This document describes the Analytic Hierarchy Process (AHP), a framework for multi-criteria decision making. AHP breaks down a decision problem into a hierarchy of criteria and alternatives. It uses pairwise comparisons to determine the relative importance of criteria and to rank alternatives. Both qualitative and quantitative information can be incorporated through informed judgments to derive weights and priorities. An example of using AHP to select a car based on style, reliability, and fuel economy is provided to illustrate the process.

1. Analytic Hierarchy Process
• Multiple-criteria decision-making
• Real world decision problems
– multiple, diverse criteria
– qualitative as well as quantitative information
Comparing apples and oranges?
Spend on defence or agriculture?
Open the refrigerator - apple or orange?

2. AHP
• Information is decomposed into a hierarchy of
alternatives and criteria
• Information is then synthesized to determine
relative ranking of alternatives
• Both qualitative and quantitative information
can be compared using informed judgements
to derive weights and priorities

3. Example: Car Selection
• Objective
– Selecting a car
• Criteria
– Style, Reliability, Fuel-economy Cost?
• Alternatives
– Civic Coupe, Saturn Coupe, Ford Escort,
Mazda Miata

4. Hierarchical tree
S t y le R e lia b ilit y F u e l E c o n o m y
S e le c t in g
a N e w C a r
- Civic
- Saturn
- Escort
- Miata
- Civic
- Saturn
- Escort
- Miata
- Civic
- Saturn
- Escort
- Miata

5. Ranking of criteria
• Weights?
• AHP
– pair-wise relative importance
[1:Equal, 3:Moderate, 5:Strong, 7:Very strong, 9:Extreme]
Style Reliability Fuel Economy
Style
Reliability
Fuel Economy
1/1 1/2 3/1
2/1 1/1 4/1
1/3 1/4 1/1

6. Ranking of priorities
• Eigenvector [Ax = λx]
Iterate
1. Take successive squared powers of matrix
2. Normalize the row sums
Until difference between successive row sums is
less than a pre-specified value

7. 1 0.5 3
2 1 4
0.333 0.25 1.0
3.0 1.75 8.0
5.3332 3.0 14.0
1.1666 0.6667 3.0
squared
Row sums
12.75
22.3332
4.8333
39.9165
Normalized
Row sums
0.3194
0.5595
0.1211
1.0
• New iteration gives normalized row sum
0.3196
0.5584
0.1220
• Difference is: -
0.3194
0.5595
0.1211
0.3196
0.5584
0.1220
=
- 0.0002
0.0011
- 0.0009

8. Preference
• Style .3196
• Reliability .5584
• Fuel Economy .1220
S t y le
. 3 1 9 6
R e lia b ilit y
. 5 5 8 4
F u e l E c o n o m y
. 1 2 2 0
S e le c t in g
a N e w C a r
1 .0

9. Ranking alternatives
Style
Civic
Saturn
Escort
1/1 1/4 4/1 1/6
4/1 1/1 4/1 1/4
1/4 1/4 1/1 1/5
Miata 6/1 4/1 5/1 1/1
Civic Saturn Escort Miata
Miata
Reliability
Civic
Saturn
Escort
1/1 2/1 5/1 1/1
1/2 1/1 3/1 2/1
1/5 1/3 1/1 1/4
Miata 1/1 1/2 4/1 1/1
Civic Saturn Escort Miata
.1160
.2470
.0600
.5770
Eigenvector
.3790
.2900
.0740
.2570

10. Fuel Economy
(quantitative
information)
Civic
Saturn
Escort
MiataMiata
34
27
24
28
113
Miles/gallon Normalized
.3010
.2390
.2120
.2480
1.0

11. S t y le
. 3 1 9 6
R e lia b ilit y
. 5 5 8 4
F u e l E c o n o m y
. 1 2 2 0
S e le c t in g
a N e w C a r
1 .0
- Civic .1160
- Saturn .2470
- Escort .0600
- Miata .5770
- Civic .3790
- Saturn .2900
- Escort .0740
- Miata .2570
- Civic .3010
- Saturn .2390
- Escort .2120
- Miata .2480

12. Ranking of alternatives
Style Reliability Fuel
Economy
Civic
Escort
MiataMiata
Saturn
.1160 .3790 .3010
.2470 .2900 .2390
.0600 .0740 .2120
.5770 .2570 .2480
*
.3196
.5584
.1220
=
.3060
.2720
.0940
.3280

13. Handling Costs
• Dangers of including Cost as another criterion
– political, emotional responses?
• Separate Benefits and Costs hierarchical trees
• Costs vs. Benefits evaluation
– Alternative with best benefits/costs ratio

14. Cost vs. Benefits
• MIATA $18K .333 .9840
• CIVIC $12K .222 1.3771
• SATURN $15K .2778 .9791
• ESCORT $9K .1667 .5639
Cost
Normalized
Cost
Cost/Benefits
Ratio

15. Complex decisions
•Many levels of criteria and sub-criteria

16. • Application areas
– strategic planning
– resource allocation
– source selection, program selection
– business policy
– etc., etc., etc..
• AHP software (ExpertChoice)
– computations
– sensitivity analysis
– graphs, tables
• Group AHP