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Module 1 Analytic Hierarchy Process

Module 1 Analytic Hierarchy Process. Prepared by Lee Revere and John Large. Learning Objectives. Students will be able to: Use the multifactor evaluation process in making decisions that involve a number of factors, where importance weights can be assigned.

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Module 1 Analytic Hierarchy Process

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  1. Module 1 Analytic Hierarchy Process Prepared by Lee Revere and John Large M1-1

  2. Learning Objectives Students will be able to: • Use the multifactor evaluation process in making decisions that involve a number of factors, where importance weights can be assigned. • Understand the use of the analytic hierarchy process in decision making. • Contrast multifactor evaluation with the analytic hierarchy process. M1-2

  3. Module Outline M1.1 Introduction M1.2 Multifactor Evaluation Process M1.3 Analytic Hierarchy Process M1.4 Comparison of MFEP and AHP M1-3

  4. Introduction • Multifactor decision making involves individuals subjectively and intuitively considering various factors prior to making a decision. • Multifactor evaluation process (MFEP) is a quantitative approach that gives weights to each alternative. • Analytic hierarchy process (AHP) is an approach designed to quantify the preferences for various factors and alternatives. M1-4

  5. Multifactor Evaluation Process Steve Markel is considering employment with three companies. He has determined three factors that are important to him and assigned each factor a weight. Weights should sum to 1 M1-5

  6. Evaluation of AA Co. Factor Factor Weighted Weight Evaluation Evaluation = X M1-6

  7. Comparison of Results Decision is AA Co: Highest weighted evaluation M1-7

  8. Analytic Hierarchy Process • Break decision into stages or levels. • Starting at the lowest level, for each level, make pairwise comparison of the factors. • 9-step scale: • equally preferred • equally to moderately preferred • moderately preferred • moderately to strongly preferred • strongly preferred • strongly to very strongly preferred • very strongly preferred • very to extremely preferred • extremely preferred M1-8

  9. Analytic Hierarchy Process • Develop the matrix representation: • Comparison matrix • Normalized matrix • Priority matrix • Develop  and the consistency ratio. • Determine factor weights. • Perform a multifactor evaluation. M1-9

  10. Decision Hierarchy for Computer System Selection Select Computer System Hardware Software Vendor Support System: System: System: 1 2 3 1 2 3 1 2 3 Judy Grim is considering purchasing a new computer system. The most important factors are hardware, software, and support. She has identified three alternatives. M1-10

  11. Beginning Comparison Matrix System-2 System-3 System-1 Hardware System-1 1 3 9 6 System-2 System-3 1 Judy Grim has used the 9-point scale for pairwise comparison to evaluate each system on hardware capabilities M1-11

  12. Comparison Matrix (continued) System-2 System-3 System-1 Hardware System-1 1 3 9 1/3 6 System-2 1 System-3 1/9 1/6 1 M1-12

  13. Normalizing the Matrix System-2 System-3 System-1 Hardware System-1 1 3 9 1/3 6 System-2 1 System-3 1/9 1/6 1 Column Totals 1.444 4.167 16.0 The totals are used to create a normalized matrix M1-13

  14. Normalized Matrix System-2 System-3 System-1 Hardware System-1 0.6923 0.7200 System-2 0.2300 0.2400 0.3750 System-3 0.0769 0.0400 0.0625 0.5625 = 1/ 1.444= .333/ 1.444 M1-14

  15. Final Matrix for Hardware M1-15

  16. The Weighted Sum Vector F = [ 0.6583 0.2819 0.0598] 1 • 3 9 • 0.33 1 6 • 0.11 0.167 1 (0.6583)(1) + (0.2819)(3) +(0.0598)(9) = 2.0423 0.6583)(0.33) + (0.2819)(1) + (0.0598)(6) = 0.8602 (0.6583)(0.167) + (0.2819)(0.167) + (0.0598)(1) = 0.1799 M1-16

  17. The Consistency Vector 2.0423 / 0.6583 3.1025 = 0.8602 0.2819 = 3.0512 0.1799/ 0.0598 3.0086 M1-17

  18. Computing Lambda Lambda is the average value of the consistency vectors. = 3.1025 + 3.0512 + 3.0086 3 = 3.0541 M1-18

  19. The Consistency Index The consistency index is: CI = 3.0541 – 3 3 – 1 = 0.0270 M1-19

  20. Consistency Ratio The consistency ratio (CR) tells how consistent the decision maker is with her answers. A higher number means less consistency. In general, a number of 0.10 or greater suggests the decision maker should reevaluate her responses during the pairwise comparison. CI RI (random index) This is a table value CR = = 0.0270 0.58 = 0.0466 Is Judy consistent in her answers regarding hardware?? M1-20

  21. Achieving a Final Ranking • We must now perform a second pairwise comparison regarding the relative importance of each of the remaining two factors. • For simplicity, computation of the software and vendor support factor evaluations are left to you. M1-21

  22. Achieving a Final Rank (continued) 0.6583 0.2819 0.0598 0.0874 0.1622 0.7504 0.4967 0.3967 0.1066 Using pairwise comparison we can obtain factor weights: M1-22

  23. Judy Grim’s Final Decision The factor weights are then multiplied by the factor evaluations to obtain a weighted evaluation. Best Decision!! M1-23

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