A network simplex algorithm for simple manufacturing network model

In this paper, we propose a network model called simple manufacturing network. Our model is a combined version of the ordinary multicommodity network and the manufacturing network flow model. It can be used to characterize the complicated manufacturing scenarios. By formulating the model as a minimum cost flow problem plus several bounded variables, we present a modified network simplex method, which exploits the special structure of the model and can perform the computation on the network. A numerical example is provided for illustrating our method.