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Agenda for This Week

Agenda for This Week. Chapter 15. Analytical Hierarchy Process – Part 2. Step 2 - Synthesization. CRITERIA. Next… divide each element by column total. Step 2 - Synthesization. Relative priorities. CRITERIA. Normalized pairwise comparison matrix. Summary - Synthesization.

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Agenda for This Week

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  1. Agenda for This Week

  2. Chapter 15 Analytical Hierarchy Process – Part 2

  3. Step 2 - Synthesization CRITERIA Next… divide each element by column total

  4. Step 2 - Synthesization Relative priorities CRITERIA Normalized pairwise comparison matrix

  5. Summary - Synthesization Summary of Relative Priorities for Rent, Size, Proximity and Criteria .266 .080 .654 .125 .750 .125 .737 .186 .077 .702 .101 .197 Rent Size Proximity Criteria

  6. AHP - Steps 1. Make pairwise comparisons  2. Synthesize judgments  3. Check for consistency

  7. AHP – Step 3 • A key step in the making of several pairwise comparisons is considering the consistency of the pairwise judgements. • Example: If A compared to B = 3 and B compared to C = 2 then A compared to C should = 3x2 = 6. If it wasn’t, some inconsistency would occur. • With AHP, we can measure the degree of consistency; and if unacceptable, we can revise pairwise comparisons

  8. Consistency – Step 3 • Step 1: Multiply pairwise comparison matrix by relative priorities • Step 2: Divide weighted sum vector elements by associated priority value • Step 3: Compute average (denoted lmax) of the values from Step 2. • Step 4: Compute consistency index (CI) • Step 5: Compute consistency ratio (CR)

  9. Consistency – Step 3 Step 1: Multiply pairwise comparison matrix (for rent) by relative priorities 4 1 7 1 1/4 3 1/3 1/7 1 .266 + .08 + .654 =

  10. Consistency – Step 3 Step 1: Multiply pairwise comparison matrix (for rent) by relative priorities .32 .08 .56 .265 .066 .795 .215 .093 .653 .80 .239 2.008 + + = Weighted Sum Vector

  11. Consistency – Step 3 Step 2: Divide weighted sum vector elements by associated relative priority value .80/.266 = 3.019 .239/.08 = 2.988 2.008/.654 = 3.075

  12. Consistency – Step 3 Step 3: Compute average (denoted lmax) of the values from Step 2. lmax = (3.019 + 2.988 + 3.075) / 3 = 3.027

  13. Consistency – Step 3 Step 4: Compute consistency index (CI) (where n = # items being compared) CI = (lmax - n) / (n-1) = (3.027 - 3) / 2 = .0135 This is called the Consistency Index

  14. Consistency – Step 3 Step 5: Compute consistency ratio (CR) CR = CI / RI RI = random index (CI of randomly generated pairwise comparison matrix) Value of RI is based on n n 3 4 5 6 7 8 RI 0.58 0.90 1.12 1.24 1.32 1.41

  15. Consistency – Step 3 Step 5: Compute consistency ratio (CR) CR = CI / RI = CR = .0135 / .58 = .023 Standard Rule states: If CR <= .10, consistency is acceptable!

  16. AHP - Steps 1. Make pairwise comparisons  2. Synthesize judgments  3. Check for consistency 

  17. Summary - Synthesization Summary of Relative Priorities for Rent, Size, Proximity and Criteria .266 .080 .654 .125 .750 .125 .737 .186 .077 .702 .101 .197 Rent Size Proximity Criteria

  18. Final Step • Develop Overall Priority Ranking • Overall Apartment 1 Priority .702(.266) + .101(.125) + .197(.737) = .344 • Overall Apartment 2 Priority .702(.08) + .101(.75) + .197(.186) = .169 • Overall Apartment 3 Priority .702(.653) + .101(.125) + .197(.076) = .486 Rent Size Proximity

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