Title: A primal-dual method for linear programming problems with fuzzy variables

Authors: A. Ebrahimnejad, S.H. Nasseri, F. Hosseinzadeh Lotfi, M. Soltanifar

Addresses: Mathematics Department, Sciences and Research Branch, Islamic Azad University, Tehran, Iran. ' Department of Mathematics, Sciences Faculty, Mazandaran University, Babolsar, Iran. ' Mathematics Department, Sciences and Research Branch, Islamic Azad University, Tehran, Iran. ' Semnan Branch, Islamic Azad University, Semnan, Iran

Abstract: Linear programming problems with fuzzy variables have been investigated by many researchers in the recent literature. Some methods to solve these problems, such as the primal simplex method and the dual simplex method, are based on the concept of comparison of fuzzy numbers by using ranking functions. In this paper, we give a new primal-dual algorithm for solving linear programming problems with fuzzy variables by using duality results, which was proposed by Mahdavi-Amiri and Nasseri (2007). This algorithm will be useful for sensitivity analysis when the activity vectors change for basic columns. [Received 29 September 2008; Revised 16 March 2009; Accepted 17 April 2009]

Keywords: fuzzy variables; linear programming; FVLP; primal-dual method; ranking function; trapezoidal fuzzy numbers; sensitivity analysis; activity vectors; basic columns.

DOI: 10.1504/EJIE.2010.031077

European Journal of Industrial Engineering, 2010 Vol.4 No.2, pp.189 - 209

Published online: 20 Jan 2010 *

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