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# Requirements analytic hierarchy process

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• ### Requirements analytic hierarchy process

1. 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. 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. 3. Example: Car Selection • Objective – Selecting a car • Criteria – Style, Reliability, Fuel-economy Cost? • Alternatives – Civic Coupe, Saturn Coupe, Ford Escort, Mazda Miata
4. 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. 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. 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. 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. 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. 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. 10. Fuel Economy (quantitative information) Civic Saturn Escort MiataMiata 34 27 24 28 113 Miles/gallon Normalized .3010 .2390 .2120 .2480 1.0
11. 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. 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. 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. 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. 15. Complex decisions •Many levels of criteria and sub-criteria
16. 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