (1974). Faber College is admitting students for the class of 2007. Data on its applicants are shown in the file P09_10.xlsx. Each row indicates the number of in-state or
The city of Bloomington has 17 neighborhoods. The number of high school students in each neighborhood and the time required to drive from each neighborhood to each of the city’s two high schools
There are 4 teachers in the Faber College Business School. Each semester, 200 students take each of the following courses: Marketing, Finance, Production, and Statistics. The “effectiveness” of
Based on Welling (1977). The Touche Young accounting firm must complete three jobs during the next month. Job 1 will require 500 hours of work, job 2 will require 300 hours, and job 3 will require
Based on Steuer (1984). Deancorp produces sausage by blending beef head, pork chuck, mutton, and water.The cost per pound, fat per pound, and protein per pound for these ingredients are listed in the
Each week, Stockco produces two products. Relevant information for each product is shown in the file P09_05.xlsx. Stockco has a goal of $48 in weekly profit and incurs a $1 penalty for each dollar it
Hiland Appliance must determine how many TVs and DVD players to stock. It costs Hiland $300 to purchase a TV and $200 to purchase a DVD player. ATV requires 3 square yards of storage space, and a DVD
Fruit Computer Company is ready to make its annual purchase of computer chips. Fruit can purchase chips(in lots of 100) from three suppliers. Each chip’s quality is rated as excellent, good, or
The average time(in minutes) it takes for an ambulance to respond to a call from district 1 is 40 3x1; for district 2, the time is 50 4x2. Gotham City has three goals (listed in order of
Gotham City must determine how to allocate ambulances during the next year. It costs $5000 per year to run an ambulance. Each ambulance must be assigned to one of two districts. Let xi be the number
For each set of priorities of goals, solve the Burnit problem and verify that the values in Figure 9.7 are correct.
Your company sells credit card services, and you are concerned with churn. (Churn occurs when your customers go to a different company.) Describe how you could use discriminant analysis to learn what
Based on Meneses et al. (2004). A string is a list of characters such as “1differ%”. The length of the string is the number of characters in the string. The distance between two strings is the
A common approach to clustering is called multidimensional scaling (MDS). To apply MDS, we rank each pair of objects we want to cluster from least similar(higher number) to most similar (lower
You are going to sell two types of electric razors.Design a product line that maximizes the number of market segments that will buy your product. For example, if you design a product that is level 2
Assume that a consumer’s purchase decision on an electric razor is based on four attributes, each of which can be set at one of three levels (1, 2, or 3). Using conjoint analysis (a type of
Steelco needs to cool 17 pieces of steel. The weight and due date for each piece are listed in the file P08_38.xlsx. Processing and cooling a batch in the furnace takes 5 minutes regardless of the
You are the Democratic campaign manager for the state of Indiana. There are 15 cities in the state of Indiana.The numbers of Democrats and Republican voters in these cities (in thousands) are listed
Xerox is trying to determine how many maintenance centers are needed in the mid-Atlantic states. Xerox earns $500 profit (excluding the cost of running maintenance centers) on each copier sale. The
Ten data sets must be assigned for storage to one of three disk drives. Each disk drive can store 885 MB.The sizes of the data sets (in MB) are listed in the file P08_35.xlsx. When many people access
We assume that town k is |k – j| miles from town j. The numbers of people in the towns who want to take the bus each hour are listed in the file P08_34.xlsx. Bus 99 will make two stops and anyone
Bus 99 serves towns 1 through
During the next 12 months, the amounts of electric power needed (in thousands of kwh) are listed in the file P08_33.xlsx. This power can be supplied using four generators. The generating capacity (in
We would like to build a quantitative model to explain the variation in quarterly revenue. A reasonable model is as follows:Predicted Sales abQuarter#cQ1dQ2eQ3 wherea, b,c, d, and e are parameters
The file P08_30.xlsx contains quarterly revenue for Nike for the years 1991 to 1998. It also contains quarterly“indicator” variables Q1, Q2, and Q3. Here Q1 is 1 for the first quarter of a fiscal
Cook County needs to build two hospitals. There are nine cities where the hospitals can be built. The number of hospital visits made annually by the inhabitants of each city and the x and y
Eight students need to be assigned to four dorm rooms (two students to a room) at Faber College. Based on incompatibility measures, the “cost” incurred if two students room together is shown in
Nine jobs need to be completed within 8 weeks.The number of weeks required to complete each job is given in the file P08_26.xlsx. For example, job 2 requires 3 weeks. Each week, 160 hours of regular
Fourteen jobs must be assigned to one of three identical machines. The goal is to minimize the total time needed to complete all 14 jobs. The machine capacities and times needed for the jobs are
The 30 teams in the NBA are each assigned to one of 6 divisions, where each division has 5 teams. Suppose we want to assign the teams to divisions so that the average distance among teams in the
You are operating a web site to match up sellers and buyers of a product. 35 sellers and 35 buyers have input their reservation prices, as listed in the file P08_23.xlsx.For example, buyer 1 is
The data from the previous problem, plus the setup times, are listed in the file P08_22.xlsx. Use Evolutionary Solver to find an optimal sequence of jobs.
Repeat the previous problem, but now assume there is a setup time for changing from any job to another job, and this setup time can depend on the jobs. For example, the setup time when changing from
An important problem in operations management is the job sequencing problem. Actually, there are many versions of this problem, but they all basically attempt to find the proper sequencing of jobs on
The traveling salesperson problem is notoriously difficult when the number of cities is even of moderate size. The file P08_20.xlsx contains two sheets, one with a distance matrix for a 30-city
The file P08_19.xlsx contains the following information for a random sample of 24 U.S. families: income(in thousands of dollars), lawn size (in thousands of square feet), and Group (1 for rider mower
For data in the file P08_17.xlsx, develop a rule to predict whether a person is likely to purchase our lasagna product. What variables appear to be the most useful?
For the data in the file P08_16.xlsx, develop a classification rule to classify students as likely admits, likely rejects, or borderline.
Continuing the previous problem, determine the portfolio that minimizes the chance that you will lose money during any month, subject to the constraint that your expected monthly return is at least
Visit http://www.yahoo.com. Under Finance, then Stock Research, and finally Historical Quotes, download the monthly returns on any four stocks for years 2000 to 2005 (or as recent a period as you can
Sales of a product over time often follow an S-shaped curve. Two functions that yield S-shaped curves are the Pearl (or logistic) curve Y 1 L aebt and the Gompertz curve Y Lebekt Here, Y is
The adoption level of a new product often can be modeled as an S-shaped curve called the Pearl (or logistic)curve. The equation of this curve is Y 1 L aebt where Y is the adoption level, L is
The file P08_10.xlsx contains data on annual advertising(per capita) and annual unit sales (per capita) in different regions of the country. Determine an Sshaped curve as described by equation (8.1)
If this cost is sufficiently small, does the company ever produce fewer than seven models in week 1 and allow some week 1 pickups to be unsatisfied?
In the lawn mower production problem in Example 8.4, experiment with the penalty cost for unsatisfied pickups in week
Modify the model appropriately, and then use Evolutionary Solver to find the new optimal solution. (Hint: Add a penalty to the objective for violating these new constraints.)
In the truck-loading problem in Example 8.3, we assumed that any product could be loaded into any compartment.Suppose the following are not allowed: product 1 in compartment 2, product 2 in
(Here, sin(x) is the sine funtion from trigonometry. You can evaluate it with Excel’s SIN function.) Plot a lot of points from 0 to 30 to see what the graph of this function looks like. Then use
Modify the function in Example 8.1 so that it becomes f (x) x sin(x) for 0 x
Plot a lot of points from 1 to 7 to see what the graph of this function looks like. Then use the standard nonlinear Solver to find its maximum.Try the following starting points: 1, 3, 5, 6, and
Modify the function in Example 8.1 so that it becomes f (x) (x1)(x2)(x3)(x4)(x5)(x6)(x7)for 1 x
For the SureStep aggregate planning example(Example 4.3 in Chapter 4), is it likely that the cost per worker of changing the size of the workforce during a month would be constant (as we assumed)?How
For the Chandler Oil blending example (Example 4.4 in Chapter 4), discuss where you think the assumptions of a linear model are most likely to break down.How might an NLP model look in this situation?
For the product mix example (Example 3.2 in Chapter 3), discuss where you think the assumptions of a linear model are most likely to break down. How might an NLP model look in this situation?
I can swim 2 miles per hour and run 6 miles per hour.I am walking north along South Beach and see someone drowning 0.5 mile out in the ocean and 1 mile north of me. What combination of running and
City B is 10 miles downstream from city A. City A is 5 miles south of the river, and city B is 20 miles north of the river. The river is 2 miles wide. Where should we build a bridge across the river
Based on Grossman and Hart (1983). A salesperson for Fuller Brush has three options: (1) quit, (2) put forth a low effort level, or (3) put forth a high effort level. Suppose for simplicity that each
If x1 units of product 1 are produced, they can be sold at 25 x1 dollars per unit. If x2 units of product 2 are produced, they can be sold at 14 x2 dollars per unit. (Negative prices are not
A company uses raw material to produce two products. For $15, a unit of raw material can be purchased and processed into four units of product 1 and two units of product
The cost of producing x units of a product during a month is x12 dollars. Show that the minimumcost method of producing 40 units during the next 2 months is to produce all 40 units during a single
Suppose that we are hiring a weather forecaster to predict the probability that next summer will be rainy or sunny. The following suggests a method that can be used to ensure that the forecaster is
Oilco must determine how many barrels of oil to extract during each of the next 2 years. If Oilco extracts x1 million barrels during year 1, each barrel can be sold for 80 x1 dollars. If Oilco
I have $1000 to invest in three stocks. Let R1 be the random variable representing the annual return on $1 invested in stock i. For example, if Ri 0.12, then $1 invested in stock i at the beginning
Consider three investments. You are given the following means, standard deviations, and correlations for the annual return on these three investments. The means are 0.12, 0.15, and 0.20.The standard
Monroe County is trying to determine where to place the county fire station. The locations of the county’s four major towns are as follows: (10, 20), (60, 20),(40, 30), and (80, 60) (see Figure
Proctor and Ramble has given you $12 million to spend on advertising Huggys diapers during the next 12 months. At the beginning of January, Huggys has a 30% market share. During any month, 10% of the
A firm is planning to spend $10,000 on advertising. It costs $3000 per minute to advertise on television and$1000 per minute to advertise on radio. If the firm buys x minutes of television
Beerco has $100,000 to spend on advertising in four markets. The sales revenue (in thousands of dollars)that can be created in each market by spending xi thousand dollars in market i is given in the
How many units of each product should the company produce, and what prices should it charge, to maximize its profit?
A company manufactures two products. If it charges price pi for product i, it can sell qi units of product i, where q1 60 3p1 p2 and q2 80 2p2 p1. It costs $25 to produce a unit of
Two firms are producing widgets. It costs the first firm q1 2 dollars to produce q1 widgets and the second firm 0.5q2 2 dollars to produce q2 widgets. If a total of q widgets are produced, consumers
The cost per day of running a hospital is 200,000 0.002x2 dollars, where x is the number of patients served per day. What number of patients served per day minimizes the cost per patient of running
In the previous problem, what is the minimum-cost method of producing 100 machines? (Ignore the$10,000 budget constraint.)

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