Results of Monte Carlo Method Application to Performance Evaluation of Chosen Prioritization Procedures in the Analytic Hierarchy Process

Abstrakt

The main goal of this research paper is to compare two procedures for preferences ranking operating within the Analytic Hierarchy Process, i.e. principal right eigenvector usually applied in this methodology and logarithmic utility approach, elaborated very recently as the alternative of the former one, with better proprieties. For examination purposes of this paper, Monte Carlo methodology was implemented with application of properly designed computer simulations. It can be noticed, that both procedures taken into consideration in this research are very competitive. Furthermore, the simulations results indicate, that the REV is not significantly better in comparison to the LUA in the process of deriving priority vectors from Pairwise Comparison Matrices. In fact, the REV and the LUA comparative evaluation leads to a conclusion that the REV, in some circumstances, may provide even worse than the LUA, estimation results of decision makers true priorities. Certainly, it is true for both types of PCMs, i.e. reciprocal and nonreciprocal. Moreover, the phenomenon observed in this research concerns the entire AHP model (not only single PCM). On the bases of this research, it seems reasonable to disagree with the concept widely distributed in the literature stating that the REV is the principal theoretical concept for deriving decision makers preferences and no other procedure qualifies. The main conclusion of the research paper is the fact, that in the Analytic Hierarchy Process, logarithmic utility approach is at least as good as principal right eigenvector procedure, and sometimes it prevails.