Deck 9: Multicriteria Decision Making 

Question 1

Solve the following goal programming model graphically and by using the computer:

Answer 1

a)
First, the integer programming model needs to be formulated and then solved. Integer programming model should be written using the slack variables in order to have = signs in order to exchange for the
signs (this is at most, hence use
).
Minimize (Units should be used)
Now, solve the equations using the QM for Window software following these instructions:
First, open the software; under module, select Transportation.
• Next, open a blank document.
• A menu will open; enter the document title if needed. Then, enter the number of Sources ( 1-3 ) which is 3 for this problem.
• Enter the number of destinations which is 3 for this problem (A, B, C).
• Select OK and a window will show in order to enter the equations.
• Enter the values for Destination and Sources; second enter the given supply and demand numbers; then, select solve on the top right corner and a series of windows with solutions. The window titled: Transportation Shipments has the values of the variables.
The equations with added variables are as follows:

Question 2

In Problem, 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
Problem
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 selection-potential 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.

Answer 2

Construct normalized matrices considering each table is a matrix.
To normalize a matrix, add each column in the table then divide each value in the corresponding column by its total. This will create a new matrix.
To create the preference vector, find the row average.
The resulting matrix and row average is as follows:
The second normalized matrix is as follows:
The third normalized matrix is as follows:
The row average is as follows:
The row vector showing the averages for the criteria is the average row. To create an overall ranking for all three, multiply the matrix created by the 3 averages from the first three tables multiplied by the vector row from the criteria.
The result is as follows;
With $85,000 to invest, the investment amounts would $27k, $71k and $39k.

Question 3

Suntrek, based in China, is a global supplier of denim jeans for apparel companies around the world. It purchases baled raw cotton from producers in the United States and then transports it to East Coast ports where it is loaded into containers and shipped to factories overseas where denim fabric and ultimately jeans are manufactured. Suntrek wants to build a major warehousing and distribution center at one of the overseas ports and is considering Shanghai, Saigon, and Karachi. The criteria it will use to select the location are building and operating costs, labor rates and availability, container and shipping availability, and location factors such as tariffs, available land, and government regulations and stability. Following are Suntrek's pairwise comparisons for the locations for each of its criterion and its pairwise comparison of the four criteria:




Using AHP, determine which port Suntrek should select and check the consistency of the pairwise comparison matrix for the criteria.

Answer 3

not answer

Question 4

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 you prefer.

Question 5

Solve the following goal programming model graphically and by using the computer:

Question 6

Alex Wall is shopping for a new four-wheel-drive utility vehicle and has identified three models from which she will choose-an 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.

Question 7

Ben Cheery, the Sox general manager, wants to sign at least one free agent player for the coming baseball season. He is considering four players-Joe Aaron, Mike Bass, Carlos Cabrera, and Josh Donald. He is using three criteria including the player's contract demands for salary and contract years, the player's history of injuries, and the metric "wins above a replacement player" called WAR that quantifies a player's total contribution to his or her team. Following are his preferences for these criteria:
Following are Ben's pairwise comparisons of the players for the criteria:


Using AHP determine how Ben should rank the free agents.

Question 8

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.

Question 9

Solve the following goal programming model by using the computer:

Question 10

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 job-June 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.

Question 11

In Problem check the general manager's pairwise comparisons for consistency.
Problem
Ben Cheery, the Sox general manager, wants to sign at least one free agent player for the coming baseball season. He is considering four players-Joe Aaron, Mike Bass, Carlos Cabrera, and Josh Donald. He is using three criteria including the player's contract demands for salary and contract years, the player's history of injuries, and the metric "wins above a replacement player" called WAR that quantifies a player's total contribution to his or her team. Following are his preferences for these criteria:
Following are Ben's pairwise comparisons of the players for the criteria:


Using AHP determine how Ben should rank the free agents.

Question 12

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.

Question 13

The Wearever Carpet Company manufactures two brands of carpet-shag and sculptured-in 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:
(1) Do not underutilize production capacity, which is 480 hours.
(2) Achieve product demand of 40 (100-yard) lots for shag and 50 (100-yard) lots for sculptured carpet. Meeting demand for shag is more important than meeting demand for sculptured, by a ratio of 5 to 2.
(3) Limit production overtime to 20 hours.
a. Formulate a goal programming model to determine the amount of shag and sculptured carpet to produce to best meet the company's goals.
b. Solve this model by using the computer.

Question 14

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 choose-the 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.

Question 15

For Problem, develop your own pairwise comparisons for the criteria you might use to select an apartment complex or other dwelling in your college community, and develop your own AHP ranking for the possible apartment complexes you might live in.
Problem
Katnis Evergreen, a junior at Tech, is moving out of the dorms where she has lived for 2 years into an apartment in town. She is considering three apartment complexes-the Terraces, the Vistas, and Foxfield. She is going to evaluate the apartments using three criteria-cost, condition (age, upkeep, etc.), and location (i.e., proximity to campus, transportation, shopping, etc.). Katnis's pairwise comparisons for each of the three apartment complexes for each criterion and her pairwise comparison matrix for the three criteria are as follows:



Determine an overall ranking of the three apartment complexes by using AHP.

Question 16

In Problem Ben Cheery, the Sox general manager, also wants to use a scoring model to determine which player(s) he might sign to a free agent contract for the coming baseball season. The following table shows a weighted list of criteria he has developed and a score for each player showing how well the player satisfies his criteria.
Rank the players according to their scores. How is this ranking different from the ranking Ben determined using AHP in Problem
Problem
Ben Cheery, the Sox general manager, wants to sign at least one free agent player for the coming baseball season. He is considering four players-Joe Aaron, Mike Bass, Carlos Cabrera, and Josh Donald. He is using three criteria including the player's contract demands for salary and contract years, the player's history of injuries, and the metric "wins above a replacement player" called WAR that quantifies a player's total contribution to his or her team. Following are his preferences for these criteria:
Following are Ben's pairwise comparisons of the players for the criteria:


Using AHP determine how Ben should rank the free agents.

Question 17

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:
(1) Eliminate underutilization of production capacity to maintain stable employment levels.
(2) Limit overtime to 10 hours.
(3) Meet demand for denim and brushed cotton weighted according to profit for each.
(4) Minimize overtime as much as possible.
a. Formulate a goal programming model to determine the number of yards (in 1,000-yard lots) to produce to satisfy the goals.
b. Solve this model by using the computer.

Question 18

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.

Question 19

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. Using AHP, rank the courses for the students.
b. Using this framework and these criteria, but with your own preferences for a course with multiple sections that you are familiar with at your school, develop a ranking of the sections.

Question 20

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

Question 21

Broderick Crawford is the district commander for the Catawba Valley highway patrol district in western Pennsylvania. He is attempting to assign highway patrol cars to different road segments in his district. The primary function of the highway patrol force is to patrol roads outside incorporated city and town limits in the district to deter traffic violators and accidents. This objective is typically achieved by maintaining a visible presence- letting motorists see patrol units on a regular basis and giving out warnings, citations, and so forth. Secondary activities of a patrol unit include providing assistance to motorists, answering distress calls, handling emergencies and accidents when called to the scene, and occasionally apprehending criminals.
Commander Crawford has 23 patrol cars that he wants to assign to the following six major road segment areas:
road segment 1, interstate, north
road segment 2, urban area, north
road segment 3, four-lane highway, east
road segment 4, two-lane highway, west
road segment 5, interstate/four-lane highway, south
road segment 6, two-lane highway (heavy truck traffic), south
Each of these road segments includes the primary arteries, as indicated earlier, plus adjoining roads. All the road segments have different levels of traffic density and accident rates, which are key factors in determining how many patrol units to assign. However, these factors do not always coincide. For example, interstate highway segments typically have high traffic density but low accident rates, whereas some two-lane highways have low traffic density but high accident rates. Differences often occur because of variations in road conditions (such as sharp curves, visibility, and width). Other conditions, such as heavy truck traffic (as on segment 6), also contribute to high accident rates.
Each segment requires different operating costs, including maintenance and repair, fuel, and so on because of different operating conditions. The commander's most pressing objective is to limit daily operating costs to $450. The daily operating costs per road segment are as follows:
The commander would like to reduce the accident rate for the district as well as increase both physical and sight contacts, which are deterrents to potential traffic violators. The commander would also like to achieve a reasonable average response time for a patrol unit to respond to a call for each road segment. The average accident rate reduction (per million miles traveled) and physical contacts and sight contacts per car for each road segment are shown in the following table:
The commander's second-most-important goal is to reduce the average accident rate for the district by five accidents per million miles traveled. The commander's next goals (in order) are to achieve 350 physical contacts and 30,000 sight contacts per day in the district.
If no patrol units are assigned in the district, the average time to respond to a distress call anywhere in the district from the main district headquarters and motor pool is 28 minutes. Each car assigned to a road segment reduces the overall average response time in the district by the following amounts:
The commander's last objective is to achieve an average response time to distress calls of 15 minutes. Because of local and political pressure, the commander has to assign at least two patrol units to each road segment. In addition, the commander believes that a maximum of five patrol units is sufficient for any particular road segment.
Formulate and solve a goal programming model to determine the number of patrol units to assign to each road segment to achieve the commander's goals.

Question 22

The Oregon Atlantic Company produces two kinds of paper-newsprint 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:
(1) Limit overtime to 480 minutes.
(2) Achieve a profit of $300 each week.
(3) Fulfill the demand for the products in order of magnitude of their profits.
(4) Avoid underutilization of production capacity.
a. Formulate a goal programming model to determine the number of yards of each type of paper to produce weekly to satisfy the various goals.
b. Solve the goal programming model by using the computer.

Question 23

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 Robin, Terry, or Kelly. She evaluates her clients according to three criteria-physical 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

Question 24

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.

Question 25

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.

Question 26

Katherine Miller is a senior in the department of information technology at Tech. For the past few months she has been involved in the job search process. She has an excellent résumé, with a high grade point average and a strong record of campus participation in clubs and activities. As a result, she has had a number of good interviews with various companies. She now has job offers from five companies-American Systems Developers, Anderssun Consulting, National Computing Software Systems (NCSS), the Gulf-South Company, and Electronic Village.
American Systems Developers and Anderssun Consulting are both large national consulting firms with offices in several major cities. If Katherine accepted the offer of either of these firms, she would primarily work on project teams assigned to develop decision support and information systems for corporate clients around the country. If she went with American Systems Developers, her home base would be in Atlanta, and if she accepted Anderssun's offer, she would be located in Washington, DC. However, in both cases she would be traveling a great deal and could sometimes be on the road at a client location for as much as 6 to 9 months. NCSS is a software and computer systems development company with a campus-like location in Chicago. Although her job with NCSS would involve some traveling, it would never be more than several weeks at any one time. Gulf-South is a bank holding company that operates eight different banks and its various branches in six southeastern states. If Katherine accepted Gulf-South's offer, she would be located in Tampa, where she would work in operations systems. She would be involved in developing information and support systems for bank operations, and she would have minimal travel. Electronic Village is a national chain of discount stores specializing in electronic products, such as televisions, DVRs, CD players, MP3 players, and computers. Her job with Electronic Village would be at its corporate headquarters in Nashville, Tennessee, where she would develop and maintain computer systems to be used for inventory control at the hundreds of Electronic Village stores across the country. She would be required to travel very little.
American Systems Developers has offered Katherine a starting salary of $38,000 annually, and Anderssun Consulting has offered her $41,000 per year. NCSS has offered her an annual salary of $46,000, whereas Gulf- South has offered her $35,000 per year, and Electronic Village has offered her a salary of $32,000 per year.
Katherine is having a difficult time making her decision. All the companies have excellent reputations, are financially healthy, and have good opportunities for advancement. All are demanding in terms of the workload they require. All five companies have given Katherine only a few weeks to make a decision regarding their offers.
Katherine has decided to use the analytical hierarchy process (AHP) to help decide which job offer she should accept. She has developed a list of criteria that are important to her in deciding which job to take. The criteria, in no particular order, are (1) salary; (2) cost of living in the city where she would be located; (3) amount of travel associated with her job; (4) climate (weather) where she would be located; (5) entertainment and cultural opportunities, including sports, theater, museums, parks, and so on; (6) universities where she can work on an MBA degree part time and at night; (7) the crime rate in the city where she would live; (8) the nature of the job and what she would be doing; and (9) her proximity to friends and relatives. Katherine realizes that she has very limited information on which to compare the five jobs, based on most of these criteria, so she knows she needs to go to the library and do some research, especially on the five different job locations.
Put yourself in Katherine's shoes and, using all or some of her criteria and your own preferences and knowledge, develop an overall ranking of the jobs, using AHP.

Question 27

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:
(1) A nurse should be available at least 30 hours per week.
(2) The weekly budget of $1,200 should not be exceeded.
(3) A GP or an internist should be available at least 20 hours per week.
(4) An internist should be available at least 6 hours per week.
a. Formulate a goal programming model to determine the number of hours to hire each staff member to satisfy the various goals.
b. Solve the model by using the computer.

Question 28

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 projects-profit 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.

Question 29

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 criteria-the 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 pairwise comparison matrix for the criteria.

Question 30

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 have 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.

Question 31

The Oakdale County School Board was meeting in special session. A federal judge had ordered the board to present an acceptable busing plan for racially balancing the four high schools in Oakdale County within a week. The judge had previously given the school board several opportunities to informally present a plan, but the members had been unable to agree among themselves. Every time they met and started to develop a plan to bus students from one high school district to another, an argument would arise before they got past the first busing move, and they would adjourn the meeting. This time, however, they knew the judge had lost patience and they had to agree on something.
Of the four schools, only West High School was racially balanced, with 500 white students and 500 black students. North High School had 1,000 white students and only 300 black students; East High School was almost as bad, with 1,050 white students and 400 black students. South High School was predominantly black, with 800 black students and 450 white students. Overall, of the 5,000 students in Oakdale County, 60% were white and 40% black.
"Look," said John Connor, a school board member from the West district, "rather than starting off by trying to shift students from one district to another, why don't we try to establish what we want to accomplish-you know, what our goals are"
Several of the other members nodded in agreement, and Fred Harvey, the board chairman, said, "Good idea, John."
"Okay, the first goal seems pretty evident to me," John said. "Sixty percent of our students are white, and 40% are black, so that's what we need our schools to be, 60% and 40%."
"That's okay for you to say, John," Betty Philips argued, "because your district has those proportions already-so you won't have any busing. But my district in the North is a long way from that ratio, and we would have to bus a lot of our students to achieve a 60%/40% ratio."
" I'm not saying it, Betty," said John. "That is basically what Judge Barry has been saying for 6 months."
"John's right, Betty, and we're not busing students yet; we're just putting down our objectives," said Fred. "I think that has to be our highest-priority objective. How about the rest of you"
They all nodded their agreement, even Betty Philips, reluctantly.
"Since we know we're going to have to bus students to achieve this ratio at each school, I think we ought to try to minimize the amount of traveling the students will have to do," suggested Mickey Gibboney, a member from the South district.
Fred Harvey noted that page 10 of their handout had a chart showing the average mileage a student in one district would have to travel on a bus to the high school in each of the other districts. The chart looked like this:
"Why don't we try to set some reasonable objectives for total busing miles, for the students' sake and for budgeting reasons" Cassandra Watkins asked. "I would suggest about 30,000 miles per day, based on the miles we bus students now. If we get much higher than that, we're not going to have the money to pay for it, and it means we'll be busing students all over the place."
The other members nodded and agreed.
"Okay," said Fred Harvey, "that'll be our number-two goal."
Betty Philips spoke up again. "I'll tell you another thing I don't want to see happen, and that's any more overcrowding at North High School. We have 100 students more than capacity now."
"You think you have problems!" Bob Wilson exclaimed. "In East we have 1,450 students and capacity for 1,000. I think no overcrowding is a great idea!"
"I agree," said Mickey Gibboney. "We're 250 over our capacity at South High School."
"That's a nice idea," John Connor responded, "and I realize that we have 200 students less than our capacity at West High School. However, let's face it, in the county we have capacity for 4,400, not 5,000, students, so there's going to be some overcrowding. I think our objective should be that all four schools share in the overcrowding proportionally."
"That sounds reasonable to me," said Fred Harvey. "How about the rest of you Okay to say our number-three goal is to be as close to capacity at each school as possible but share proportionally in the overcrowding"
They all voiced their approval.
"Well," John Connor concluded, "I think we have identified the things we want to accomplish in our plan. Now if we could just use some magic trick to find a plan for busing students between the districts that would achieve all these goals."
The others nodded and frowned.
A. Formulate a goal programming model to help the board with its dilemma.
B. Solve the goal programming model by using the computer.

Question 32

The Eaststate Manufacturing Company produces four different airplane parts from fabricated sheet metal for several major aircraft companies. The manufacturing process consists of four operations-stamping, 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:
(1) Avoid overtime, which would erode profit levels.
(2) Meet parts demand.
(3) Achieve an annual profit of $700,000.
(4) Avoid ordering more material because a surcharge is required by the supplier for changing the standard monthly order.
a. Formulate a goal programming model to determine the amount of each part to produce to achieve the company's objectives.
b. Solve this model by using the computer.
c. How would the solution be affected if the first two priorities were reversed

Question 33

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.

Question 34

The four most famous generals during the American Civil War were Ulysses S. Grant, William
Tecumseh Sherman, Robert E. Lee, and Stonewall Jackson. Historians have always debated who the greatest general from among these four was. Following are the pairwise comparisons for five criteria that might be used to evaluate the generals: leadership, including interpersonal skills and the ability to communicate with others and delegate responsibility; tactical and technical skills in planning and directing their armies, including the efficient use of their resources; their direct impact on the battles they were involved in; their decision-making skills both between and during battles; and their overall success in the war.





Using AHP, rank these four Civil War generals.

Question 35

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.

Question 36

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:
(1) Because of recent labor relations difficulties, management wants to avoid underutilization of normal production capacity.
(2) Management has established a satisfactory profit level of $500 per day.
(3) Overtime is to be minimized as much as possible.
(4) Management wants to minimize the purchase of additional materials to avoid handling and storage problems.
Formulate a goal programming model to determine the number of each product to produce to best satisfy the goals.

Question 37

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:
(1) The store would like to avoid hiring any additional employees.
(2) The most important days for the store to be fully staffed are Saturday and Sunday.
(3) The next most important day to be fully staffed is Friday.
(4) The store would like to be fully staffed the remaining 4 days in the week.
a. Formulate a goal programming model to determine the number of employees who should begin their 5-day workweek each day of the week to achieve the store's objectives.
b. Solve this model by using the computer.

Question 38

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.

Question 39

For Problem, develop your own pairwise comparisons for and among the criteria using your own knowledge of Civil War history and any Internet research you might perform, and develop your own AHP ranking of the four generals.
Problem
The four most famous generals during the American Civil War were Ulysses S. Grant, William
Tecumseh Sherman, Robert E. Lee, and Stonewall Jackson. Historians have always debated who the greatest general from among these four was. Following are the pairwise comparisons for five criteria that might be used to evaluate the generals: leadership, including interpersonal skills and the ability to communicate with others and delegate responsibility; tactical and technical skills in planning and directing their armies, including the efficient use of their resources; their direct impact on the battles they were involved in; their decision-making skills both between and during battles; and their overall success in the war.





Using AHP, rank these four Civil War generals.

Question 40

The New River Rapids Under-15 Girls' Travel Soccer Team is determining which tournaments 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

Question 41

Suntrek is a global denim fabric and jeans manufacturer. It purchases raw, baled cotton from locations around the world (primarily the United States and Mexico) and ships it (in containers) to various factories it operates to manufacture denim fabric and jeans, primarily in the Asia-Pacific and Indian Ocean areas. It also ships some of the fabric to other factories where it produces denim jeans. It ultimately ships all of the jeans (and a small amount of fabric) to retail clothing companies primarily in the United States, Europe, and Japan. It is considering building a new denim jeans factory with a warehousing and distribution center for baled cotton, denim fabric, and denim jeans. The five possible port locations for the new facility are Da Nang, Mumbai, Manila, Shanghai, and Karachi. Suntrek's weighted decision criteria are labor wage rates (0.20), cotton and fabric supply (0.18), shipping/transport availability and cost (0.15), infrastructure (0.12), risk (0.10), import/export regulations and tariffs (0.09), government stability (0.06), labor sustainability (0.05), and environmental sustainability (0.05). Using the Internet, research the five possible port locations and assign a grade for each location for each criterion, and determine an overall ranking of the locations for Suntrek.

Question 42

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:
(1) The company would like to remain within a total developmental budget of $5,000,000.
(2) The number of available research personnel is 27, and Infocomp would like to avoid obtaining extra researchers.
(3) The company would like the expected future annual sales from the implemented projects to be at least $6,500,000.
(4) Projects 1, 3, 4, and 6 are considered offensive in that they represent new product initiatives, while projects 2, 5, 7, and 8 are existing product upgrades and thus defensive in nature. The lab would like to select at least two projects from each group.
(5) Projects 2, 3, 5, 6, and 7 are considered the most risky of the projects, and the company would prefer not to select any more than three of these projects.
(6) The lab's owner has indicated that she would like to see projects 5 and 6 initiated if doing so would not interfere with the achievement of any of the more important goals determined by the lab's top management.
a. Formulate a goal programming model to determine which projects Infocomp Systems Lab should select to best achieve its goals.
b. Solve this model by using the computer. (Note that the solution requires 0-1 integer values for the variables in the model.)

Question 43

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 criteria-weather, 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

Question 44

The owners of the Blitz professional soccer team are disappointed in their team's home attendance, so they are considering moving to one of four cities: Atlanta, Birmingham, Charlotte, or Durham. The criteria the owners are using to make their decision are population in the 15-40 age group, soccer interest (measured by youth, high school, and college soccer game participation and attendance), media market, entertainment and sports competition, and the proposed playing facility. Following are the owners' pairwise comparisons for the four potential cities for each of the five criteria, and the owners' pairwise comparisons for the criteria:





Using AHP determine which city the owners should select to relocate to.

Question 45

As part of an aggressive expansion plan, StarTrack Coffee is planning to open three new retail stores in the city. The following table shows the location factors it considers to be important indicators of future profitability and how management has graded each location according to each of these factors:

Question 46

Each November the Baseball Writers' Association of America (BBWAA) releases its list of that year's nominees for induction into the National Baseball Hall of Fame in Cooperstown, New York. There are 575 voting members of the BBWAA, and candidates must be named on 75% of the ballots cast to gain entry into the National Baseball Hall of Fame. There is no limit to the number of players who can be nominated or who can be elected. Go to the BBWAA Web site at http://bbwaa.com/ and from the list of this year's nominees select the five or six "field players" (as opposed to pitchers) who you think are the top candidates for selection, and develop an AHP model using your own criteria to rank these candidates. Criteria might include, among other things, hits, lifetime batting average, home runs, runs batted in, runs, stolen bases, awards, years played, fielding percentage, number of World Series participated in, and a comparison with Hall of Famers overall and at their field position (e.g., catcher, first base, outfield). Player bios including their playing statistics can be obtained by searching the Internet.

Question 47

Texmart is a locally owned "big-box" retail store chain in Texas with 75 stores, primarily located in the Dallas-Fort Worth area. In order to compete with national big-box store chains, Texmart is planning to undertake several "sustainability" (i.e., "green") projects at its stores. These national chains have been heavily publicizing their sustainability efforts, including the reduction of greenhouse gas (GHG) emissions, which has had a positive effect on their sales. They have also demonstrated that sustainability projects can have a positive impact on cost (especially energy) savings. The projects Texmart is considering include installing solar panels at some or all of its stores, installing small wind turbines, replacing some or all of its 165 trucks with more fuel-efficient hybrid trucks, and implementing waste reduction programs at its stores, including recycling and reducing the use of plastic bags in stores. The costs for these projects (per store or truck), the resulting reduction in GHG emissions, the energy savings, and the annual costs savings are shown in the following table:
Texmart has established the following four goals, in order of importance:
(1) It doesn't want to exceed is program budget of $30 million for sustainable projects.
(2) It wants to achieve GHG emission reductions of at least 250,000 metric tons per year.
(3) It wants to achieve annual cost savings of at least $4 million.
(4) It wants to achieve annual energy savings of at least 5 million kilowatt hours (kWh).
a. Formulate a goal programming model to determine the number of each type of project to undertake to satisfy the goals.
b. Solve the model by using the computer.

Question 48

Check the pairwise comparisons in Problem for consistency.
Problem
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 criteria-weather, 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

Question 49

Check the pairwise comparisons for the five criteria in Problem for consistency.
Problem
The owners of the Blitz professional soccer team are disappointed in their team's home attendance, so they are considering moving to one of four cities: Atlanta, Birmingham, Charlotte, or Durham. The criteria the owners are using to make their decision are population in the 15-40 age group, soccer interest (measured by youth, high school, and college soccer game participation and attendance), media market, entertainment and sports competition, and the proposed playing facility. Following are the owners' pairwise comparisons for the four potential cities for each of the five criteria, and the owners' pairwise comparisons for the criteria:





Using AHP determine which city the owners should select to relocate to.

Question 50

Suntrek manufactures denim jeans, which it sells to clothing retailers around the world. It wants to construct a new warehouse and distribution center in Asia to serve emerging markets there. It has identified potential sites in the port cities of Shanghai, Singapore, Pusan, Kaohsiung, and Hong Kong. The following table shows the factors in the location decision and the grade of each location for each factor:
The weights indicating the importance of each location factor are not included. Determine what you think these weights should be and recommend the best location for the new distribution center.

Question 51

In Problem in Chapter, 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:
(1) A M has been one of its better long-term customers, so Computers Unlimited wants to meet all of A M 's demands.
(2) Because of recent problems with a trucking union, it wants to ship at least 80 units from the Washington warehouse to Central University.
(3) To maintain the best possible relations with all its customers, Computers Unlimited would like to meet no less than 80% of each customer's demand.
(4) It would like to keep total transportation costs to no more than 110% of the $22,470 total cost achieved with the optimal allocation, using the transportation solution method.
(5) Because of dissatisfaction with the trucking firm it uses for the Atlanta-to-State deliveries, it would like to minimize the number of units shipped over this route.
a. Formulate a goal programming model for this problem to determine the number of microcomputers to ship on each route to achieve the goals.
b. Solve this model by using the computer.
Problem
Computers Unlimited sells microcomputers to universities and colleges on the East Coast and ships them from three distribution warehouses. The firm is able to supply the following numbers of microcomputers to the universities by the beginning of the academic year:
Four universities have ordered microcomputers that must be delivered and installed by the beginning of the academic year:
The shipping and installation costs per microcomputer from each distributor to each university are as follows:
Solve this problem by using the computer.

Question 52

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.

Question 53

The management science and information technology majors at Tech select one of two available options within the major-decision 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

Question 54

Texmart is a locally owned "big-box" retail store chain in Texas, with stores primarily located in the Dallas-Fort Worth area. In order to compete with national big-box store chains, it is planning to undertake several "sustainability" (i.e., "green") projects at its stores. These national chains have been heavily publicizing their sustainability efforts, including the reduction of greenhouse gas (GHG) emissions (in metric tons per year) and energy savings (in kilowatt hours), which have had a positive effect on their sales. They have also demonstrated that sustainability projects can have a positive impact on cost (especially energy) savings. The projects Texmart is considering include installing solar panels at its stores, installing small wind turbines at its stores, replacing their trucks with more fuel-efficient hybrid trucks, and implementing waste reduction programs at its stores, including recycling and reducing the use of plastic bags. The criteria Texmart wants to use to evaluate the projects include the media and public response to the projects they undertake, the cost of the projects, the amount of GHG emissions reduction, and the amount of energy savings. Following are the pairwise comparisons for the projects for these four criteria, and the pairwise comparisons for the criteria:




Using AHP, rank the projects for Texmart.

Question 55

Select four fast-food restaurants (e.g., McDonald's, Burger King, Wendy's, Domino's, or a local restaurant) in your area and develop a scoring model that includes decision criteria, weights, and grades to rank the restaurants from best to worst.

Question 56

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 facilities-gymnasiums, 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:
(1) The department wants to spend the total grant because any amount not spent must be returned to the government.
(2) The department wants the facilities to be used by a total of at least 20,000 people each week.
(3) The department wants to avoid having to secure more than the 50 acres of land already located.
(4) The department would like to meet the demands of the city council for new facilities. However, this goal should be weighted according to the number of people expected to use each facility.
a. Formulate a goal programming model to determine how many of each type of facility should be constructed to best achieve the city's goals.
b. Solve this model by using the computer so that the solution values are integers.

Question 57

Check the pairwise comparisons for Dampier Associates in Problem for consistency.
Problem
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.

Question 58

The Des Moines Twisters, a women's professional basketball team, needs a new point guard and is considering signing one of three college players-Keisha 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.

Question 59

Labran Jones has played for the Cleveland professional basketball team for the past eight seasons and has established himself as one of the top players in the league. He has recently become a free agent, meaning he can sign a new contract with Cleveland or with any other team in the league. While he has enjoyed playing for Cleveland, which is near his hometown, the team has never seriously contended for a championship, so Labran is strongly considering moving to one of three other teams that he thinks have more championship potential. Other factors he is considering are salary (although Cleveland is offering him more money than the other teams), the possible media attention and endorsements he might receive by playing in another city, and the city itself and lifestyle where he would be playing. Following are the pairwise comparisons for the four teams for these four criteria and the pairwise comparisons for the criteria:




Using AHP, determine which team Labran should select to sign a new contract with.

Question 60

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:
(1) To maintain good relations with the union, the labor contract must be honored; that is, the full 6,000 worker-days of labor contracted for must be used.
(2) Preparation costs should not exceed the loan amount so that additional loans will not have to be secured.
(3) The farmer desires a profit of at least $105,000 to remain in good financial condition.
(4) Contracting for excess labor should be avoided.
(5) The farmer would like to use as much of the available acreage as possible.
(6) The farmer would like to meet the sales agreement with the granary. However, the goal should be weighted according to the profit returned by each crop.
a. Formulate a goal programming model to determine the number of acres of each crop the farmer should plant to satisfy the goals in the best possible way.
b. Solve this model by using the computer.

Question 61

Katnis Evergreen, a junior at Tech, is moving out of the dorms where she has lived for 2 years into an apartment in town. She is considering three apartment complexes-the Terraces, the Vistas, and Foxfield. She is going to evaluate the apartments using three criteria-cost, condition (age, upkeep, etc.), and location (i.e., proximity to campus, transportation, shopping, etc.). Katnis's pairwise comparisons for each of the three apartment complexes for each criterion and her pairwise comparison matrix for the three criteria are as follows:



Determine an overall ranking of the three apartment complexes by using AHP.

Question 62

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 school-renovate 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:
a. Based on the AHP analysis conducted by the management science professors, which proposal should the school board select
b. Check the school board's pairwise comparison of the criteria for consistency.

Question 63

For Problem, check the consistency of the pairwise comparison matrices for all four criteria and the criteria
Problem
Labran Jones has played for the Cleveland professional basketball team for the past eight seasons and has established himself as one of the top players in the league. He has recently become a free agent, meaning he can sign a new contract with Cleveland or with any other team in the league. While he has enjoyed playing for Cleveland, which is near his hometown, the team has never seriously contended for a championship, so Labran is strongly considering moving to one of three other teams that he thinks have more championship potential. Other factors he is considering are salary (although Cleveland is offering him more money than the other teams), the possible media attention and endorsements he might receive by playing in another city, and the city itself and lifestyle where he would be playing. Following are the pairwise comparisons for the four teams for these four criteria and the pairwise comparisons for the criteria:




Using AHP, determine which team Labran should select to sign a new contract with.

Question 64

The Growall Fertilizer Company produces three types of fertilizer-Supergro, 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:
(1) The company does not want to spend over $20,000 per week on production, if possible.
(2) The company would like to limit overtime to 100 hours per week.
(3) The company wants to meet demand for all three fertilizers; however, it is twice as important to meet the demand for Supergro as it is to meet the demand for Dynaplant, and it is twice as important to meet the demand for Dynaplant as it is to meet the demand for Soilsaver.
(4) It is desirable to avoid producing under capacity, if possible.
(5) Because of union agreements, the company wants to avoid underutilization of labor.
a. Formulate a goal programming model to determine the number of tons of each brand of fertilizer to produce to satisfy the goals.
b. Solve this model by using the computer.

Question 65

Check the pairwise comparisons for the criteria in Problem for consistency and indicate whether the level of consistency is acceptable.
Problem
Katnis Evergreen, a junior at Tech, is moving out of the dorms where she has lived for 2 years into an apartment in town. She is considering three apartment complexes-the Terraces, the Vistas, and Foxfield. She is going to evaluate the apartments using three criteria-cost, condition (age, upkeep, etc.), and location (i.e., proximity to campus, transportation, shopping, etc.). Katnis's pairwise comparisons for each of the three apartment complexes for each criterion and her pairwise comparison matrix for the three criteria are as follows:



Determine an overall ranking of the three apartment complexes by using AHP.

Question 66

Given the following pairwise comparisons, indicate your preferences according to the preference scale in Table.
a. Steak to chicken
b. Hot dogs to hamburgers
c. Republicans to Democrats
d. Soccer to football
e. College basketball to professional basketball
f. Management science to management
g. Domino's to Pizza Hut
h. McDonald's to Wendy's
i. Ford to Honda
j. Dickens to Faulkner
k. Beatles to Beethoven
l. New York to Los Angeles
m. Chicago to Atlanta
n. American League to National League
Table

Question 67

Balston Healthcare operates three hospitals and a number of clinics in its citywide network. It is planning to open a new wellness center and clinic facility that focuses on geriatric clients in one of four suburbs. The following table shows the weighted criteria for each location:
Recommend a site for the new Balston Healthcare facility, based on these weighted location factors and scores.

Question 68

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 will 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:
(1) Do not exceed the budget constraint of $52,000.
(2) Achieve the percentage increases in compliance necessary to achieve 100% compliance in each category.
(3) Achieve total accident frequency reduction of 20 accidents/105 hours of exposure. (This goal denotes management's desire to minimize the frequency of accidents even if 100% compliance cannot be achieved in all categories.)
(4) Reduce the total accident cost per worker by $115.
a. Formulate a goal programming model to determine the percentage points of compliance needed in each category to satisfy the goals.
b. Solve this model by using the computer.

Question 69

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 selection-potential 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.

Question 70

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 General-that have full-service emergency rooms. Federated wants to designate one of the hospitals as its primary care emergency room 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.

Question 71

The owners of the Blitz professional soccer team in Problem have decided to also use a scoring model, with an expanded set of criteria, to help them decide in which city-Atlanta, Birmingham, Charlotte, or Durham-they should relocate their team. They have graded the possible cities according to the following weighted criteria:
Develop a scoring model to help the owners decide which city to select to relocate to. Based on these scoring model results and the results of the AHP model in Problem 48, which city would you recommend
Problem
The owners of the Blitz professional soccer team are disappointed in their team's home attendance, so they are considering moving to one of four cities: Atlanta, Birmingham, Charlotte, or Durham. The criteria the owners are using to make their decision are population in the 15-40 age group, soccer interest (measured by youth, high school, and college soccer game participation and attendance), media market, entertainment and sports competition, and the proposed playing facility. Following are the owners' pairwise comparisons for the four potential cities for each of the five criteria, and the owners' pairwise comparisons for the criteria:





Using AHP determine which city the owners should select to relocate to.