An iterative procedure for reducing problem size in large scale AHP problems

Abstract

The Analytic Hierarchy Process (AHP) is a multiple objective decision making tool that consolidates information about tangible and intangible criteria and alternatives in the decision making process. This consolidation of information is completed on data collected using a form of paired comparisons. Each criterion is compared to all other criteria to determine the relative importance of each and, within each criterion, each alternative is compared to all other alternatives. As a result, the number of comparisons required of the decision maker quickly becomes burdensome. The results presented here indicate the existence of a point where one alternative becomes dominant to such degree that, regardless of the effects of the remainder of the comparisons, it cannot be overtaken as the preferred choice. By identifying this dominance point as a stopping criterion, problem size is reduced. This reduction in problem size is based on the decision maker's time frame, not the computation time. Computation time is also reduced, but it is a minor savings compared to the reduction of human decision making time. While this dominance point differs for every problem, results indicate that, on the average, about 50% of the comparisons can be eliminated. An iterative procedure is presented whereby the decision maker and/or analyst is informed when no further comparisons are necessary.