Application of ranking functions to develop the network simplex algorithm on minimum cost flow problem with fuzzy parameters

In this paper, we consider the minimum cost fuzzy flow (MCFF) problems which involve fuzzy numbers in the supply/demand of nodes and flows on the arcs. Then, by using linear ranking functions we give a fuzzy flow network simplex algorithm to solve the (MCFF) problems as well as the linear programming problem with fuzzy variables which is proposed by Mahdavi-Amiri and Nasseri in [2]. This algorithm is a simplification of the fuzzy primal simplex method so that it can be applied directly on the network without the need of a simplex tableau.

Keywords:

Minimum Cost Network Problem , Network Simplex Algorithm , Ranking Function , Trapezoidal Fuzzy Number