A primal-dual method for solving linear programming problems with fuzzy cost coefficients based on linear ranking functions and its applications

Ali Ebrahimnejad

International Journal of Industrial and Systems Engineering, 2012, vol. 12, issue 2, 119-140

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. (search for similar items in EconPapers)
Date: 2012
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.inderscience.com/link.php?id=48851 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ids:ijisen:v:12:y:2012:i:2:p:119-140

Access Statistics for this article

More articles in International Journal of Industrial and Systems Engineering from Inderscience Enterprises Ltd
Bibliographic data for series maintained by Sarah Parker ().