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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.

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analytic hierarchy process
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?

slide2
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
Example: Car Selection
  • Objective
    • Selecting a car
  • Criteria
    • Style, Reliability, Fuel-economy Cost?
  • Alternatives
    • Civic Coupe, Saturn Coupe, Ford Escort, Mazda Miata
hierarchical tree
Hierarchical tree

- Civic

- Saturn

- Escort

- Miata

- Civic

- Saturn

- Escort

- Miata

- Civic

- Saturn

- Escort

- Miata

ranking of criteria

Style

Reliability

Fuel Economy

Style

1/1 1/2 3/1

2/1 1/1 4/1

Reliability

1/3 1/4 1/1

Fuel Economy

Ranking of criteria
  • Weights?
  • AHP
    • pair-wise relative importance

[1:Equal, 3:Moderate, 5:Strong, 7:Very strong, 9:Extreme]

ranking of priorities
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 is

less than a pre-specified value

slide7

1 0.5 3

2 1 4

0.333 0.25 1.0

0.3196

0.5584

0.1220

0.3194

0.5595

0.1211

0.3196

0.5584

0.1220

3.0 1.75 8.0

5.3332 3.0 14.0

1.1666 0.6667 3.0

squared

Normalized

Row sums

0.3194

0.5595

0.1211

1.0

Row sums

12.75

22.3332

4.8333

39.9165

  • New iteration gives normalized row sum

- 0.0002

0.0011

- 0.0009

  • Difference is:

-

=

slide8
Preference
  • Style .3196
  • Reliability .5584
  • Fuel Economy .1220
ranking alternatives

.1160

.2470

.0600

.5770

.3790

.2900

.0740

.2570

Ranking alternatives

Eigenvector

Style

Civic

Saturn

Escort

Miata

Civic

1/1 1/4 4/1 1/6

Saturn

4/1 1/1 4/1 1/4

Escort

1/4 1/4 1/1 1/5

Miata

Miata

6/1 4/1 5/1 1/1

Reliability

Civic

Saturn

Escort

Miata

Civic

1/1 2/1 5/1 1/1

Saturn

1/2 1/1 3/1 2/1

Escort

1/5 1/3 1/1 1/4

Miata

1/1 1/2 4/1 1/1

slide10

Normalized

Miles/gallon

Civic

34

.3010

Fuel Economy

(quantitative

information)

Saturn

27

.2390

Escort

24

.2120

Miata

Miata

28

113

.2480

1.0

slide11

-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

.3196

.5584

.1220

.3060

.2720

.0940

.3280

Civic

.1160 .3790 .3010

.2470 .2900 .2390

.0600 .0740 .2120

.5770 .2570 .2480

*

Saturn

=

Escort

Miata

Miata

Ranking of alternatives

Style Reliability Fuel

Economy

handling costs
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
Cost vs. Benefits

Normalized

Cost

Cost/Benefits

Ratio

Cost

  • MIATA $18K .333 .9840
  • CIVIC $12K .222 1.3771
  • SATURN $15K .2778 .9791
  • ESCORT $9K .1667 .5639
complex decisions
Complex decisions
  • Many levels of criteria and sub-criteria
slide16
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
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