Introducing a nonlinear programming model and using genetic algorithm to rank the alternatives in analytic hierarchy process


Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.


As ranking is one of the most important issues in data envelopment analysis (DEA), many researchers have comprehensive studies on the subject and presented different approaches. In some papers, DEA and Analytic hierarchy process (AHP) are integrated to rank the alternatives. AHP utilizes pairwise comparisons between criteria and units, assessed subjectively by the decision maker, to rank the units. In this paper, a nonlinear programming (NLP) model is introduced to derive the true weights for pairwise comparison matrices in AHP. Genetic algorithm (GA) is used in order to solve this model. We use MATLAB software to solve proposed model for ranking the alternatives in AHP. A numerical example is applied to illustrate the proposed model.