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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?. AHP.

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Analytic Hierarchy Process

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  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 - Civic - Saturn - Escort - Miata - Civic - Saturn - Escort - Miata - Civic - Saturn - Escort - Miata

  5. 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]

  6. 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

  7. 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: - =

  8. Preference • Style .3196 • Reliability .5584 • Fuel Economy .1220

  9. .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

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

  11. -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. .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

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

  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

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