Modified bounded dual network simplex algorithm for solving minimum cost flow problem with fuzzy costs based on ranking functions

In this paper, we generalize the bounded dual simplex algorithm for solving minimum cost flow problem with fuzzy cost, which its aim is to find the least fuzzy cost of a commodity through a capacitated network in order to satisfy demands at certain nodes using available supplies at other nodes. This algorithm begins with dual feasibility and iterates between dual and primal problems until optimality is achieved. Here, we use the linear ranking functions to compare fuzzy numbers. By using the proposed method the optimal solution of minimum cost flow problems with fuzzy costs can be easily obtained. To illustrate the proposed method a numerical example is solved and the obtained results are discussed.