A nonlinear program model to obtain consensus priority vector in the analytic hierarchy process

In group decision making, because the decision-makers usually represent different interest backgrounds, it is worth to study how to make the different decision makers coordinate and cooperate for aggregating group opinions. In this paper, based on the analytic hierarchy process, we propose a nonlinear program model to obtain consensus priority vector, and point that the model can make decision-makers reach consensus by improving compatibility of judgement matrices. Moreover, we use the genetic-simulated annealing algorithm to obtain its optimal solution. Finally, a numerical example is presented to illustrate the application of this method.