1. Decision Technology Modeling, Software and Applications Matthew J. Liberatore Robert L. Nydick John Wiley & Sons, Inc.

2. Chapter 10 The Analytic Hierarchy Process Using Decision Lens

3. CAR PURCHASE EXAMPLE We now consider an example to illustrate the basics of the AHP. After completing this example, you will understand the application of the AHP through Decision Lens. We want to apply the AHP to help a couple decide which car they should purchase.

4. 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 Decision Lens.

5. After launching Decision Lens, begin to create a model by following the five steps in order: 1. Build Model, 2. Compare Criteria, 3. Evaluate Alternatives, 4. Allocate Resources, and 5. Reporting. From the Build Model step, select “Create Tree- View” in the upper left hand corner and enter a description in “Goal Name,” such as, “Select the best car” and click OK. DECISION LENS: FILE SETUP

6. To enter the criteria, for example, cost, safety, and appearance, select “Add Child” and add the three criteria. Select cancel when all criteria has been entered. To add the alternative cars select the “Identify Alternatives” option in the upper left hand corner. Enter a criteria and alternative description in the Definition location. This is done using the notation button (looks like a piece of paper) to the right of the criteria and alternatives in the tree view and alternatives section. DECISION LENS: FILE SETUP

7. Select the “Add Alternative” option three times to enter the alternatives: Honda, Mazda, Volvo. Identify “musts” to limit alternatives. For example, the car must get at least 20 mpg and must have at least dual airbags. Select the “Identify Participants” and enter the wife and husband (Mary and Joe) as one decision maker. In this example, we will assume that Mary and Joe will only enter one set of judgments. We will show later how to have each participant add their own judgments.

8. ANALYZING THE HIERARCHY 1.Determine the priorities or weights of the criteria in achieving the goal. 2.Determine the weights of the alternatives for each criterion. 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.

9. 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.

10. DETERMINING PRIORITIES The couple begins by making pairwise comparison judgments between each pair of criteria. In our example, three judgments are needed: Cost to Safety, Safety to Appearance, and Cost to Appearance. The scale on the next page is the standard one to nine developed by Saaty.

11. 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.

12. 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 criteria. If we compare the Cost to Cost, obviously they are equal. Therefore, a 1 (equal preferred) is placed in the first row, first column entry of the matrix.

13. A. ORIGINAL CRITERIA PAIRWISE COMPARISON MATRIX CostSafetyAppearance Cost1 SafetyAppearance COST PAIRWISE COMPARISONS

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

15. A. ORIGINAL CRITERIA PAIRWISE COMPARISON MATRIX CostSafetyAppearance Cost1 Safety1 Appearance1 COST PAIRWISE COMPARISONS

16. Suppose we believe that Safety is equally to moderately more important than Cost. Place a 1/2 in the row 1, column 2 entry and its reciprocal value (2) in row 2, column 1 entry. This actually means that Cost is one half times as important as Safety and that Safety it twice as important as Cost. COST PAIRWISE COMPARISONS

17. A. ORIGINAL CRITERIA PAIRWISE COMPARISON MATRIX CostSafetyAppearance Cost11/2 Safety21 Appearance1 COST PAIRWISE COMPARISONS

18. Suppose that we judge Safety to be strongly more important than Appearance. The following judgments would be entered in the matrix. COST PAIRWISE COMPARISONS

19. A. ORIGINAL CRITERIA PAIRWISE COMPARISON MATRIX CostSafetyAppearance Cost11/2 Safety215 Appearance1/51 COST PAIRWISE COMPARISONS

20. The last set of judgments that are needed for this problem are that Cost is moderately more important than Appearance. These judgments are also shown. COST PAIRWISE COMPARISONS

21. A. ORIGINAL CRITERIA PAIRWISE COMPARISON MATRIX CostSafetyAppearance Cost11/23 Safety215 Appearance1/31/51 COST PAIRWISE COMPARISONS

22. The matrix is now complete and the weights for each criterion can be computed. The exact computational procedure is implemented in Decision Lens, however, we show a simple three step procedure can be used to approximate the weights for each criterion. Essentially, this procedure normalizes the ratios of the judgments between any pair of criteria. COST PAIRWISE COMPARISONS

23. 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 CRITERIA PAIRWISE COMPARISON MATRIX CostSafetyAppearance Cost11/23 Safety215 Appearance1/31/51 -------- ------- ----- -------- ------- ----- COLUMN TOTALS COST PAIRWISE COMPARISONS

24. 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 CRITERIA PAIRWISE COMPARISON MATRIX CostSafetyAppearance Cost11/23 Safety215 Appearance1/31/51 -------- ------- ----- -------- ------- ----- COLUMN TOTALS10/317/109 COST PAIRWISE COMPARISONS

25. 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 CRITERIA PAIRWISE COMPARISON MATRIX CostSafetyAppearance Cost11/23 Safety215 Appearance1/31/51 -------- ------- ----- -------- ------- ----- COLUMN TOTALS10/317/109 COST PAIRWISE COMPARISONS

26. 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 CRITERIA PAIRWISE COMPARISON MATRIX CostSafetyAppearance Cost11/23 Safety215 Appearance1/31/51 -------- ------- ----- -------- ------- ----- COLUMN TOTALS10/317/109 B. ADJUSTED CRITERIA PAIRWISE COMPARISON MATRIX B. ADJUSTED CRITERIA PAIRWISE COMPARISON MATRIX CostSafetyAppearance Cost3/10*5/173/9 Safety6/1010/175/9 Appearance1/102/171/9 * This entry is obtained by dividing the Cost entry in the original matrix (1) by the Cost column total (10/3). * This entry is obtained by dividing the Cost entry in the original matrix (1) by the Cost column total (10/3). COST PAIRWISE COMPARISONS

27. For the third column, judgments totaling 9 were awarded. Cost received 3 of 9 (33.3%), Safety 5 of 9 (55.6%), and Appearance 1 of 9 (11.1%) of the weight. Similar comparisons can be made for the other two columns. COST PAIRWISE COMPARISONS

28. 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 CRITERIA PAIRWISE COMPARISON MATRIX CostSafetyAppearance Cost11/23 Safety215 Appearance1/31/51 -------- ------- ----- -------- ------- ----- COLUMN TOTALS10/317/109 B. ADJUSTED CRITERIA PAIRWISE COMPARISON MATRIXWEIGHTS B. ADJUSTED CRITERIA PAIRWISE COMPARISON MATRIXWEIGHTS CostSafetyAppearanceRow Avg. Cost3/10*5/173/9.309 Safety6/1010/175/9.581 Appearance1/102/171/9.110 ------- TOTAL1.000 * This entry is obtained by dividing the Cost entry in the original matrix (1) by the Cost column total (10/3). * This entry is obtained by dividing the Cost entry in the original matrix (1) by the Cost column total (10/3). COST PAIRWISE COMPARISONS

29. Entering judgments in Decision Lens is simple. Choose “Compare Criteria” (step 2) and the “Pairwise Comparison” option (upper left hand corner) to enter the criteria comparisons. Since Safety is judged to be twice as important as Cost, Mary and Joe would click on the 2 option on the right hand side of the bar. Since there is only one decision maker, once Mary and Joe enter their judgment the same value appears in the average row. If Cost was judged to be twice as important to Safety, the 2 on the left would be selected. To enter a decimal judgment right click on the bar and select Decimal Vote. Entering Judgments

30. Choosing the “Next Vote” button allows the other comparisons to be entered. Make sure you notice which judgment is being entered next. For example, after hitting the “Next Vote” button once the Safety to Appearance comparison is entered (5). In this example, Decision Lens only requires three judgments. 1’s along the main diagonal and reciprocal judgments are not entered. DECISION LENS: Entering Judgments

31. After entering all pairwise comparisons, select the “Compute” button to display the criteria weights. Decision Lens reports that the weights for Cost, Safety, and Appearance are 0.309, 0.582, and 0.109, respectively. Remember that the 3-step approximation produced weights of 0.309, 0.581, and 0.110, respectively. This difference is not due to rounding – Decision Lens gives the exact weights. DECISION LENS: Entering Judgments

32. INCONSISTENCY OF JUDGMENTS Decision Lens also reports the inconsistency at 0.004. If this ratio is greater than 0.1 some revision of judgments may be required. Select “Inconsistency Analysis” in the upper left hand corner and then “Matrix View” for information about inconsistent judgments.

33. INCONSISTENCY OF JUDGMENTS Inconsistency of judgments may result from: problems of estimation; errors between the comparisons; or, the comparisons may be naturally inconsistent. One example of natural inconsistency is in sports. 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.

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

35. INCONSISTENCY OF JUDGMENTS We knew that Safety was more important than Cost, but now we know how much more important. We judged Safety to be 2 times more important than Cost. The weights tell us that Safety is 1.88 times more important than Cost (0.582/0.309). Which is “correct” and why is there a difference?

36. REMAINING COMPUTATIONS Next, the cars must be pairwise compared for the three criteria: cost, safety and appearance. The couple can base their judgments on the following (hypothetical) performance information. All alternative pairwise comparisons should be based on data. We need to compare Honda to Mazda, Mazda to Volvo, and Honda to Volvo for each criterion.

37. HYPOTHETICAL DATA FOR CAR PURCHASE EXAMPLE Car Cost Safety*Appearance Car Cost Safety*Appearance Honda$22,000AverageSporty Honda$22,000AverageSporty Mazda 28,500Above AverageSlick Mazda 28,500Above AverageSlick Volvo 33,000ExcellentDull Volvo 33,000ExcellentDull * Safety Rating from a consumer testing service.

38. COST JUDGMENTS Cost Pairwise Comparison Matrix HondaMazdaVolvo $22k Honda124 $28.5kMazda1/213 $33k Volvo1/41/31

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

40. ENTERING JUDGMENTS IN DECISION LENS These judgments now need to be entered in Decision Lens. Select the third step: “Evaluate Alternatives,” click on the “Pairwise Alternatives” button, Yes, and “Next.” You will then be taken through screens that will allow you to enter the 9 pairwise comparison judgments (3 each for the three criteria). Select “Next Vote” to enter all of the judgments.

41. ENTERING JUDGMENTS IN DECISION LENS Again, be careful to make sure that you know which judgments are being entered at each step. After all 9 judgments have been entered select “Next Vote” again to display the final weights.

42. REMAINING COMPUTATIONS The alternative weights are computed just like the criteria weights and are based on the alternative pairwise comparisons for each criterion. To compute the final weights, 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.

43. FINAL CAR 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

44. FINAL CAR 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

45. FINAL CAR 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

46. FINAL CAR 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

47. 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.

48. 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.

49. INTERPRETING THE RESULTS Should the couple 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.

50. SYNTHESIS MODES The process used to compute the final weights is called distributive synthesis. Distributive synthesis should be used when you are concerned about the priorities of all the alternatives or when you want to allocate a fixed amount of resources across all alternatives. Ideal synthesis should be used when you are choosing one alternative and don’t really care about the alternatives you do not choose. For example, you are buying one car.

51. SYNTHESIS MODES In some cases after completing an AHP analysis, an additional alternative may need to be considered. It is possible that a rank reversal could occur. Our rankings are: Volvo, Honda, and Mazda. If another Volvo is added that is similar to the original Volvo, it is possible that the Honda will be ranked higher than the original Volvo.

52. SYNTHESIS MODES In some cases this is acceptable, in others it is not. Distributive synthesis should not be used if preservation of rank is important. Ideal Synthesis should be used to prevent rank reversal.

53. IDEAL MODE The ideal mode gives the full weight of the criterion to the alternative that ranks highest under that criterion. The other alternatives are given a portion of the criterion weight based on their local weight.

54. IDEAL MODE The local weights for the three cars with respect to cost are: 0.558, 0.320, and 0.122, respectively. The cost criterion weight is 0.309. Since the Honda has the highest cost weight it is initially assigned the full cost weight of 0.309. Mazda would be (0.320 / 0.558)*(0.309) = 0.177. Volvo would be (0.122 / 0.558)*(0.309) = 0.068.

55. IDEAL MODE Using the same approach, the weights for the three cars with respect to safety are: 0.100, 0.170, and 0.582, respectively. The weights for the three cars with respect to appearance are: 0.109, 0.023, and 0.012, respectively.

56. IDEAL MODE For each car, add the three criteria weights: HondaMazdaVolvo Cost0.3090.1770.068 Safety0.1000.1700.582 Appearance0.1090.0230.012 Total0.5180.3700.662

57. IDEAL MODE For each car, add the three criteria weights: HondaMazdaVolvo Cost0.3090.1770.068 Safety0.1000.1700.582 Appearance0.1090.0230.012 Total0.5180.3700.662 Since the sum of the three weights is 1.550, we divide each weight by 1.550 to normalize the results.

58. IDEAL MODE For each car, add the three criteria weights: HondaMazdaVolvo Cost0.3090.1770.068 Safety0.1000.1700.582 Appearance0.1090.0230.012 Total0.5180.3700.662 Total/1.5500.3350.2390.427 At this time Decision Lens does not report ideal weights. This feature will be added in the next release. Since the sum of the three weights is 1.550, we divide each weight by 1.550 to normalize the results.

59. 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.

60. DECISION LENS: Sensitivity Analysis In Decision Lens sensitivity analysis is performed by selecting “Analysis/Sensitivity” within the Evaluate Alternatives step. We use two options to display the sensitivity results: Scoresheet Sensitivity and Barchart Sensitivity. These show how a change in a criterion weight affects the final weights of the alternatives.

61. 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 Decision Lens. DECISION LENS: Sensitivity Analysis

62. Drag the cost criterion bar.309 to approximately.458, 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 weight since it had to be increased by almost 50% to get a change in the final rankings. Sensitivity analysis could also be performed for the other criteria. The sensitivity results are different for the ideal mode. DECISION LENS: Sensitivity Analysis

63. Step 4 allows you to use Decision Lens to allocate limited resources. The purpose of the optimizer is the maximize the overall priority within the defined constraints on limited resources using the ratio of Benefit/Cost, where Benefit is the AHP final weight. We will use the file called Resource Allocation Example.ANP. This model is already setup with five criteria, ten alternatives, three participants, and all necessary pairwise comparisons. Go to Step 4: Allocate Resources. ALLOCATING RESOURCES

64. The define constraints screen is a summary of the basic information entered for this problem. The three dropdowns across the top are used to enter different resource types, different scenarios, and different years. This information can be changed by selecting the edit button. To edit the funding pools: double click on Default Pool and rename as New Systems, enter 150000 as the pool budget, and then click OK. To add a new pool: type Infrastructure under Pool Name, 75000 under Pool Budget, and then Add Funding Pool. ALLOCATING RESOURCES

65. This means that we have two resource pools and the different projects will compete for the resources. To specify a budget for a project 1: click the cell in the Project 1 row under Requested Budget, type 30000 and Enter. To specify that project 5 requires funding from both resource pools: click on the dropdown under the header Funding Pool for this project, select mixed pools, type 10000 under Request for New Systems and 9000 for Infrastructure, click the F button once to change to H (discussed later), and then Update. ALLOCATING RESOURCES

66. To assign funding pools: for Projects 1-4, click on the dropdown under the header Funding Pool and select Infrastructure for each. This means that these projects will compete for funding from the Infrastructure budget while projects 6-10 will compete for resources from the New Systems budget. To add funding minimums: click in the row for Project 1 under Minimums and enter 10000. We have now set a Hard Minimum of $10,000 for this project meaning that Project 1 cannot receive less than $10,000. ALLOCATING RESOURCES

67. To add a Fixed Amount Funding Minimum: click in the row for Project 2 under the Minimums and enter 15000, and then click on the H twice to make it an F. We now specify that Project 2 will receive exactly $15,000. If you click the F twice to make it an S you have now changed Project 2 to a Soft Minimum meaning that it must get at least $15,000 if it gets any money at all, otherwise it gets $0. For our problem, change this setting back to F for Project 2. ALLOCATING RESOURCES

68. To add Project Dependencies: click Edit Dependencies, then click the upper left green cell twice so that an up arrow appears and then click X to close window. This means that Project 2 cannot receive resources unless Project 1 gets funded. You can also enter other dependencies as needed. We are now ready to optimize by selecting the Optimization step in the upper left hand corner and then clicking on the yellow Optimize button. The results show the amount funded for each project. Notice that project 3 is not funded due to its low priority (0.690) and its high requested budget ($65,000). ALLOCATING RESOURCES

69. The Optimizer tries to get the highest possible priority while staying within budget. Sensitivity analysis can be performed by sliding the arrow at the end of the criteria weight bar to another level to see how project funding changes. Proceeding to step 5, “Reporting,” will allow you to customize a report with selected output in RTF format. ALLOCATING RESOURCES

70. This chapter discussed the application of the AHP and Decision Lens. The example was a couple trying to decide which car to purchase. We showed how to build and analyze the hierarchy, enter and process all pairwise comparison judgments, and compute final weights. Summary

71. The differences between the ideal and distributive modes are discussed. Sensitivity analysis is used to study how changes to criteria weights impact the final alternative weights. Resource allocation and printing were also presented. Summary

72. COPYRIGHT Copyright  Matthew J. Liberatore and Robert L. Nydick. All rights reserved. Reproduction or translation of this work beyond that named in Section 117 of the United States Copyright Act without the express written consent of the copyright owners is unlawful. Requests for further information should be addressed to Matthew J. Liberatore and Robert L. Nydick. Adopters of the textbook are granted permission to make back-up copies for their own use only, to make copies for distribution to students of the course the textbook is used in, and to modify this material to best suit their instructional needs. Under no circumstances can copies be made for resale. Matthew J. Liberatore and Robert L. Nydick assume no responsibility for errors, omissions, or damages, caused by the use of these programs or from the use of the information contained herein.