IMPROVING THE EFFICIENCY OF THE ANALYTIC HIERARCHY PROCESS

Purpose: The Analytic Hierarchy Process (AHP) is a well-established multi-criteria decision making approach, which is ideal for use when decisions have no clear best alternative, and decisions are highly preference-based. AHP consists of identifying the goal of the decision, the alternatives available, and the criteria by which to evaluate the alternatives. However, the time needed to perform the pair-wise comparisons required in AHP can become onerous and is an important limitation of standard AHP. Wedley (2009) has proposed a modified AHP using incomplete (imputed) comparisons. We sought to replicate and externally validate this approach.

Method: We created a web-based decision task using AHP in which subjects complete pair-wise comparisons of 5 shapes based on their area. Subjects were recruited via email from author contacts. In the modified AHP approach, users first rank the items. Using the lowest ranked item as referent, the first n-1 comparisons are generated to form an interconnected spanning tree. Missing priorities are solved as the eigenvector of an augmented matrix with the number of row missing values plus one in the diagonal. Once a subject reaches a satisfactory consistency ratio of <0.10 (CR=CI/RI where CI=(λmax-n)/(n-1), RI=random consistency index) participants are given the opportunity to stop the comparisons. Average priorities, number of comparisons completed, mean consistency ratio, mean absolute error and percent error were calculated.

Result: 40 subjects participated. Thirty-three percent were male, 42% were white and 58% were from racial/ethnic minorities. Twenty percent had less than a college education. The average number of comparisons was 8.5 (range 7-10), a reduction of 1.5 comparisons for each criteria. The mean consistency ratio was 0.015 ± 0.002, mean absolute error in priorities was 0.018 ± 0.016 and the mean absolute percent error 9.7 ± 4.2%.

Conclusion: We have externally validated Wedley's modified approach, achieving improved efficiency while maintaining accuracy. Although the reduction in comparisons was modest, for decisions with many criteria and alternatives, this reduction is significant. When developing decision aids for complex decisions that incorporate AHP, the modified approach should be considered as it can reduce subject burden and improve usability.