A manufacturing company produces products 1, 2, and 3. The three products have the following resource requirements and produce the following profit:
At present the firm has a daily labor capacity of 240 available hours and a daily supply of 400 pounds of material. The general linear programming formulation for this problem is as follows :
Management has developed the following set of goals, arranged in order of their importance to the firm:
Formulate a goal programming model to determine the number of each product to produce to best satisfy the goals.
In Problem 15 in Chapter 6, Computers Unlimited sells microcomputers and distributes them from three warehouses to four universities. The available supply at the three warehouses, demand at the four universities, and shipping costs are shown in the following table:
Instead of its original objective of cost minimization, Computers Unlimited has indicated the following goals, arranged in order of their importance:
The Bay City Parks and Recreation Department has received a federal grant of $600,000 to expand its public recreation facilities. City council representatives have demanded four different types of facilitiesgymnasiums, athletic fields, tennis courts, and swimming pools. In fact, the demand by various communities in the city has been for 7 gyms, 10 athletic fields, 8 tennis courts, and 12 swimming pools. Each facility costs a certain amount, requires a certain number of acres, and is expected to be used a certain amount, as follows:
The Parks and Recreation Department has located 50 acres of land for construction (although more land could be located, if necessary). The department has established the following goals, listed in order of their priority:
A farmer in the Midwest has 1,000 acres of land on which she intends to plant corn, wheat, and soybeans. Each acre of corn costs $100 for preparation, requires 7 worker-days of labor, and yields a profit of $30. An acre of wheat costs $120 to prepare, requires 10 worker-days of labor, and yields $40 profit. An acre of soybeans costs $70 to prepare, requires 8 worker-days, and yields $20 profit. The farmer has taken out a loan of $80,000 for crop preparation and has contracted with a union for 6,000 worker-days of labor. A midwestern granary has agreed to purchase 200 acres of corn, 500 acres of wheat, and 300 acres of soybeans. The farmer has established the following goals, in order of their importance:
The Growall Fertilizer Company produces three types of fertilizerSupergro, Dynaplant, and Soilsaver. The company has the capacity to produce a maximum of 2,000 tons of fertilizer in a week. It costs $800 to produce a ton of Supergro, $1,500 for Dynaplant, and $500 for Soilsaver. The production process requires 10 hours of labor for a ton of Supergro, 12 hours for a ton of Dynaplant, and 18 hours for a ton of Soilsaver. The company has 800 hours of normal production labor available each week. Each week the company can expect a demand for 800 tons of Supergro, 900 tons of Dynaplant, and 1,100 tons of Soilsaver. The company has established the following goals, in order of their priority:
The Barrett Textile Mill was checked by inspectors enforcing Occupational Safety and Health Administration (OSHA) codes. The inspectors found violations in four categories: hazardous materials, fire protection, hand- powered tools, and machine guarding. In each category the mill was not in 100% compliance. Each percentage point of increase in the compliance level in each category will reduce the frequency of accidents, decrease the accident cost per worker, and constitute progress toward satisfying the OSHA compliance level. However, achieving compliance does cost the mill money. The following table shows the benefits (in accident frequency and accident cost per worker) and the costs of a percentage point increase in compliance in each category:
To achieve 100% compliance in all four categories, the mill would have to increase compliance in hazardous materials by 60 percentage points (i.e., it is now at 40% compliance), in fire protection by 28 percentage points, in hand-powered tools by 35 percentage points, and in machine guarding by 17 percentage points. However, the management of the mill faces a dilemma, in that only $52,000 is available to spend on safety. Any larger expenditure could jeopardize the financial standing of the mill. Thus, management hopes to achieve a level of accident reduction and compliance that is within the company's budget limitation and that will satisfy OSHA authorities enough to temporarily delay punitive action. Therefore, management has established four goals, listed here in order of importance:
Solve the following goal programming model graphically and by using the computer:
Solve the following goal programming model graphically and by using the computer:
Solve the following goal programming model by using the computer:
The Wearever Carpet Company manufactures two brands of carpetshag and sculpturedin 100-yard lots. It requires 8 hours to produce one lot of shag carpet and 6 hours to produce one lot of sculptured carpet. The company has the following production goals, in prioritized order:
The East Midvale Textile Company produces denim and brushed-cotton cloth. The average production rate for both types of cloth is 1,000 yards per hour , and the normal weekly production capacity (running two shifts) is 80 hours. The marketing department estimates that the maximum weekly demand is for 60,000 yards of denim and 35,000 yards of brushed cotton. The profit is $3.00 per yard for denim and $2.00 per yard for brushed cotton. The company has established the following four goals, listed in order of importance:
The Oregon Atlantic Company produces two kinds of papernewsprint and white wrapping paper (butcher paper). It requires 5 minutes to produce a yard of newsprint and 8 minutes to produce a yard of wrapping paper. The company has 4,800 minutes of normal production capacity available each week. The profit is $0.20 for a yard of newsprint and $0.25 for a yard of wrapping paper. The weekly demand is for 500 yards of newsprint and 400 yards of wrapping paper. The company has established the following goals, in order of priority:
A rural clinic hires its staff from nearby cities and towns on a part-time basis. The clinic attempts to have a general practitioner (GP), a nurse, and an internist on duty during at least a portion of each week. The clinic has a weekly budget of $1,200. A GP charges the clinic $40 per hour, a nurse charges $20 per hour, and an internist charges $150 per hour. The clinic has established the following goals, in order of priority:
The Eaststate Manufacturing Company produces four different airplane parts from fabricated sheet metal for several major aircraft companies. The manufacturing process consists of four operationsstamping, assembly, finishing, and packaging. The processing times per unit for each operation and total available hours per year to produce these parts are as follows:
The sheet metal required for each part, the estimated annual demand, and the profit per part are as follows:
The company has 15,000 square feet of fabricated metal delivered each month. The company has the following prioritized production goals:
Mac's Warehouse is a large discount store that operates 7 days per week. The store needs the following number of full-time employees working each day of the week:
Each employee must work 5 consecutive days each week and then have 2 days off. For example, any employee who works Sunday through Thursday has Friday and Saturday off. The store currently has a total of 60 employees available to work. Mac's has developed the following set of prioritized goals for employee scheduling:
Infocomp Systems Lab is a research and development (R&D) company that develops computer systems and software primarily for the medical industry. The lab has proposals from its own researchers for eight new projects. Each of the proposed research projects requires limited resources, and it is not possible to undertake all of them. The following table shows the developmental budget, the number of researchers, and the expected annual sales from each project if successfully developed and implemented:
The lab has developed the following set of prioritized goals for selecting which projects to initiate:
Dampier Associates is a holding company that specializes in buying out small to medium- sized textile companies. The company is currently considering purchasing three companies in the Carolinas: Alton Textiles, Bonham Mills, and Core Textiles. The main criteria the company uses to determine which companies it will purchase are current profitability and growth potential. Dampier moderately prefers growth potential over profitability in making a purchase decision. Dampier's pairwise comparisons for the three target textile companies it is considering are as follows:
Develop an overall ranking of the three companies for Dampier Associates by using AHP.
Check the pairwise comparisons for Dampier Associates in Problem 17 for consistency.
Bernard Mee, the head of the department of management science at Tech, is evaluating faculty for raises at the end of the academic year. He is considering three faculty members for raises: John Abbott, Megan Bates, and Debbie Cook. Faculty evaluations are based on three criteriateaching, research, and service. Professor Mee's pairwise comparisons for each of the three faculty members for each criterion and his pairwise comparison matrix for the three criteria are as follows:
Determine an overall ranking of the three faculty members by using AHP.
Check the pairwise comparisons for the criteria in Problem 19 for consistency and indicate whether the level of consistency is acceptable.
Megan Moppett is a sales representative for Technical Software Systems (TSS), and she receives a commission for every new system installation she sells to a client. Her earnings during the past few years have been very high, and she wants to invest in a mutual fund. She is considering three funds: the Temple Global Fund, the Alliance Blue Chip Fund, and the Madison Bond Fund. She has three criteria for selectionpotential return (based on historical trends and forecasts), risk, and the fund's load factor. Megan's pairwise comparisons for the funds for each of their criteria and her pairwise comparison of the three criteria are as follows:
Determine the fund in which Megan should invest.
In Problem 21, if Megan Moppett has $85,000 to invest and she wants to diversify by investing in all three funds, how much should she invest in each?
Alex Wall is shopping for a new four-wheel-drive utility vehicle and has identified three models from which she will choosean Explorer, a Trooper, and a Passport. She will make her selection based on Consumer Digest ratings, price, and each vehicle's appearance. Following are Alex's pairwise comparisons for the vehicles for each of her criteria and her criteria preferences:
Using AHP, determine which vehicle Alex should purchase.
Station WRCH in Richmond, Virginia, is interviewing candidates for the job of news anchor on its 6:00 P.M. Eyewitness News show. There are three final candidates for the jobJune Pawlie, Kellie Cooric, and Tim Brokenaw. The criteria the station manager will use to make the selection are camera appearance, intelligence, and speaking ability (or speech). The station manager's pairwise comparisons for the job for each of these candidates and for the three criteria are as follows:
Using AHP, determine which candidate the station manager should hire as news anchor.
Carol Latta is visiting hotels in Los Angeles to decide where to hold a convention for a national organization of college business school teachers she represents. There are three hotels from which to choosethe Cheraton, the Milton, and the Harriott. The criteria she is to use to make her selection are ambiance, location (based on safety and walking distance to attractions and restaurants ), and cost to the organization. Following are the pairwise comparisons she has developed that indicate her preference for each hotel for each criterion and her pairwise comparisons for the criteria:
Develop an overall ranking of the three hotels, using AHP, to help Carol Latta decide where to hold the meeting.
Aaron Zeitel is a high school senior deciding which college to attend in the fall. He has narrowed his choices to three liberal arts schools: Arrington, Barton, and Claiborne. His criteria for selection are the school's academic reputation, location (and especially proximity to his home), the cost of tuition and room and board, and the social and cultural opportunities available. Following are Aaron's pairwise comparisons of the schools for each of the four criteria and his pairwise comparisons for the criteria:
Using AHP, determine which college Aaron should select and check the consistency of the pairwise comparison matrix for the criteria.
Whitney Eggleston operates a computerized dating service for students at Tech. She uses AHP to help match her clients . Whitney is attempting to match Chris with either Robin, Terry, or Kelly. She evaluates her clients according to three criteriaphysical attractiveness, intelligence, and personality, and she had Chris do pairwise comparisons on this set of criteria, as follows:
Whitney herself did the pairwise comparisons for Robin, Terry, and Kelly, based on their data sheets and a personal interview with each:
Who is the best match for Chris, according to Whitney's AHP analysis?
Rockingham Systems is considering three R&D projects it has identified as A, B, and C. Rockingham is not sure it will undertake all three projects, so it wants to rank them in terms of preferability. Rockingham will use three criteria to rank the projectsprofit potential, probability of success, and cost. Following are Rockingham's pairwise comparisons for the projects for each of the three criteria and for the criteria:
Rank the projects for Rockingham Systems by using AHP.
Professor Rakes is selecting a new graduate assistant from a pool of second-year MBA students. He will make his selection based on the student's grade point average (GPA) to date, the overall GMAT ( entrance exam) score, and the undergraduate degree discipline. Professor Rakes has developed the following pairwise comparisons for these criteria:
The files of the three students, Adrian, Bon, and Corey, provide the following data:
Use AHP to help Professor Rakes select a graduate assistant.
The Bay City Parks and Recreation Department is considering building several new facilities, including a gym, an athletic field, a tennis pavilion, and a pool. It will base its decision on which facilities to build depending on projected usage (from surveys) and construction and operating costs. The department strongly prefers usage to cost as a criterion for selection. Following are the department's pairwise comparisons, reflecting its preferences for each facility for the two criteria:
Rank the facilities, using AHP, and check the pairwise comparisons for consistency.
Students at a college in Ohio are planning a spring break vacation to one of three locations: Myrtle Beach (MB), Daytona Beach (DB), or Ft. Lauderdale (FL). They are to base their decision on three criteriaweather, cost, and potential fun (based on an Internet survey of friends and acquaintances at other colleges). The students have developed the following pairwise comparisons for the locations for each criterion and for the three criteria:
If the students use AHP to help make a decision, which location will they select for their spring break vacation?
Check the pairwise comparisons in Problem 31 for consistency.
The management science and information technology majors at Tech select one of two available options within the majordecision support systems (DSS) or operations management (OM). Student advisers use AHP with the students to determine which option they should select. The criteria used by the advisers are student aptitude and interests, faculty who teach in the options, and potential job availability. An adviser has helped one major develop the following pairwise comparisons:
Which option should the student select?
The Des Moines Twisters, a women's professional basketball team, needs a new point guard and is considering signing one of three college playersKeisha Jones, Natasha Franklin, and Kathleen Taylor. The team will base its decision of which player to sign on four criteria: the player's shooting ability, rebounding ability, ball handling skills, and attitude. Following is a survey of the three players' college game statistics for their senior year:
Although the coach can base some of her pairwise comparisons on these statistics, it is more difficult to assess attitude. She has interviewed each player, and she moderately prefers Keisha Jones's attitude to Kathleen Taylor's and strongly prefers Keisha Jones's attitude to Natasha Franklin's.
Assume the coach's role and develop pairwise comparisons for all four of the criteria and between the criteria. Use AHP to determine which player you would select.
The town of Blacksburg needs a larger modern middle school. The current middle school is in the center of town and is over 40 years old. There are two proposals for a new schoolrenovate and expand the current facility and keep it in town or build a new school on the outskirts of town. Different groups in town have strong feelings about the proposals. Some citizens want to retain the sense of tradition of the old school and like it in town, where it helps engender a sense of community. Others view the old school as antiquated and beyond saving and believe keeping the school in town near bars, traffic, and college students to be negative. The county school board will make the final decision. The school board has asked several management science professors from the local college to use AHP to help evaluate the proposals. The school board has identified four groups from which it wants to solicit input regarding their preferences: the middle school PTA, the middle school teachers, current and former middle school students, and the town council. The management science professors have developed the following pairwise comparison matrices for each of these groups:
The school board's pairwise comparison of the four groups from which it is soliciting preferences is as follows:
Given the following pairwise comparisons, indicate your preferences according to the preference scale in Table 9.1.
Federated Health Care has contracted to be Tech's primary health care provider for faculty and staff. There are three major hospitals in the area (within 35 miles)County, Memorial, and Generalthat have full-service emergency rooms. Federated wants to designate one of the hospitals as its primary care emergency rooms for its members. The company's criteria for selection are quality of medical care, as determined by a patient survey; distance to the emergency room by the majority of its members; speed of medical attention at the emergency room; and cost. Following are the pairwise comparisons of the emergency rooms for each of the four criteria and the pairwise comparisons for the criteria:
Using AHP, determine which hospital emergency room Federated Health Care should designate as its primary care provider.
The department of management science at Tech offers four sections of introductory quantitative methods in the fall semester, each taught by a different teacher. A group of students have developed the following criteria to rank the sections: time and day, grading history of the instructor, classroom atmosphere (i.e., relaxed or formal), amount of homework, and the teacher's sense of humor. Following are the students' preferences for these criteria:
Following are the students' pairwise comparisons of the sections for the criteria:
A faculty committee in the department of management science at Tech is evaluating three new textbooks for its introductory management science course, which all business students are required to take. The texts , identified by the authors, are Adams/Jones, Barnes, and Cook/Smith. The committee's selection criteria are topical coverage, readability, cost, and the available supplements. Following are the committee's pairwise comparisons of the three textbooks for each of the four criteria and the committee's pairwise comparisons for the criteria:
Using AHP, determine which textbook the committee should select. Check the consistency of the pairwise comparison matrix for the criteria.
On the day of the professional football draft, the owner, general manager, and coaching staff of the New York Gladiators are attempting to decide which of the available players they should select as their pick approaches. They have three players on their big board whom they would like: Al Stonecrusher, a defensive lineman, Bruce Kowslaski, a tight end, and Charlie Speedman, a running back. They evaluate players according to four criteriathe player's projected salary demands, speed, and size (i.e., height and weight) and the team's position needs. Following are the group's pairwise comparisons for the players for each of the four criteria and the pairwise comparisons for the criteria:
Using AHP, determine which player the Gladiators should select. Check the consistency of the pair-wise comparison matrix for the criteria.
Visit one or more local car dealers and select four new models of cars you might like to purchase. Using AHP and your own preferences, rank your selections according to the following criteria: price, style/appearance, reliability/maintenance, engine size, gas mileage, safety, and features/options. (You may need to access some additional references, such as Consumer Reports , to facilitate your judgments .) After you have ranked your car selections using AHP, develop a scoring model to perform the same analysis. Then compare the results of the two models and discuss which method your prefer.
Arsenal Electronics is to construct a new $1.2 billion semiconductor plant and has selected four small towns in the Midwest as potential sites. The important decision criteria and grades for each town are as follows:
Develop a scoring model to determine in which town the plant should be built.
The Dynaco Manufacturing Company is to build a new plant to make ring bearings (used in automobiles and trucks ). The site selection team is evaluating three sites, and it has graded the important weighted criteria for each as follows:
Develop a scoring model to determine which site the selection team should recommend.
Exotech Computers manufactures computer components such as chips, circuit boards , motherboards, keyboards, LCD panels, and the like and sells them around the world. It wants to construct a new warehouse and distribution center in Asia to serve emerging markets there. It has identified sites in Shanghai, Hong Kong, and Singapore and has graded the important weighted decision criteria for each site as follows:
Recommend a site based on these decision criteria and grades.
State University is to construct a new student center and athletic complex that will include a bookstore, a post office, theaters, a market, a minimall, meeting rooms, a swimming pool, and weight and exercise rooms. The university administration has hired a site selection specialist to identify the best potential sites on campus for the new facility. The site specialist has identified four sites on campus and has graded the important weighted decision criteria for each site as follows:
Which site should the specialist recommend?
Following an all-star school soccer career, Kelly Williams has been offered scholarships to five universities. She has had a difficult time making a decision and has decided to use a scoring model to help evaluate the different offers. The following table includes a weighted list of criteria she has developed and a grade showing how well each school satisfies the criteria:
Rank the universities according to their scores to assist Kelly in making her decision.
The Carter family wants to purchase a time-share condominium for 1 week during the summer in Hilton Head, South Carolina. There are many resort complexes from which to choose, and the Carters narrowed their list to five. They have graded their choices according to the following weighted criteria:
Use a scoring model to determine a recommended resort for the Carters' time-share purchase.
Robin Dillon has recently accepted a new job in the Washington, DC, area and has been hunting for a condominium to purchase. From friends and coworkers she has compiled a list of five possible condominium complexes that she might move into. The following table indicates the weighted criteria that Robin intends to use in her decision-making process and a grade indicating how well each complex satisfies each criterion:
Use a scoring model to help Robin determine which condominium she should purchase.
The New River Rapids Under-15 Girls' Travel Soccer Team is determining which tournments it should enter during the fall season . The manager has identified six possible tournaments, and the team wants to enter three of them. The team manager first surveyed the parents and players and determined a list of decision criteria and their relative weights. The manager then asked the parents and players to grade the tournaments on how well they satisfied the criteria. The criteria, weights, and average grades are summarized as follows:
To what three tournaments should the manager recommend the team apply, given the preferences indicated by the parents and players?
Select four fast-food restaurants (e.g., McDonald's, Burger King, Wendy's, Domino's) in your area and develop a scoring model that includes decision criteria, weights, and grades to rank the restaurants from best to worst.