1. Agenda for This Week Wednesday, April 27 AHP Friday, April 29 AHP Monday, May 2 Exam 2

2. Chapter 15 Analytical Hierarchy Process – Part 2

3. Step 2 - Synthesization CRITERIA Next… divide each element by column total RentSizeProx Rent156 Size1/511/3 Prox1/631 SUM41/30922/3

4. Step 2 - Synthesization RentSizeProxAvg Rent.732.556.820.702 Size.146.111.046.101 Prox.122.333.136.197 CRITERIA Normalized pairwise comparison matrix Relative priorities

5. Summary - Synthesization Summary of Relative Priorities for Rent, Size, Proximity and Criteria.266.080.654.125.750.125.737.186.077 Rent Size Proximity Criteria.702.101.197

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 max) 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.266 +.08 +.654 = 1 1/4 3 417417 1/3 1/7 1

10. Consistency – Step 3 Step 1: Multiply pairwise comparison matrix (for rent) by relative priorities.265.066.795.32.08.56.215.093.653 + + =.80.239 2.008 Weighted Sum Vector

11. 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 Consistency – Step 3

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

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

14. Step 5: Compute consistency ratio (CR) CR = CI / RI RI = random index (CI of randomly generated pairwise comparison matrix) Consistency – Step 3 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. Step 5: Compute consistency ratio (CR) CR = CI / RI = CR =.0135 /.58 =.023 Standard Rule states: If CR <=.10, consistency is acceptable! Consistency – Step 3

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 Rent Size Proximity Criteria.702.101.197

18. 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 Final Step RentSizeProximity