Title: A primal-dual method for solving linear programming problems with fuzzy cost coefficients based on linear ranking functions and its applications
Author: Ali Ebrahimnejad
Address: Department of Mathematics, Qaemshahr Branch, Islamic Azad University, P.O. Box 163, Qaemshahr, Iran
Abstract: There are two important approaches based on linear ranking functions for solving linear programming problems with cost coefficients as an auxiliary problem to obtain a fuzzy solution of fuzzy variable linear programming problem. The first approach uses the primal simplex method that assumes an initial primal feasible basic solution is at hand. The second approach is based on dual simplex method that begins with a basic dual feasible basic solution and proceeds by pivoting through a series of dual basic solutions until the associated complementary primal basic fuzzy solution is feasible. In this paper, we propose a new method called the primal-dual algorithm, which is similar to the dual simplex method and begins with dual feasibility and proceeds to obtain primal feasibility while maintaining complementary slackness. An important difference between the dual simplex method and the primal-dual method is that the primal-dual algorithm does not require a dual feasible solution to be basic. This algorithm is useful specially for solving minimum fuzzy cost flow problem in which finding an initial dual feasible solution turns out to be a trivial task.
Keywords: FNLP; fuzzy number linear programming; primal-dual simplex method; ranking functions; TRFN; trapezoidal fuzzy numbers; fuzzy cost coefficients; minimum fuzzy cost flow.
Int. J. of Industrial and Systems Engineering, 2012 Vol.12, No.2, pp.119 - 140
Available online: 17 Aug 2012