1. Agenda for This Week

2. Chapter 15 Analytical Hierarchy Process – Part 1

3. Analytical Hierarchy Process • Designed to solve multicriteria decision problems • Model under conditions of certainty where we know all of the info but we need to trade-off many factors. • We are comparing several alternatives on the basis of the same set of attributes.

4. Developing the Hierarchy • Develop a visual representation of the problem in terms of the overall goal, the criteria to be used and the decision alternatives GOAL Attributes Alternatives

5. AHP Example • Decision Hierarchy • Select Best Apartment Criteria Rent Size Proximity Apt. 1 Apt. 2 Apt. 3 Apt. 1 Apt. 2 Apt. 3 Apt. 1 Apt. 2 Apt. 3 Alternatives

6. AHP • Major question is how to assign relative weights across alternatives, as well as for the attributes (assigning weights is the crux of AHP). • People have been found to be more consistent when they do pairwise comparisons than when they just try to assign relative weights.

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

8. AHP – Pairwise Comparison Scale (Always Use) Verbal Judgement of PreferencesNumerical Rating Extremely preferred 9 Very strongly to extremely 8 Very strongly preferred 7 Strongly to very strongly 6 Strongly preferred 5 Moderately to strongly 4 Moderately preferred 3 Equally to moderately 2 Equally preferred 1

9. Step 1 – Pairwise Comparison • Make pairwise comparison for CRITERIA CRITERIA

10. Step 1 – Pairwise Comparison • Make pairwise comparison for each attribute • Apt 1 compared to Apt 2 • Apt 2 compared to Apt 3 • Apt 1 compared to Apt 3 For RENT

11. Step 1 – Pairwise Comparison RENT

12. Step 1 – Pairwise Comparison SIZE

13. Step 1 – Pairwise Comparison PROXIMITY

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

15. AHP – Step 2 • Synthesization – the process of calculating the priority of each criterion in terms of its contribution to the overall goal of achieving your goal

16. Step 2 - Synthesization Step 1: Sum values in each column of pairwise comparison matrix Step 2: Divide each element by its column total (gives normalized pairwise comparison matrix) Step 3: Compute average of elements in each row (gives estimate of relative priorities of elements being compared)

17. Step 2 - Synthesization RENT Next… divide each element by column total

18. Step 2 - Synthesization Relative priorities RENT Normalized pairwise comparison matrix

19. AHP – Relative Priorities Relative Priorities for Rent .266 .080 .654 Apt. 1 Apt. 2 Apt. 3 What do these mean?

20. AHP – Relative Priorities Relative Priorities for Rent .266 .080 .654 Apt. 1 Apt. 2 Apt. 3 These mean that with respect to Rent, Apt. 3 is preferred first (65%), then Apt. 1 (27%), then Apt. 2 (8%)

21. Step 2 - Synthesization SIZE Next… divide each element by column total

22. Step 2 - Synthesization Relative priorities SIZE Normalized pairwise comparison matrix

23. Step 2 - Synthesization PROXIMITY Next… divide each element by column total

24. Step 2 - Synthesization Relative priorities PROXIMITY Normalized pairwise comparison matrix

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

26. 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