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-economyCost? Alternatives –Civic Coupe, Saturn Coupe, Ford Escort, Mazda Miata

Hierarchical tree - 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] StyleReliabilityFuel Economy Style Reliability Fuel Economy 1/11/23/1 2/11/14/1 1/31/41/1

1 -9 Scale

Example - Pairwise Comparisons Consider following criteria Purchase CostMaintenance CostGas Mileage Want to find weights on these criteria AHP compares everything two at a time (1) Compare Purchase Cost to Maintenance Cost – Which is more important? Say purchase cost – By how much? Say moderately 3

Example - Pairwise Comparisons (2) Compare Purchase Cost to – Which is more important? Say purchase cost – By how much? Say more important 5 Gas Mileage (3) Compareto – Which is more important? Say maintenance cost – By how much? Say more important 3 Gas MileageMaintenance Cost

Example - Pairwise Comparisons This set of comparisons gives the following matrix: P M G PMG /3 1/5 3 1/3 Ratings mean that P is 3 times more important than M and P is 5 times more important than G What’s wrong with this matrix? The ratings are inconsistent!

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

squared Row sums Normalized Row sums New iteration gives normalized row sum Difference is: =

Preference Style.3196 Reliability.5584 Fuel Economy.1220

Ranking alternatives Style Civic Saturn Escort 1/1 1/44/1 1/6 4/1 1/14/1 1/4 1/4 1/4 1/11/5 Miata6/1 4/1 5/1 1/1 CivicSaturnEscortMiata Reliability Civic Saturn Escort 1/1 2/15/1 1/1 1/2 1/1 3/1 2/1 1/5 1/3 1/11/4 Miata1/1 1/2 4/1 1/1 CivicSaturnEscortMiata Eigenvector

Fuel Economy (quantitative information) Civic Saturn Escort Miata Miles/gallon Normalized

- Civic Saturn Escort Miata Civic Saturn Escort Miata Civic Saturn Escort Miata.2480

Ranking of alternatives Style Reliability Fuel Economy Civic Escort Miata Saturn * =

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 CIVIC$12K SATURN$15K ESCORT$9K Cost Normalized 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