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practical management science
Practical Management Science, Revised 3rd Edition Wayne L Winston, S. Christian Albright - Solutions
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 1, 500 units of product 2, and 300 units of product 3 will be demanded. The cost and space taken up
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 who are qualified to teach history and science have applied for jobs, and each of these 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 review(method 1), confirmations (method 2), or test of subsequent collections (method 3). The three
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 determined by cholesterol and sodium level. Three types of dinners are under consideration. The pairwise
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 have assessed the pairwise comparison matrix for the three objectives in the file P09_30.xlsx.
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: cost, starting salary for graduates, and ambience of school(can we party there?). Your pairwise
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 matrices shown in the file P09_28.xlsx.a. How would you rank these investments?b. Now suppose another
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 matrix for these objectives is shown in the file P09_27.xlsx. Three people (Chris, Jamie, and Pat)
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 comparison matrix for these objectives is shown in the file P09_26.xlsx.Three computers are being considered
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 comparison matrix for these objectives as shown in the file P09_25.xlsx. The administration has compared
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 return. Do it the opposite way. That is, calculate the efficient frontier by maximizing the
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, with a lower bound constraint on the NPV obtained. What lower bounds should you use? Do you get the
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 for each type of car depends on the prices of the three types of cars, also given in this file. In
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 producing the product is $6. Construct a trade-off curve between the objectives of maximizing profit and
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 spent the whole day producing each type of product is given in the file P09_20.xlsx. The company is
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 overtime labor purchased) for each type of widget are given in the file P09_19.xlsx. At present, 200
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 fill up to 100 orders per year. Six different types of orders must be filled during the coming year.
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 shown in the file P09_17.xlsx. The Marines available to fill these jobs have been classified into six
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 dollars)of the project; (2) the annual growth rate in sales generated by the project; (3) the
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 costs).■ Goal 2: Cut spending by at most $150 billion.■ Goal 3: Raise at most $550 billion in
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 system.■ Project 4: Buy a new lathe and deburring system.■ Project 5: Institute an FMS (Flexible
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 maintenance cost (in thousands of dollars) for each facility, and the land (in thousands of square feet)
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 consideration: golf courses, swimming pools, gymnasiums, and tennis courts. Six sites are under consideration. If
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 employees. Each fulltime employee is paid $6 per hour for work up to 40 hours per week and can sell 5
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 has set the following goals in order of importance:■ Goal 1: Each quarter’s demand should be met
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 out-of-state applicants with a given SAT score who plan to be business or nonbusiness majors. For example,
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 (North and South) are listed in the file P09_09.xlsx. The Bloomington Board of Education needs to
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 each teacher in teaching each course is given in the file P09_08.xlsx.Each teacher can teach a total
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 100 hours. At present, the firm consists of 5 partners, 5 senior employees, and 5 junior employees,
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 file P09_06.xlsx. Deancorp needs to produce 100 pounds of sausage and has set the following goals,
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 falls short of this goal. A total of 32 hours of labor are available. A$2 penalty is incurred for
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 player requires 1 square yard. The sale of a TV earns Hiland a profit of $150, and each DVD player
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 mediocre. During the coming year, Fruit needs 5000 excellent chips, 3000 good chips, and 1000 mediocre
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 priority):■ Goal 1: At most $100,000 per year should be spent on ambulance service.■ Goal 2: Average
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 of ambulances assigned to district i, i 1,
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 distinguishes the customers who switch to another company from those who stay loyal to your
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 number of positions in which the two strings differ. For example, the distance between the strings
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 number).For example, in the file P08_42.xlsx, we compared the similarity of 10 banks and found banks 5 and
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 of each attribute, then customer 1 will not buy the product because he values the current product at
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 analysis used in marketing research), our analysts have divided the market into five segments (labeled as
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 weight in the furnace. The furnace can handle up to 1000 pounds at a time. Jobs 6 and 7 (size 640 and
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 in the file P08_37.xlsx. The Democrats control the state legislature, so they can redistrict as they
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 sales of copiers in each major market (Boston, New York, Philadelphia, Washington, Providence, and
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 a disk drive, there is a significant reduction in the speed at which the data are retrieved. To
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 who wants to take the bus will walk to the closest bus stop.a. If the goal is to minimize the total
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 thousands of kwh), the operating cost, the startup cost, and the shutdown cost (all costs 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 to estimate.a. Find the values ofa, b,c, d, and e that best fit this model.b. What does your model
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 year (July–September)and 0 otherwise. Q2 and Q3 are defined similarly for the second and third
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 coordinates of each city are listed in the file P08_29.xlsx. To minimize the total distance that patients
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 the file P08_28.xlsx.How would you assign these students to rooms?
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 time labor are available. Up to 40 hours of overtime labor can be purchased each week at a cost of
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 given in file P08_25.xlsx. For example, job 8 requires 3 units of capacity on a machine for 2 hours. At
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 divisions is minimized.In other words, we want to make the assignments so that teams within a division
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 willing to pay up to $8 for an item, and seller 1 is willing to accept $9 or more for an item. This means
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 job 2 to job 4 can be different from the setup time when changing from job 3 to job
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 a machine.Here is one version of the problem. There are 10 jobs to perform on a single machine.
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 problem and the other with a distance matrix for a 45-city problem. See whether Evolutionary Solver can
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 owners and 0 for others). Use these data to develop a rule for predicting whether a family is a
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 1%.
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 find)and determine the portfolio that maximizes the chance of beating the S&P 500 for those years.
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 annual sales, t is time (in years), L is the upper limit on sales, anda, b, and k are parameters to
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 an (unknown) upper limit on adoptions, and a and b are parameters to be estimated. The file
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) that can be used to determine how advertising influences sales.
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 compartment 1, and product 3 in compartment
(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 the standard nonlinear Solver to find its maximum.Try the following starting points: 1, 6, 15, 20, and
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 6.9.Report what you find. Then try Evoluationary Solver.Does it get the correct solution?
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 could an NLP model account for a situation in which the cost per worker of changing the size of the
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 swimming is the quickest way to reach the swimmer?
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 to make the travel distance between cities A and B as small as possible?Can you generalize this
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 salesperson will sell $0, $5000, or $50,000 worth of brushes. The probability of each sales amount
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 permitted.) The company can choose the number of units of raw material that are purchased and processed.
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 month.
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 accurate. Suppose that the actual probability of next summer being rainy is 0.6. (For simplicity, we
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 extracts x2 million barrels during year 2, each barrel can be sold for 85 x2 dollars. The cost of
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 of a year is worth$1.12 at the end of the year. The means are E(R1) 0.14, E(R2) 0.11, and E(R3)
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 deviations are 0.20, 0.30, and 0.40.The correlation between stocks 1 and 2 is 0.65, between stocks 1
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 7.41). Town 1 averages 20 fires per year; town 2, 30 fires; town 3, 40 fires; and town 4, 25 fires. The
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 people who purchase Huggys defect to brand X, and a fraction 0.2a12 of customers who usually buy
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 advertising and y minutes of radio advertising, its revenue in thousands of dollars is given by 2x2 y2 xy
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 file P07_56.xlsx.a. To maximize its sales revenue, how much money should Beerco spend in each
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 product 1 and $72 to produce a unit of product
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 will pay 200 q dollars for each widget. If the two manufacturers want to collude in an attempt to
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 the hospital?
In the previous problem, what is the minimum-cost method of producing 100 machines? (Ignore the$10,000 budget constraint.)
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