Nonlinear programming applied to the reduction of inconsistency in the AHP method

Analytic Hierarchy Process is one of the most known multicriteria decision aid methods. Nevertheless, as it relies on decision makers (DM) pairwise comparisons, a problem may occur if some comparisons are not well done. This issue, known as inconsistency, appears when an inconsistency threshold is violated. One way to deal with inconsistency is to redo all judgments, as many times as needed, in order to reach acceptable levels. This work proposes a nonlinear programming model that reduces inconsistency to zero or near zero, without needing to redo all judgments. The reduction is achieved by adjusting the original judgments in a minimum way, keeping the DM's decisions within a tolerable range. Only discrete values are generated, so the solution respects the limits of the Saaty scale (1-9). To illustrate the efficiency of the nonlinear model, a comparison between the proposed model and other models taken from recent literature was made. The results show that the proposed model performed better, since the original judgments were changed in a minimum way, also the inconsistency was completely removed. Alternatively, if some inconsistency is allowed more original judgments can be preserved.