Title: Application of linear programming to derive the local weight in the analytic hierarchy process

Authors: Ümran Şengül; Miraç Eren; Seyedhadi Eslamian Shiraz

Addresses: Department of Business, Faculty of Economics and Administrative Sciences, Çanakkale Onsekiz Mart University, Terzioğlu Kampüsü, Çanakkale, Turkey ' Department of Econometrics, Faculty of Economics and Administrative Sciences, Atatürk University, Erzurum, Turkey ' Department of Management, Faculty of Humanities, University College of Nabi Akram (UCNA), Tabriz, No. 1283, Rah Ahan Street, Iran

Abstract: The analytic hierarchy process (AHP) has become more developed in both the areas of theory and practice. The important topic here, is how to drive the local weight vector from a pairwise reciprocal matrix. In the literature, there are several methods used to accomplish this. Most recently, Hosseinian et al. (2009) suggested the LP-GW-AHP because it obviously provides better weights. In this article, the LP-GW-AHP method is applied to multi-level decision problems, and the weights were compared with Saaty's eigenvector. According to our findings, of the LP-GW-AHP method, Saaty's eigenvector method differs slightly from that derived in the local weight values.

Keywords: analytical hierarchy process; AHP; linear programming; weight generation; fitting performance; eigenvector method; ranking; operational research; local weight vector; pairwise reciprocal matrix.

DOI: 10.1504/IJOR.2016.078937

International Journal of Operational Research, 2016 Vol.27 No.3, pp.450 - 468

Received: 17 Mar 2014
Accepted: 01 Oct 2014
Published online: 06 Sep 2016 *

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