Introducing Simplex Mass Balancing Method for Multi-commodity Flow Network with a Separator

Maximization of flow through the network has remained core issue in the field of optimization. In this paper a new advanced network problem is introduced, i.e., a multi-commodity network with a separator. This network consists of several sub-networks linked through a commodity separator. The objective is to maximize the flow of the commodity of interest from the commodity mixture at the output of the commodity separator, while observing the capacity constraints of all sub-networks. Such networks are present in Oil and Gas development fields. Such networks are also conceptual representation of material flows of many other manufacturing systems. In this paper an algorithm is developed for maximization of flow in these networks. Maximization of flow in such networks has direct practical relevance and industrial application. The developed algorithm brings together two distinct branches of computer science i.e., graph theory and linear programming to solve the problem.