An exact global optimization method for deriving weights in the AHP

In the Analytic Hierarchy Process, AHP, a set of actions is to be ranked by deriving weights from a pairwise comparison matrix A. There is a vast literature on modelling issues of AHP, as well as a series of proposals of different mathematical-programming methods to infer weights from A. However, it is seldom observed that such optimization problems may be multimodal, thus the standard local-search resolution techniques suggested may be trapped in local optima, yielding a wrong ranking of alternatives. In this note we show that standard tools of Global Optimization based on Interval Analysis, lead to globally optimal weights in reason-able time