An effective Markov based approach for calculating the Limit Matrix in the analytic network process

Analytic network process is a multiple criteria decision analysis (MCDA) method that aids decision makers to choose among a number of possible alternatives or prioritize the criteria for making a decision in terms of importance. It handles both qualitative and quantitative criteria, that are compared in pairs, in order to forge a best compromise answer according to the different criteria and influences involved. The method has been widely applied and the literature review reveals a rising trend of ANP-related articles. The ‘power’ matrix method, a procedure necessary for the stability of the decision system, is one of the critical calculations in the mathematical part of the method. The present study proposes an alternative mathematical approach that is based on Markov chain processes and the well-known Gauss–Jordan elimination. The new approach obtains practically the same results as the power matrix method, requires slightly less time and number of calculations and handles effectively cyclic supermatrices, optimizing thus the whole procedure.

► Analytic network process uses the power matrix method for reaching the limit matrix.
► An alternative method based on Markov chains and Gauss–Jordan elimination is given.
► The new approach obtains practically the same results in slightly less time.
► It needs less number of calculations and handles effectively cyclic supermatrices.