1. Agenda for This Week Monday, April 25 AHP Wednesday, April 27
Friday, April 29
Monday, May 2
Exam 2

2. Analytical Hierarchy Process – Part 1
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 Preferences Numerical 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
Rent
Size
Proximity 1 5 6
1/5
1/3
1/6 3

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
Apt 1
Apt 2
Apt 3 1 4
1/3
1/7 3 7

12. Step 1 – Pairwise Comparison
SIZE
Apt 1
Apt 2
Apt 3 1
1/6 6

13. Step 1 – Pairwise Comparison
PROXIMITY
Apt 1
Apt 2
Apt 3 1 5 8
1/5 3
1/8
1/3

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 Apt 1 Apt 2 Apt 3 1 4 1/3 ¼ 1/7 3 7 SUM
17/4 12
31/21
Next… divide each element by column total

18. Step 2 - Synthesization RENT Relative priorities
Apt 1
Apt 2
Apt 3
Avg
.235
.334
.226
.266
.059
.083
.097
.080
.706
.583
.677
.654
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 Apt 1 Apt 2 Apt 3 1 1/6 6 SUM 8 8/6
Next… divide each element by column total

22. Step 2 - Synthesization SIZE Relative priorities
Apt 1
Apt 2
Apt 3
Avg
.125
.75
Normalized pairwise comparison matrix

23. Step 2 - Synthesization PROXIMITY Apt 1 Apt 2 Apt 3 1 5 8 1/5 3 1/8
1/3
SUM
53/40
19/3 12
Next… divide each element by column total

24. Step 2 - Synthesization PROXIMITY Relative priorities
Apt 1
Apt 2
Apt 3
Avg
.755
.790
.667
.737
.151
.158
.25
.186
.094
.053
.083
.077
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