1. DIT 1141: OPERATIONS MANAGEMENT DEPARTMENT OF DECISION AND INFORMATION TECHNOLOGIES COLLEGE OF COMMERCE AND FINANCE VILLANOVA UNIVERSITY

2. INTRODUCTION

3. INTRODUCTION Operations management is the process of obtaining and utilizing resources to produce useful goods and services so as to meet the goals of the organization.

4. INTRODUCTION Production management is concerned with the manufacturing of goods: Examples of goods: carsbookschairscomputershousesetc.

5. INTRODUCTION Operations management is also concerned with the management of service industries as well as the manufacturing of goods.

6. INTRODUCTION Examples of services: retailing/foodbankingeducation health care utilitiesinsurance government agencies etc.

7. OVERVIEW OF OPERATIONS MANAGEMENT MODEL Transformation Process Process Output Goods or Services Control Input: resources raw materials raw materials machines machines personnel personnel capital capital land/buildings land/buildings utilities utilities information information etc. etc.

8. OVERVIEW OF OPERATIONS MANAGEMENT MODEL Operations management considers how the input are transformed into goods or services. Control is when something is learned about the goods or services that is used to more effectively transform future goods or services.

9. EXAMPLE OF OPERATIONS MANAGEMENT PROCESS Automobile factory Input

10. EXAMPLE OF OPERATIONS MANAGEMENT PROCESS Automobile factory Input steel, plastic glass, paint tools equipment machines personnel, buildings utilities, etc.

11. EXAMPLE OF OPERATIONS MANAGEMENT PROCESS Automobile factory Input steel, plastic glass, paint tools Transformation equipment process machines personnel, buildings utilities, etc.

12. EXAMPLE OF OPERATIONS MANAGEMENT PROCESS Automobile factory InputOutput steel, plastic glass, paint tools Transformation equipment process machines personnel, buildings utilities, etc.

13. EXAMPLE OF OPERATIONS MANAGEMENT PROCESS Automobile factory InputOutput steel, plasticCar glass, paint tools Transformation equipment process machines personnel, buildings utilities, etc.

14. OPERATIONS MANAGEMENT QUESTIONS 1. How many items will be demanded next month? 2. How many items should be produced next month? 3. How many workers are needed to satisfy the proposed production level?

15. OPERATIONS MANAGEMENT QUESTIONS 4. If a plant is built, how should the activities be scheduled so that the project is completed on time, within budget, and with acceptable quality? 5. How is the quality of our output measured and how is it improved? 6. If tires are needed, how many should be ordered?

16. EXAMPLE OF OPERATIONS MANAGEMENT PROCESS HospitalInput

17. HospitalInput patients, doctors nurses, drugs bedsbuilding medical equipment support staff, computers utilities, etc.

18. EXAMPLE OF OPERATIONS MANAGEMENT PROCESS HospitalInput patients, doctors nurses, drugs Transformation beds Process building medical equipment support staff, computers utilities, etc.

19. EXAMPLE OF OPERATIONS MANAGEMENT PROCESS Hospital Input Output patients, doctors nurses, drugs Transformation beds Process building medical equipment support staff, computers utilities, etc.

20. EXAMPLE OF OPERATIONS MANAGEMENT PROCESS Hospital Input Output patients, doctors A treated patient nurses, drugs Transformation beds Process building medical equipment support staff, computers utilities, etc.

21. EXAMPLE OF OPERATIONS MANAGEMENT PROCESS UniversityInput

22. UniversityInput students, professors secretaries

23. EXAMPLE OF OPERATIONS MANAGEMENT PROCESS UniversityInput students, professors secretaries, drugs

24. EXAMPLE OF OPERATIONS MANAGEMENT PROCESS UniversityInput students, professors secretaries, drugs

25. EXAMPLE OF OPERATIONS MANAGEMENT PROCESS UniversityInput students, professors secretaries, lab equipment dormitories staff, computers buildingsetc.

26. EXAMPLE OF OPERATIONS MANAGEMENT PROCESS UniversityInput students, professors secretaries, lab equipment dormitories staff, computers Transformation buildings process etc.

27. EXAMPLE OF OPERATIONS MANAGEMENT PROCESS University InputOutput students, professors secretaries, lab equipment dormitories staff, computers Transformation buildings process etc.

28. EXAMPLE OF OPERATIONS MANAGEMENT PROCESS University InputOutput students, professors A more highly secretaries, lab equipment educated dormitories student staff, computers Transformation buildings process etc.

29. DECISION MAKING IN OPERATIONS: THE ANALYTIC HIERARCHY PROCESS

30. What is the Analytic Hierarchy Process (AHP)? The AHP, developed by Tom Saaty, is a decision- making method for prioritizing alternatives when multi-criteria must be considered. An approach for structuring a problem as a hierarchy or set of integrated levels. INTRODUCTION

31. AHP problems are structured in at least three levels: The goal, such as selecting the best car to purchase, The criteria, such as cost, safety, and appearance, The alternatives, namely the cars themselves. INTRODUCTION

32. The decision-maker: measures the extent to which each alternative achieves each criterion, and determines the relative importance of the criteria in meeting the goal, and synthesizes the results to determine the relative importance of the alternatives in meeting the goal. INTRODUCTION

33. APPROACH How does AHP capture human judgments? AHP never requires you to make an absolute judgment or assessment. You would never be asked to directly estimate the weight of a stone in kilograms. AHP does require you to make a relative assessment between two items at a time. AHP uses a ratio scale of measurement.

34. APPROACH Suppose the weights of two stones are being assessed. AHP would ask: How much heavier (or lighter) is stone A compared to stone B? AHP might tell us that, of the total weight of stones A and B, stone A has 65% of the total weight, whereas, stone B has 35% of the total weight.

35. APPROACH Individual AHP judgments are called pairwise comparisons. These judgments can be based on objective or subjective information. For example, smoothness might be a subjective criterion used to compare two stones. Pairwise comparisons could be based on touch.

36. APPROACH However, suppose stone A is a diamond worth $1,000.00 and stone B is a ruby worth $300.00. This objective information could be used as a basis for a pairwise comparison based on the value of the stones.

37. APPROACH Consistency of judgments can also be measured. Consistency is important when three or more items are being compared. Suppose we judge a basketball to be twice as large as a soccer ball and a soccer ball to be three times as large as a softball. To be perfectly consistent, a basketball must be six times as large as a softball.

38. APPROACH AHP does not require perfect consistency, however, it does provide a measure of consistency. We will discuss consistency in more detail later.

39. AHP APPLICATIONS AHP has been successfully applied to a variety of problems. 1.R&D projects and research papers; 2.vendors, transport carriers, and site locations; 3.employee appraisal and salary increases; 4.product formulation and pharmaceutical licensing; 5.capital budgeting and strategic planning; 6.surgical residents, medical treatment, and diagnostic testing.

40. AHP APPLICATIONS The product and service evaluations prepared by consumer testing services is another potential application. Products and services, such as self propelled lawn mowers are evaluated. Factors include: bagging, mulching, discharging, handling, and ease of use. An overall score for each mower is determined.

41. AHP APPLICATIONS Would you make your purchasing decision based solely on this score? Probably not! Some of the information will be helpful. Some additional questions are: How important is each criterion? Would you weigh the criteria the same way? Are all of the criteria considered important to you? Are there other criteria that are important to you? Have you ever thought about these issues?

42. RANKING SPORTS RECORDS The AHP has been used to rank outstanding season, career, and single event records across sports. Season 1.Babe Ruth, 1920:.847 slugging average 2.Joe DiMaggio, 1944: 56 game hitting streak 3.Wilt Chamberlain, 1961-62: 50.4 points per game scoring average

43. RANKING SPORTS RECORDS Career 1.Johnny Unitas, 1956-70: touchdown passes in 47 consecutive games 2.Babe Ruth, 1914-35:.690 slugging average 3.Walter Payton, 1975-86: 16,193 rushing yardage Single event 1.Wilt Chamberlain, 1962: 100 points scored 2.Norm Van Brocklin, 1951: 554 passing yards 3.Bob Beamon, 1968: 29' 2.5" long jump

44. RANKING SPORTS RECORDS How do we compare records from different sports? It all depends on the criteria that you select! Golden and Wasil (1987) used the following criteria: 1.Duration of record - years record has stood, years expected to stand 2.Incremental improvement - % better than previous record 3.Other record characteristics - glamour, purity (single person vs. team)

45. RANKING SPORTS RECORDS Did this article end all arguments about sports records? Absolutely not! In bars and living rooms across the country, people still argue about sports. AHP provides a methodology to structure the debate. Different criteria and different judgments could produce different results.

46. A FINAL POINT ABOUT SPORTS In reading the sports pages we often see discussion of how well teams match up across different positions. These match-ups are often used to predict a winner. Match-ups is a pairwise comparison concept!

47. AHP APPLICATIONS Our culture is obsessed with quantitative rankings of all sorts of things. There are many measurement problems associated with rankings of products, sports teams, universities, and the like. Many of these issues are discussed on a web site at: http://www.expertchoice.com/annie.personhttp://www.expertchoice.com/annie.person. http://www.expertchoice.com/annie.person

48. The discussion of how to compare records from different sports recalls a saying from childhood: APPLES AND ORANGES

49. The discussion of how to compare records from different sports recalls a saying from childhood: You can’t compare apples and oranges. All you get is mixed fruit! APPLES AND ORANGES

50. The discussion of how to compare records from different sports recalls a saying from childhood: You can’t compare apples and oranges. All you get is mixed fruit! After the discussion about sports, do you still believe this statement? APPLES AND ORANGES

51. The discussion of how to compare records from different sports recalls a saying from childhood: You can’t compare apples and oranges. All you get is mixed fruit! After the discussion about sports, do you still believe this statement? We hope not!!!

52. What criteria might you use when comparing apples and oranges? There are a vast set of criteria that may change depending upon time of day or season of year: taste,texture,smell, ripeness,juiciness,nutrition, shape,weight,color, and cost. Can you think of others? APPLES AND ORANGES

53. The point is that people are often confronted with the choice between apples and oranges. Their choice is based on some psychological assessment of: relevant criteria, their importance, and how well the alternatives achieve the criteria. APPLES AND ORANGES

54. CAR PURCHASE EXAMPLE We now consider a motivating example. After completing this example, you will have an understanding of the basics of AHP and its application through Expert Choice (www.expertchoice.com). We want to apply the AHP to help a couple decide which car they should purchase.

55. CAR PURCHASE EXAMPLE The couple is considering three criteria: cost, safety, and appearance. They have narrowed their alternatives to three specific cars: Honda, Mazda, and Volvo. We demonstrate how to build the AHP hierarchy in Expert Choice.

56. Select the File, New option and enter a file name such as CARS.EC1. (You must use the EC1 file extension.) Choose the Direct option to create the model. Next, specify the description of the goal, such as, “Select the best car.” EXPERT CHOICE: FILE SETUP

57. To enter the criteria, use the Edit, Insert command. Use the Esc key when finished entering the criteria. To add the alternative cars under the cost node, simply highlight the cost node and again use the Edit, Insert command. Use the Esc key when finished. EXPERT CHOICE: FILE SETUP

58. To include the same alternatives under the other criteria nodes, first highlight the cost node, then select Edit, Replicate children of current node, To Peers, Yes. Double-click on the goal node to display the complete hierarchy. Additional details can be found in the Expert Choice tutorial provided with the software. EXPERT CHOICE: FILE SETUP

59. ANALYZING THE HIERARCHY 1.Determine the weights of the alternatives for each criterion. 2.Determine the priorities or weights of the criteria in achieving the goal. 3.Determine the overall weight of each alternative in achieving the goal. This is accomplished by combining the results of the first two stages and is called synthesis.

60. HYPOTHETICAL DATA FOR CAR PURCHASE EXAMPLE Car Cost Safety*Appearance Car Cost Safety*Appearance Honda$22,00028Sporty Honda$22,00028Sporty Mazda 28,50039Slick Mazda 28,50039Slick Volvo 33,00052Dull Volvo 33,00052Dull * Safety Rating from a consumer testing service - the higher the number, the safer the car.

61. DETERMINING PRIORITIES The couple begins by making pairwise comparison judgments between each pair of cars for the cost criterion. In our example, three judgments are needed: Honda to Mazda, Mazda to Volvo, and Honda to Volvo.

62. STANDARD 1 - 9 MEASUREMENT SCALE Intensity of Importance Definition Explanation 1Equal importanceTwo activities contribute equally 3Moderate importanceExperience and judgment slightly favor one activity over another 5Strong importanceExperience and judgment strongly favor one activity over another 7Very strongAn activity is favored very strongly over another 9Extreme importanceThe evidence favoring one activity over another is of the highest possible order of affirmation 2, 4, 6, 8For compromiseSometimes one needs to interpolate a 2, 4, 6, 8For compromiseSometimes one needs to interpolate a valuescompromise between the above judgment numerically because there is no good word to describe it 1.1 - 1.9For tied activitiesWhen elements are close and nearly 1.1 - 1.9For tied activitiesWhen elements are close and nearly indistinguishable; moderate is 1.3 and extreme is 1.9 Reciprocals of aboveIf activity A hasFor example, if the pairwise comparison of one of the above A to B is 3.0, then the pairwise comparison numbers assignedof B to A is 1/3 to it when compared with activity B, then B has the reciprocal value when compared to A.

63. COST PAIRWISE COMPARISONS The pairwise comparisons are represented in the form of pairwise comparison matrices. The computation of the weights are also shown. Consider the pairwise comparison matrix to compare the cars for the cost criterion. Remember that the costs of the three cars are: $22000, $28500, and $33000, respectively.

64. If we compare the Honda to the Honda, obviously they are equal. Therefore, a 1 (equal preferred) is placed in the first row, first column entry of the matrix. COST PAIRWISE COMPARISONS

65. A. ORIGINAL COST PAIRWISE COMPARISON MATRIX Honda Mazda Volvo Honda Mazda Volvo 22KHonda 1 28.5KMazda 33KVolvo COST PAIRWISE COMPARISONS

66. The other entries along the main diagonal of the matrix are also 1. This simply means that everything is equally preferred to itself. COST PAIRWISE COMPARISONS

67. A. ORIGINAL COST PAIRWISE COMPARISON MATRIX Honda Mazda Volvo Honda Mazda Volvo 22KHonda 1 28.5KMazda 1 33KVolvo 1 COST PAIRWISE COMPARISONS

68. Suppose we believe the Honda ($22000) is equally to moderately preferred to the Mazda ($28500). Place a 2 in the row 1, column 2 entry. Some might argue that the Honda should be 1.295 times better than the Mazda (28,500/22,000). COST PAIRWISE COMPARISONS

69. Do you agree? It depends! For some, $28,500 is significantly greater than $22,000, implying a judgments greater than 1.295. Others with a lot of money may perceive virtually no difference between the two costs, implying a judgment somewhere between 1 and 1.295. COST PAIRWISE COMPARISONS

70. A. ORIGINAL COST PAIRWISE COMPARISON MATRIX Honda Mazda Volvo Honda Mazda Volvo 22KHonda 1 2 28.5KMazda 1 33KVolvo 1 COST PAIRWISE COMPARISONS

71. If the Honda is 2 times better than the Mazda, this implies that the Mazda ($28500) is one half as good as the Honda ($22000). The reciprocal judgment, (1/2), should be placed in the row 2, column 1 entry of the matrix. COST PAIRWISE COMPARISONS

72. A. ORIGINAL COST PAIRWISE COMPARISON MATRIX Honda Mazda Volvo Honda Mazda Volvo 22KHonda 1 2 28.5KMazda 1/2 1 33KVolvo 1 COST PAIRWISE COMPARISONS

73. Suppose that we judge the Mazda ($28500) to be equally to moderately preferred to the Volvo ($33000). The following judgments would be entered in the matrix. COST PAIRWISE COMPARISONS

74. A. ORIGINAL COST PAIRWISE COMPARISON MATRIX Honda Mazda Volvo Honda Mazda Volvo 22KHonda 1 2 28.5KMazda 1/2 1 2 33KVolvo 1/2 1 COST PAIRWISE COMPARISONS

75. Assuming perfect consistency of judgments, we would expect that the Honda ($22000) is 4 times (that is, moderately to strongly) preferred to the Volvo ($33000). We will relax this assumption later. COST PAIRWISE COMPARISONS

76. A. ORIGINAL COST PAIRWISE COMPARISON MATRIX Honda Mazda Volvo Honda Mazda Volvo 22KHonda 1 2 4 28.5KMazda 1/2 1 2 33KVolvo 1/4 1/2 1 COST PAIRWISE COMPARISONS

77. The matrix is now complete and the weights for each car (for the cost criterion) can be computed. The exact computational procedure is implemented in Expert Choice. For details see Expert Choice homepage and download AHPDEMO.EXE. COST PAIRWISE COMPARISONS

78. A simple three step procedure can be used to approximate the weights for each alternative. Essentially, this procedure normalizes the ratios of the judgments between any pair of alternatives. COST PAIRWISE COMPARISONS

79. 1.SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX. 2.DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM. THIS RESULTS IN THE ADJUSTED MATRIX. 3.COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS. A. ORIGINAL COST PAIRWISE COMPARISON MATRIX Honda Mazda Volvo Honda Mazda Volvo 22KHonda 1 2 4 28.5KMazda 1/2 1 2 33KVolvo 1/4 1/2 1 ------- ------- ------- ------- ------- ------- COLUMN TOTALS COST PAIRWISE COMPARISONS

80. 1.SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX. 2.DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM. THIS RESULTS IN THE ADJUSTED MATRIX. 3.COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS. A. ORIGINAL COST PAIRWISE COMPARISON MATRIX Honda Mazda Volvo Honda Mazda Volvo 22KHonda 1 2 4 28.5KMazda 1/2 1 2 33KVolvo 1/4 1/2 1 ------- ------- ------- ------- ------- ------- COLUMN TOTALS 7/4 7/2 7 COST PAIRWISE COMPARISONS

81. 1.SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX. 2.DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM. THIS RESULTS IN THE ADJUSTED MATRIX. 3.COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS. A. ORIGINAL COST PAIRWISE COMPARISON MATRIX Honda Mazda Volvo Honda Mazda Volvo 22KHonda 1 2 4 28.5KMazda 1/2 1 2 33KVolvo 1/4 1/2 1 ------- ------- ------- ------- ------- ------- COLUMN TOTALS 7/4 7/2 7 COST PAIRWISE COMPARISONS

82. 1.SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX. 2.DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM. THIS RESULTS IN THE ADJUSTED MATRIX. 3.COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS. A. ORIGINAL COST PAIRWISE COMPARISON MATRIX Honda Mazda Volvo Honda Mazda Volvo 22KHonda 1 2 4 28.5KMazda 1/2 1 2 33KVolvo 1/4 1/2 1 ------- ------- ------- ------- ------- ------- COLUMN TOTALS 7/4 7/2 7 B. ADJUSTED COST PAIRWISE COMPARISON MATRIX B. ADJUSTED COST PAIRWISE COMPARISON MATRIX Honda Mazda Volvo Honda Mazda Volvo Honda 4/7* 4/7 4/7 Mazda 2/7 2/7 2/7 Volvo 1/7 1/7 1/7 * This entry is obtained by dividing the Honda entry in the original matrix (1) by the Honda column total (7/4). * This entry is obtained by dividing the Honda entry in the original matrix (1) by the Honda column total (7/4). COST PAIRWISE COMPARISONS

83. Notice that no variation is seen across the rows because the judgments are perfectly consistent. For the third column, judgments totaling 7 were awarded. The Honda received 4 of 7 (57.1%), the Mazda 2 of 7 (28.6%), and the Volvo 1 of 7 (14.3%) of the weight. Similar comparisons can be made for the other two columns. COST PAIRWISE COMPARISONS

84. 1.SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX. 2.DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM. THIS RESULTS IN THE ADJUSTED MATRIX. 3.COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS. A. ORIGINAL COST PAIRWISE COMPARISON MATRIX Honda Mazda Volvo Honda Mazda Volvo 22KHonda 1 2 4 28.5KMazda 1/2 1 2 33KVolvo 1/4 1/2 1 ------- ------- ------- ------- ------- ------- COLUMN TOTALS 7/4 7/2 7 B. ADJUSTED COST PAIRWISE COMPARISON MATRIX B. ADJUSTED COST PAIRWISE COMPARISON MATRIX Honda Mazda Volvo Honda Mazda Volvo Honda 4/7* 4/7 4/7 Mazda 2/7 2/7 2/7 Volvo 1/7 1/7 1/7 * This entry is obtained by dividing the Honda entry in the original matrix (1) by the Honda column total (7/4). * This entry is obtained by dividing the Honda entry in the original matrix (1) by the Honda column total (7/4). COST PAIRWISE COMPARISONS

85. 1.SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX. 2.DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM. THIS RESULTS IN THE ADJUSTED MATRIX. 3.COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS. A. ORIGINAL COST PAIRWISE COMPARISON MATRIX Honda Mazda Volvo Honda Mazda Volvo 22KHonda 1 2 4 28.5KMazda 1/2 1 2 33KVolvo 1/4 1/2 1 ------- ------- ------- ------- ------- ------- COLUMN TOTALS 7/4 7/2 7 B. ADJUSTED COST PAIRWISE COMPARISON MATRIX WEIGHTS B. ADJUSTED COST PAIRWISE COMPARISON MATRIX WEIGHTS Honda Mazda Volvo (ROW AVG.) Honda Mazda Volvo (ROW AVG.) Honda 4/7* 4/7 4/7 0.571 Mazda 2/7 2/7 2/7 0.286 Volvo 1/7 1/7 1/7 0.143 --------- --------- TOTAL 1.000 TOTAL 1.000 * This entry is obtained by dividing the Honda entry in the original matrix (1) by the Honda column total (7/4). * This entry is obtained by dividing the Honda entry in the original matrix (1) by the Honda column total (7/4). COST PAIRWISE COMPARISONS

86. Expert Choice offers a variety of modes for entering the judgments. Highlight the cost node, select Assessment. There are three options: Pairwise, Data, and Ratings. Ratings will be discussed later. EXPERT CHOICE: Entering Judgments

87. The Data option allows the user to enter data items for each alternative, for example, costs, miles per gallon, and number of defects. Expert Choice takes the ratio of these data items and converts them into pairwise comparisons. What assumption are you making if you use the Data option? The data items have a linear preference scale, that is, a $20,000 car is twice as good as a $40,000 car. EXPERT CHOICE: Entering Judgments

88. To enter our cost judgments choose Pairwise. When comparing alternatives select Preference for Type; for criteria select Importance. Modes options are: Verbal, Matrix (numerical), Questionnaire, and Graphic. Assessment, Pairwise, Matrix is demonstrated. Enter judgments, Calculate and Record. EXPERT CHOICE: Entering Judgments

89. INCONSISTENCY OF JUDGMENTS Since our pairwise comparisons were perfectly consistent, Expert Choice reports INCONSISTENCY RATIO = 0.0. If this ratio is greater than 0.1 some revision of judgments is required. Select Inconsistency (within Assessment, Pairwise) to identify the most inconsistent judgments.

90. INCONSISTENCY OF JUDGMENTS Inconsistency of judgments may result from: problems of estimation; errors between the comparisons; or, the comparisons may be naturally inconsistent.

91. INCONSISTENCY OF JUDGMENTS One example of natural inconsistency is in a sporting contest. If team A is twice as likely to beat team B, and if team B is three times as likely to beat team C, this does not necessarily imply that team A is six times as likely to beat team C. This inconsistency may result because of the way that the teams “match-up” overall.

92. INCONSISTENCY OF JUDGMENTS The point is not to stop inconsistency from occurring. Make sure that the level of inconsistency remains within some reasonable limit.

93. INCONSISTENCY OF JUDGMENTS How does a judgment change affect the car weights? Suppose the Mazda to Volvo changes from 2 to 3. This obviously changes the comparison for Volvo to Mazda from (1/2) to (1/3). The judgments are now somewhat inconsistent.

94. A. ORIGINAL COST PAIRWISE COMPARISON MATRIX Honda Mazda Volvo Honda Mazda Volvo 22KHonda 1 2 4 28.5KMazda 1/2 1 3 33KVolvo 1/4 1/3 1 COST PAIRWISE COMPARISONS

95. 1.SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX. 2.DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM. THIS RESULTS IN THE ADJUSTED MATRIX. 3.COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS. A. ORIGINAL COST PAIRWISE COMPARISON MATRIX Honda Mazda Volvo Honda Mazda Volvo 22KHonda 1 2 4 28.5KMazda 1/2 1 3 33KVolvo 1/4 1/3 1 ------- ------- ------- ------- ------- ------- COLUMN TOTALS 7/4 10/3 8 COST PAIRWISE COMPARISONS

96. 1.SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX. 2.DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM. THIS RESULTS IN THE ADJUSTED MATRIX. 3.COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS. A. ORIGINAL COST PAIRWISE COMPARISON MATRIX Honda Mazda Volvo Honda Mazda Volvo 22KHonda 1 2 4 28.5KMazda 1/2 1 3 33KVolvo 1/4 1/3 1 ------- ------- ------- ------- ------- ------- COLUMN TOTALS 7/4 10/3 8 B. ADJUSTED COST PAIRWISE COMPARISON MATRIX B. ADJUSTED COST PAIRWISE COMPARISON MATRIX Honda Mazda Volvo Honda Mazda Volvo Honda 4/7* 6/10 4/8 Mazda 2/7 3/10 3/8 Volvo 1/7 1/10 1/8 * This entry is obtained by dividing the Honda entry in the original matrix (1) by the Honda column total (7/4). * This entry is obtained by dividing the Honda entry in the original matrix (1) by the Honda column total (7/4). COST PAIRWISE COMPARISONS

97. 1.SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX. 2.DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM. THIS RESULTS IN THE ADJUSTED MATRIX. 3.COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS. A. ORIGINAL COST PAIRWISE COMPARISON MATRIX Honda Mazda Volvo Honda Mazda Volvo 22KHonda 1 2 4 28.5KMazda 1/2 1 3 33KVolvo 1/4 1/3 1 ------- ------- ------- ------- ------- ------- COLUMN TOTALS 7/4 10/3 8 B. ADJUSTED COST PAIRWISE COMPARISON MATRIX WEIGHTS B. ADJUSTED COST PAIRWISE COMPARISON MATRIX WEIGHTS Honda Mazda Volvo (ROW AVG.) Honda Mazda Volvo (ROW AVG.) Honda 4/7* 6/10 4/8 0.557 Mazda 2/7 3/10 3/8 0.320 Volvo 1/7 1/10 1/8 0.123 -------- -------- TOTAL 1.000 TOTAL 1.000 * This entry is obtained by dividing the Honda entry in the original matrix (1) by the Honda column total (7/4). * This entry is obtained by dividing the Honda entry in the original matrix (1) by the Honda column total (7/4). COST PAIRWISE COMPARISONS

98. INCONSISTENCY OF JUDGMENTS The new weights are: 0.557, 0.320, and 0.123. The inconsistency resulted in some change in the original weights of 0.571, 0.286, and 0.143. As expected, the weight for the Mazda increased while the weight for the Volvo decreased. The weights now vary across each row. Essentially, inconsistency measures the degree of variation across the rows.

99. Highlight cost node, select Assessment, Pairwise. Enter a 3 in the Mazda to Volvo cell then Calculate. The weights of 0.558, 0.320, and 0.122 are slightly different from the three-step procedure weights. This is not due to rounding -- Expert Choice gives the exact results. The INCONSISTENCY RATIO is now 0.02. EXPERT CHOICE: Revising Judgments

100. INCONSISTENCY OF JUDGMENTS The weights can also be used to measure the effectiveness of the alternatives. For example, based on all pairwise comparisons, we determined that the Honda is 1.74 (0.558/0.320) times better than the Mazda. Why is this ratio 1.74 and not the pairwise comparison of 2? Inconsistency in the judgments!

101. REMAINING COMPUTATIONS Next, the cars must be pairwise compared for the safety criterion and then for the appearance criterion. These judgments are shown on the next page. Since the Mazda to Honda safety comparison is 2, highlight the Honda to Mazda cell, click Invert, and enter 2. This judgment now appears in red.

102. SAFETY & APPEARANCE JUDGMENTS Safety Pairwise Comparison Matrix HondaMazdaVolvo 28 Honda11/21/5 39 Mazda211/4 52 Volvo541 Appearance Pairwise Comparison Matrix HondaMazdaVolvo SportyHonda159 SlickMazda1/512 DullVolvo1/91/21

103. REMAINING COMPUTATIONS Next, the criteria must be pairwise compared. These judgments are shown on the next page. There are no data to support these judgments since they are purely a reflection of your preferences.

104. CRITERIA JUDGMENTS Original Criteria Pairwise Comparison Matrix CostSafetyAppearance Cost11/23 Safety215 Appearance1/31/51

105. REMAINING COMPUTATIONS The last stage computes the final weights for each car. Multiply the criteria weight by the car weight for each criterion and then sum over all criteria. This is nothing more than a weighted average. The computational results are shown next.

106. FINAL CAR WEIGHTS CRITERIA WEIGHTS CRITERIA WEIGHTS COST SAFETY APPEARANCE COST SAFETY APPEARANCE 0.309 0.582 0.109 0.309 0.582 0.109 CARS FINAL WEIGHTS CARS FINAL WEIGHTS Honda 0.558 0.117 0.761 Honda 0.558 0.117 0.761 Mazda 0.320 0.200 0.158 Mazda 0.320 0.200 0.158 Volvo 0.122 0.683 0.082 Volvo 0.122 0.683 0.082

107. FINAL CAR WEIGHTS CRITERIA WEIGHTS CRITERIA WEIGHTS COST SAFETY APPEARANCE COST SAFETY APPEARANCE 0.309 0.582 0.109 0.309 0.582 0.109 CARS FINAL WEIGHTS CARS FINAL WEIGHTS Honda 0.558 0.117 0.761 0.324 Honda 0.558 0.117 0.761 0.324 Mazda 0.320 0.200 0.158 Mazda 0.320 0.200 0.158 Volvo 0.122 0.683 0.082 Volvo 0.122 0.683 0.082 Honda: (0.558)(0.309) + (0.117)(0.582) + (0.761)(0.109) = 0.324 0.173 0.068 0.083 0.173 0.068 0.083

108. FINAL CAR WEIGHTS CRITERIA WEIGHTS CRITERIA WEIGHTS COST SAFETY APPEARANCE COST SAFETY APPEARANCE 0.309 0.582 0.109 0.309 0.582 0.109 CARS FINAL WEIGHTS CARS FINAL WEIGHTS Honda 0.558 0.117 0.761 0.324 Honda 0.558 0.117 0.761 0.324 Mazda 0.320 0.200 0.158 0.232 Mazda 0.320 0.200 0.158 0.232 Volvo 0.122 0.683 0.082 Volvo 0.122 0.683 0.082 Honda: (0.558)(0.309) + (0.117)(0.582) + (0.761)(0.109) = 0.324 0.173 0.068 0.083 0.173 0.068 0.083 Mazda: (0.320)(0.309) + (0.200)(0.582) + (0.158)(0.109) = 0.232 0.099 0.116 0.017 0.099 0.116 0.017

109. FINAL CAR WEIGHTS CRITERIA WEIGHTS CRITERIA WEIGHTS COST SAFETY APPEARANCE COST SAFETY APPEARANCE 0.309 0.582 0.109 0.309 0.582 0.109 CARS FINAL WEIGHTS CARS FINAL WEIGHTS Honda 0.558 0.117 0.761 0.324 Honda 0.558 0.117 0.761 0.324 Mazda 0.320 0.200 0.158 0.232 Mazda 0.320 0.200 0.158 0.232 Volvo 0.122 0.683 0.082 0.444 Volvo 0.122 0.683 0.082 0.444 Honda: (0.558)(0.309) + (0.117)(0.582) + (0.761)(0.109) = 0.324 0.173 0.068 0.083 0.173 0.068 0.083 Mazda: (0.320)(0.309) + (0.200)(0.582) + (0.158)(0.109) = 0.232 0.099 0.116 0.017 0.099 0.116 0.017 Volvo: (0.122)(0.309) + (0.683)(0.582) + (0.082)(0.109) = 0.444 0.038 0.397 0.009 0.038 0.397 0.009

110. LOCAL VS GLOBAL WEIGHTS For cost, the local weights for the cars are 0.558, 0.320, and 0.122 and sum to 1.000. The global weights are computed by multiplying the cost criterion weight by the local car weights. The global weights are 0.173, 0.099, and 0.038 and sum to the cost criterion weight of 0.309.

111. To compute the final weights select Synthesis (from GOAL). Choose Distributive Mode and Display Summary. Details provides the global weights. The output can also be exported to a spreadsheet using the Utilities, Export Model(s) to Spreadsheet commands. EXPERT CHOICE: Synthesis

112. The Print icon can be used to select certain options. The recommended print options are: Entire Tree, Tree Views, Judgments/Data, and Synthesis. EXPERT CHOICE: Printing

113. INTERPRETING THE RESULTS The final weights provide a measure of the relative performance of each alternative. It is important to properly interpret the meaning of these numbers. The Volvo is ranked first, the Honda second, and Mazda third. The Volvo is preferred 1.37 (0.444/0.324) times more than the Honda.

114. INTERPRETING THE RESULTS Should we buy the Volvo? The output is a decision-making aid and cannot replace the decision-maker. The results can be used to support discussion and possibly the judgments will be revised. This iterative process is quite normal. AHP can help to facilitate communication and generate consensus between different groups.

115. SENSITIVITY ANALYSIS Sensitivity analysis is an important aspect of any decision-making process. Sensitivity analysis determines whether small changes in judgments affects the final weights and rankings of the alternatives. If so, the decision-maker may want to review the sensitive judgments.

116. EXPERT CHOICE: Sensitivity Analysis In Expert Choice sensitivity analysis from the GOAL shows how the weights and the rankings of the alternatives change if some or all of the criteria weights change. There are five graphical sensitivity analysis modes available: Performance, Dynamic, Gradient, Two- Dimensional, and Difference. The first three show how a change in a criterion weight affects the final weights of the alternatives.

117. The last two show how the alternatives perform with respect to any two criteria. Performance: places all sensitivity information on a single chart with horizontal line graphs for the alternatives linked to vertical bars for the criteria. Dynamic: two sets of dynamically linked horizontal bar graphs: one for criteria and one for alternatives. EXPERT CHOICE: Sensitivity Analysis

118. Gradient: a line graph that shows how the weights of the alternatives vary according to the weight assigned to a specific criterion. (Use the X-Axis to change the selected criterion.) Two-Dimensional: shows how well the alternatives perform with respect to any two criteria. Difference: a graph that shows the differences between any two alternatives for any criterion. EXPERT CHOICE: Sensitivity Analysis

119. An important use of sensitivity analysis is to determine how much a given criterion weight must change before there is a change in the rankings of the two highest alternatives. This type of breakeven analysis can be easily done in Expert Choice. EXPERT CHOICE: Sensitivity Analysis

120. Choose Dynamic from the Sensitivity-Graphs option. Drag the cost criterion bar 30.9% to approximately 45.9%, and see that the Volvo and Honda have the same highest final weight. The final rankings are relatively insensitive to a change in the cost criterion weight because the cost weight had to be increased by almost 50% to get a change in the rankings. EXPERT CHOICE: Sensitivity Analysis

121. NEW PRODUCT INTRODUCTION CHOCK-FUL-O-CHIPS developed the following hierarchy and data that can be used to help decide which chocolate chip recipe they should use. Select the best recipe Taste Cost Fat Content Recipe 1 Recipe 2 Recipe 3 Recipe 4 Recipe 1 Recipe 2 Recipe 3 Recipe 4 Recipe 1 Recipe 2 Recipe 3 Recipe 4

122. RECIPE DATA Taste Fat Content Taste Fat Content Recipe Cost* Rating** (Grams)* Recipe Cost* Rating** (Grams)* 1 $0.16654%8.0 2 0.09924%7.0 3 0.26520%3.5 4 0.22443%6.0 * Per one ounce cookie ** Percentage of people who rated a cookie either an 8 or 9 on a 9-point scale, where 9 means extremely liked, 8 means liked very much, and down to one which means extremely disliked.

123. TASTE PAIRWISE COMPARISON MATRIX 54% 24% 20% 43% 54% 24% 20% 43% Recipe 1 Recipe 2 Recipe 3 Recipe 4 Recipe 1 Recipe 2 Recipe 3 Recipe 4 Recipe 1 1 Recipe 21 Recipe 3 1 Recipe 4 1

124. COST PAIRWISE COMPARISON MATRIX 0.166 0.099 0.265 0.224 0.166 0.099 0.265 0.224 Recipe 1 Recipe 2 Recipe 3 Recipe 4 Recipe 1 Recipe 2 Recipe 3 Recipe 4 Recipe 1 1 Recipe 21 Recipe 3 1 Recipe 4 1

125. FAT CONTENT PAIRWISE COMPARISON MATRIX 8.0 7.0 3.5 6.0 8.0 7.0 3.5 6.0 Recipe 1 Recipe 2 Recipe 3 Recipe 4 Recipe 1 Recipe 2 Recipe 3 Recipe 4 Recipe 1 1 Recipe 21 Recipe 3 1 Recipe 4 1

126. CRITERIA PAIRWISE COMPARISON MATRIX TasteCostFat Content TasteCostFat Content Taste 1 Cost 1 Fat Content1

127. FINAL WEIGHTS FROM EXPERT CHOICE Criteria Weights Criteria Weights Taste Cost Fat Content Taste Cost Fat Content Final Final Weights Weights Recipe 1 Recipe 1 Recipe 2 Recipe 2 Recipe 3 Recipe 3 Recipe 4 Recipe 4

128. SUMMARY In this chapter: we provided an overview of operations management; and offered the AHP as a decision-making process with application in operations management.

129. SUMMARY AHP benefits include: natural way to elicit judgments; measure degree of inconsistency; easy to use; allows broad participation; and fully supported by Expert Choice.