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?

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

Example: Car Selection

• Objective– Selecting a car

• Criteria– Style, Reliability, Fuel-economy

Cost?

• Alternatives– Civic Coupe, Saturn Coupe, Ford Escort,

Mazda Miata

Hierarchical tree

S tyle R e lia b ility F u e l E con o m y

S e lec tinga N e w C ar

- Civic- Saturn- Escort- Miata

- Civic- Saturn- Escort- Miata

- Civic- Saturn- Escort- Miata

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

Ranking of priorities

• Eigenvector [Ax = x]Iterate

1. Take successive squared powers of matrix

2. Normalize the row sums

Until difference between successive row sums isless than a pre-specified value

1 0.5 32 1 40.333 0.25 1.0

3.0 1.75 8.05.3332 3.0 14.01.1666 0.6667 3.0

squared

Row sums 12.75 22.3332 4.8333

39.9165

NormalizedRow 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

Preference

• Style .3196

• Reliability .5584

• Fuel Economy .1220

S tyle.3 196

R e lia b ility.5 584

F u e l E con o m y.1 220

S e lec tinga N e w C ar

1 .0

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

Fuel Economy(quantitative information)

Civic

Saturn

Escort

MiataMiata

34

27

24

28 113

Miles/gallon Normalized

.3010

.2390

.2120

.2480 1.0

S tyle.3 196

R e lia b ility.5 584

F u e l E con o m y.1 220

S e lec tinga N e w C ar

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

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

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

Cost vs. Benefits

• MIATA $18K .333.9840

• CIVIC $12K .2221.3771

• SATURN $15K .2778 .9791

• ESCORT $9K .1667 .5639

CostNormalized Cost

Cost/Benefits Ratio

Complex decisions

•Many levels of criteria and sub-criteria

• 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