Abstract
In this paper, we expand the network simplex algorithm for solving network structured linear programming problems. This algorithm performs the simplex operations directly on the graph or network itself. We expand this algorithm by means of a fuzzilize and multiplize of objective functions. And we apply this expanded algorithm to minimum cost network flow problems with multiple objective functions such as cost, time and so on. The numerical example is also given, and it shows that the algorithm is very effective with respect to the real-world network problems under the computer configurations.
