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THE ANALYTIC HIERARCHY PROCESS CAR PURCHASE EXAMPLE

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  • 1. THE ANALYTIC HIERARCHY PROCESS CAR PURCHASE EXAMPLE
  • 2. 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.
  • 3. 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.
  • 4.
    • After launching Expert Choice, select the F ile, N ew option, and after selecting a destination folder, enter a file name such as CARS. (Expert Choice add the AHP file extension.)
    • Next, enter a description for your goal, such as, “Select the best car.”
    EXPERT CHOICE: FILE SETUP
  • 5.
    • To enter the criteria, for example, cost, safety, and appearance, use the E dit, and Insert C hild of Current Node commands.
    • Use the Esc key or hit an extra enter when finished entering the criteria.
    • To add the alternative cars select the E dit, A lternative, and I nsert commands.
    EXPERT CHOICE: FILE SETUP
  • 6.
    • You can also use the “Add Alternative” button in the upper right hand corner of the model window.
    • Repeat for all alternatives.
    • Additional details can be found in the Expert Choice tutorial provided with the software.
    EXPERT CHOICE: FILE SETUP
  • 7. 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.
  • 8. ANALYZING THE HIERARCHY
    • To complete the first stage, the couple can base their judgments on the following (hypothetical) performance information.
    • All alternative pairwise comparisons should be based on data.
  • 9. HYPOTHETICAL DATA FOR CAR PURCHASE EXAMPLE Car Cost Safety* Appearance Honda $22,000 28 Sporty Mazda 28,500 39 Slick Volvo 33,000 52 Dull * Safety Rating from a consumer testing service - the higher the number, the safer the car.
  • 10. 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.
    • The scale on the next page is the standard one.
  • 11. STANDARD 1 - 9 MEASUREMENT SCALE
    • Intensity of Importance Definition Explanation
    • 1 Equal importance Two activities contribute equally
    • 3 Moderate importance Experience and judgment slightly favor one
    • activity over another
    • 5 Strong importance Experience and judgment strongly favor one
    • activity over another
    • 7 Very strong An activity is favored very strongly over
    • another
    • 9 Extreme importance The evidence favoring one activity over
    • another is of the highest possible order
    • of affirmation
    • 2, 4, 6, 8 For compromise Sometimes one needs to interpolate a
    • values compromise between the above judgment
    • numerically because there is no good
    • word to describe it
    • 1.1 - 1.9 For tied activities When elements are close and nearly
    • indistinguishable; moderate is 1.3 and
    • extreme is 1.9
    • Reciprocals of above If activity A has For example, if the pairwise comparison of
    • one of the above A to B is 3.0, then the pairwise comparison
    • numbers assigned of 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 cars for the cost criterion.
    • Remember that the costs of the three cars are: $22000, $28500, and $33000, respectively.
  • 13.
    • 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
  • 14.
    • A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
    • Honda Mazda Volvo
    • 22K Honda 1
    • 28.5K Mazda
    • 33K Volvo
    COST PAIRWISE COMPARISONS
  • 15.
    • 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
  • 16.
    • A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
    • Honda Mazda Volvo
    • 22K Honda 1
    • 28.5K Mazda 1
    • 33K Volvo 1
    COST PAIRWISE COMPARISONS
  • 17.
    • 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
  • 18.
    • 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
  • 19.
    • A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
    • Honda Mazda Volvo
    • 22K Honda 1 2
    • 28.5K Mazda 1
    • 33K Volvo 1
    COST PAIRWISE COMPARISONS
  • 20.
    • 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
  • 21.
    • A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
    • Honda Mazda Volvo
    • 22K Honda 1 2
    • 28.5K Mazda 1/2 1
    • 33K Volvo 1
    COST PAIRWISE COMPARISONS
  • 22.
    • 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
  • 23.
    • A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
    • Honda Mazda Volvo
    • 22K Honda 1 2
    • 28.5K Mazda 1/2 1 2
    • 33K Volvo 1/2 1
    COST PAIRWISE COMPARISONS
  • 24.
    • 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
  • 25.
    • A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
    • Honda Mazda Volvo
    • 22K Honda 1 2 4
    • 28.5K Mazda 1/2 1 2
    • 33K Volvo 1/4 1/2 1
    COST PAIRWISE COMPARISONS
  • 26.
    • 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
  • 27.
    • 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
  • 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 COST PAIRWISE COMPARISON MATRIX
    • Honda Mazda Volvo
    • 22K Honda 1 2 4
    • 28.5K Mazda 1/2 1 2
    • 33K Volvo 1/4 1/2 1
    • ------- ------- -------
    • COLUMN TOTALS
    COST PAIRWISE COMPARISONS
  • 29.
    • 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
    • 22K Honda 1 2 4
    • 28.5K Mazda 1/2 1 2
    • 33K Volvo 1/4 1/2 1
    • ------- ------- -------
    • COLUMN TOTALS 7/4 7/2 7
    COST PAIRWISE COMPARISONS
  • 30.
    • 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
    • 22K Honda 1 2 4
    • 28.5K Mazda 1/2 1 2
    • 33K Volvo 1/4 1/2 1
    • ------- ------- -------
    • COLUMN TOTALS 7/4 7/2 7
    COST PAIRWISE COMPARISONS
  • 31.
    • 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
    • 22K Honda 1 2 4
    • 28.5K Mazda 1/2 1 2
    • 33K Volvo 1/4 1/2 1
    • ------- ------- -------
    • COLUMN TOTALS 7/4 7/2 7
    • B. ADJUSTED COST PAIRWISE COMPARISON MATRIX
    • 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).
    COST PAIRWISE COMPARISONS
  • 32.
    • 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
  • 33.
    • 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
    • 22K Honda 1 2 4
    • 28.5K Mazda 1/2 1 2
    • 33K Volvo 1/4 1/2 1
    • ------- ------- -------
    • COLUMN TOTALS 7/4 7/2 7
    • B. ADJUSTED COST PAIRWISE COMPARISON MATRIX
    • 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).
    COST PAIRWISE COMPARISONS
  • 34.
    • 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
    • 22K Honda 1 2 4
    • 28.5K Mazda 1/2 1 2
    • 33K Volvo 1/4 1/2 1
    • ------- ------- -------
    • COLUMN TOTALS 7/4 7/2 7
    • B. ADJUSTED COST PAIRWISE COMPARISON MATRIX WEIGHTS
    • 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
    • * This entry is obtained by dividing the Honda entry in the original matrix (1) by the Honda column total (7/4).
    COST PAIRWISE COMPARISONS
  • 35.
    • Expert Choice offers a variety of modes for entering the judgments.
    • Highlight the cost node and select the Pairwise Numerical comparison button (3:1).
    • This button appears on the top left-hand side of the toolbar to the right of the model view button.
    EXPERT CHOICE: Entering Judgments
  • 36.
    • Sliding the bar between Honda and Mazda to the left so that it rests on the 2 means that the Honda is two times better than the Mazda when considering cost.
    • If the Mazda were 2 times better than the Honda, the bar would be slid to the 2 on the right.
    • The other comparisons are entered in a similar fashion.
    EXPERT CHOICE: Entering Judgments
  • 37.
    • For our problem, Expert Choice only displays three judgments.
    • 1’s along the main diagonal and reciprocal judgments do not appear.
    EXPERT CHOICE: Entering Judgments
  • 38.
    • There are different modes for entering judgments.
    • The Pairwise Verbal Comparisons (ABC) and the Pairwise Graphical Comparisons (the button that looks like a bar graph) are available.
    • The only difference between these modes is how the pairwise comparison questions are displayed.
    EXPERT CHOICE: Entering Judgments
  • 39.
    • A 1-9 scale is used for numerical comparisons.
    • The verbal comparisons are: equal, moderate, strong, very strong, and extreme.
    • The graphical mode makes comparisons based on the length of two bars.
    • The user selects the desired mode.
    EXPERT CHOICE: Entering Judgments
  • 40.
    • After entering all pairwise comparisons, record judgments by clicking Yes.
    • The model view will be displayed with alternative weights for the cost criterion now appearing.
    EXPERT CHOICE: Entering Judgments
  • 41. INCONSISTENCY OF JUDGMENTS
    • Since our pairwise comparisons were perfectly consistent, Expert Choice reports Incon: 0.00.
    • If this ratio is greater than 0.1 some revision of judgments is required.
    • Select Inconsis t ency (within any Pairwise Comparison mode) to identify the most inconsistent judgments.
  • 42. INCONSISTENCY OF JUDGMENTS
    • Inconsistency of judgments may result from:
    • problems of estimation;
    • errors between the comparisons;
    • or, the comparisons may be naturally inconsistent.
  • 43. 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.
  • 44. INCONSISTENCY OF JUDGMENTS
    • The point is not to stop inconsistency from occurring.
    • Make sure that the level of inconsistency remains within some reasonable limit.
  • 45. 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.
  • 46.
    • A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
    • Honda Mazda Volvo
    • 22K Honda 1 2 4
    • 28.5K Mazda 1/2 1 3
    • 33K Volvo 1/4 1/3 1
    COST PAIRWISE COMPARISONS
  • 47.
    • 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
    • 22K Honda 1 2 4
    • 28.5K Mazda 1/2 1 3
    • 33K Volvo 1/4 1/3 1
    • ------- ------- -------
    • COLUMN TOTALS 7/4 10/3 8
    COST PAIRWISE COMPARISONS
  • 48.
    • 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
    • 22K Honda 1 2 4
    • 28.5K Mazda 1/2 1 3
    • 33K Volvo 1/4 1/3 1
    • ------- ------- -------
    • COLUMN TOTALS 7/4 10/3 8
    • B. ADJUSTED COST PAIRWISE COMPARISON MATRIX
    • 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).
    COST PAIRWISE COMPARISONS
  • 49.
    • 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
    • 22K Honda 1 2 4
    • 28.5K Mazda 1/2 1 3
    • 33K Volvo 1/4 1/3 1
    • ------- ------- -------
    • COLUMN TOTALS 7/4 10/3 8
    • B. ADJUSTED COST PAIRWISE COMPARISON MATRIX WEIGHTS
    • 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
    • * This entry is obtained by dividing the Honda entry in the original matrix (1) by the Honda column total (7/4).
    COST PAIRWISE COMPARISONS
  • 50. 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.
  • 51.
    • To make this change in Expert Choice, highlight cost node and select any Pairwise Comparison mode .
    • Within the numerical mode, slide the comparison bar to the left from 2 to 3, select the Model View, and record the judgments to see the new weights.
    • 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.
    EXPERT CHOICE: Revising Judgments
  • 52. INCONSISTENCY OF JUDGMENTS
    • The inconsistency ratio is now 0.02.
    • The weights can also be used to measure the effectiveness of the alternatives.
    • For example, based on all comparisons, the Honda is 1.74 (0.558/0.320) times better than the Mazda.
  • 53. INCONSISTENCY OF JUDGMENTS
    • We knew that a $22,000 car is better than a $28,500 car, but now we know how much better.
    • Why is this ratio 1.74 and not the pairwise comparison of 2?
    • Inconsistency in the judgments!
  • 54. 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.
    • The safety comparisons are all inverted, that is, for each comparison, the top bar was moved to the left.
    • This means that the Mazda is 2 times more preferred than the Honda, with respect to safety.
  • 55. SAFETY & APPEARANCE JUDGMENTS
    • Safety Pairwise Comparison Matrix
    • Honda Mazda Volvo
    • 28 Honda 1 1/2 1/5
    • 39 Mazda 2 1 1/4
    • 52 Volvo 5 4 1
    • Appearance Pairwise Comparison Matrix
    • Honda Mazda Volvo
    • Sporty Honda 1 5 9
    • Slick Mazda 1/5 1 2
    • Dull Volvo 1/9 1/2 1
  • 56. 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.
  • 57. CRITERIA JUDGMENTS
    • Original Criteria Pairwise Comparison Matrix
    • Cost Safety Appearance
    • Cost 1 1/2 3
    • Safety 2 1 5
    • Appearance 1/3 1/5 1
  • 58. 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.
  • 59. FINAL CAR WEIGHTS
    • CRITERIA WEIGHTS
    • COST SAFETY APPEARANCE
    • 0.309 0.582 0.109
    • CARS FINAL WEIGHTS
    • Honda 0.558 0.117 0.761
    • Mazda 0.320 0.200 0.158
    • Volvo 0.122 0.683 0.082
  • 60. FINAL CAR WEIGHTS
    • CRITERIA WEIGHTS
    • COST SAFETY APPEARANCE
    • 0.309 0.582 0.109
    • CARS FINAL WEIGHTS
    • Honda 0.558 0.117 0.761 0.324
    • Mazda 0.320 0.200 0.158
    • 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
  • 61. FINAL CAR WEIGHTS
    • CRITERIA WEIGHTS
    • COST SAFETY APPEARANCE
    • 0.309 0.582 0.109
    • CARS FINAL WEIGHTS
    • Honda 0.558 0.117 0.761 0.324
    • Mazda 0.320 0.200 0.158 0.232
    • 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
    • Mazda: (0.320)(0.309) + (0.200)(0.582) + (0.158)(0.109) = 0.232
    • 0.099 0.116 0.017
  • 62. FINAL CAR WEIGHTS
    • CRITERIA WEIGHTS
    • COST SAFETY APPEARANCE
    • 0.309 0.582 0.109
    • CARS FINAL WEIGHTS
    • Honda 0.558 0.117 0.761 0.324
    • Mazda 0.320 0.200 0.158 0.232
    • 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
    • Mazda: (0.320)(0.309) + (0.200)(0.582) + (0.158)(0.109) = 0.232
    • 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
  • 63. 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.
  • 64.
    • The final weights are shown in Expert Choice after all comparisons are entered and when the Model View is displayed and the goal is highlighted.
    • Choose Dis t ributive Mode.
    • The difference between the Distributive and Ideal modes will be discussed later.
    EXPERT CHOICE: Synthesis
  • 65. 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.
  • 66. 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.
  • 67. SYNTHESIS MODES
    • The process used to compute the final weights is called distributive synthesis .
    • This method works well when there is a fixed amount of resources that must be distributed to a fixed set of alternatives.
  • 68. 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.
  • 69. 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.
  • 70. 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.
  • 71. 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.
  • 72. 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.
  • 73. IDEAL MODE
    • For each car, add the three criteria weights:
    • Honda Mazda Volvo
    • Cost 0.309 0.177 0.068
    • Safety 0.100 0.170 0.582
    • Appearance 0.109 0.023 0.012
    • Total 0.518 0.370 0.662
  • 74. IDEAL MODE
    • For each car, add the three criteria weights:
    • Honda Mazda Volvo
    • Cost 0.309 0.177 0.068
    • Safety 0.100 0.170 0.582
    • Appearance 0.109 0.023 0.012
    • Total 0.518 0.370 0.662
    Since the sum of the three weights is 1.550, we divide each weight by 1.550 to normalize the results.
  • 75. IDEAL MODE
    • For each car, add the three criteria weights:
    • Honda Mazda Volvo
    • Cost 0.309 0.177 0.068
    • Safety 0.100 0.170 0.582
    • Appearance 0.109 0.023 0.012
    • Total 0.518 0.370 0.662
    • Total/1.550 0.335 0.239 0.427
    • These are the ideal weights reported in
    • Expert Choice.
    Since the sum of the three weights is 1.550, we divide each weight by 1.550 to normalize the results.
  • 76. 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.
  • 77. 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.
  • 78.
    • 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
  • 79.
    • 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
  • 80.
    • 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
  • 81.
    • Choose D ynamic from the Sensitivit y -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 weight since it had to be increased by almost 50% to get a change in the final rankings.
    • The sensitivity results are different for the ideal mode.
    EXPERT CHOICE: Sensitivity Analysis

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