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

Kirytopoulos, K; Voulgaridou, D; Platis, A; Leopoulos, V

dc.contributor.author	Kirytopoulos, K	en
dc.contributor.author	Voulgaridou, D	en
dc.contributor.author	Platis, A	en
dc.contributor.author	Leopoulos, V	en
dc.date.accessioned	2014-03-01T01:35:07Z
dc.date.available	2014-03-01T01:35:07Z
dc.date.issued	2011	en
dc.identifier.issn	0377-2217	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20972
dc.subject	Markov processes	en
dc.subject	Multiple criteria decision analysis	en
dc.subject	Analytic network process	en
dc.subject	'Power' matrix method	en
dc.subject.classification	Management	en
dc.subject.classification	Operations Research & Management Science	en
dc.subject.other	HIERARCHY PROCESS	en
dc.subject.other	DECISION-MAKING	en
dc.subject.other	PROCESS MODEL	en
dc.subject.other	FORMULATION	en
dc.subject.other	PRIORITIES	en
dc.subject.other	LOGISTICS	en
dc.subject.other	SELECTION	en
dc.subject.other	GEOMETRY	en
dc.subject.other	SYSTEM	en
dc.subject.other	CHAIN	en
dc.title	An effective Markov based approach for calculating the Limit Matrix in the analytic network process	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.ejor.2011.03.043	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.ejor.2011.03.043	en
heal.language	English	en
heal.publicationDate	2011	en
heal.abstract	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. (C) 2011 Elsevier B.V. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	EUROPEAN JOURNAL OF OPERATIONAL RESEARCH	en
dc.identifier.doi	10.1016/j.ejor.2011.03.043	en
dc.identifier.isi	ISI:000292433900009	en
dc.identifier.volume	214	en
dc.identifier.issue	1	en
dc.identifier.spage	85	en
dc.identifier.epage	90	en