AHP (Analytic Hierarchy Process)

AHP is a multi-criteria decision making method developed by Thomas L. Saaty (1980, 'The Analytic Hierarchy Process', McGraw-Hill) that models a decision problem as a hierarchy (goal at the top, main criteria below, sub-criteria, and finally alternatives). Mechanically: at each level the decision maker performs pairwise comparisons of elements using Saaty's 1-9 verbal-numerical scale (1 equal, 3 slightly more important, 5 strongly, 7 very strongly, 9 absolutely). The principal right eigenvector of the resulting n×n comparison matrix, once normalized, yields the criterion weights; the principal eigenvalue λ_max measures consistency. The Consistency Index CI=(λ_max-n)/(n-1) and Consistency Ratio CR=CI/RI (with RI the random index) are computed; CR<0.10 indicates acceptable judgments, otherwise the comparisons should be revisited. The most-cited weakness is rank reversal — adding an alternative can change the ranking among existing ones (Belton and Gear 1983) — addressed by Saaty's ANP (Analytic Network Process) extension and ideal-mode normalization. AHP dominates supplier selection (Weber et al. 1991), project prioritization, facility location, and personnel evaluation contexts. Complexity class: polynomial (eigenvector computation).