A Fuzzy Residual Network Approach to Minimum Cost Flow Problem with Fuzzy Parameters

968 A Fuzzy Residual Network Approach to Minimum Cost Flow Problem with Fuzzy Parameters M. Bagherian Department of Applied Mathematics, Faculty of Mathematical Science, University of Guilan, Rasht, Iran. [email protected] . ABSTRACT The Minimum Cost Flow (MCF) problem has been defined as to determine a least cost shipment of a commodity through a network in order to satisfy demands at certain nodes from available supplies at other nodes. In this paper the minimum cost flow problem with fuzzy parameters is considered. Based on integer solution property of the problem, the Yager ranking indices can be calculated for fuzzy arc costs to change the fuzzy arc costs to crisp ones. Consequently the problem can be converted to a MCF problem with fuzzy arc capacities and fuzzy supply\demands. Then by defining the fuzzy residual network, the MCF algorithms are developed to solve this problem efficiently. In fact the aim of this paper is to consider the theoretical aspects of the problem, not numerical results of the presented algorithm. So the computational complexity of the proposed method is discussed.