Application Of Mass Balancing Theorem To Multi-Commodity Flow Network With Multi-Separators

Some time ago the mass balancing theorem was developed for network flow maximization. Based on that theorem not only unit-commodity but also the multi-commodity flow was maximized through the network. Later, the mass balancing method was hybridized with linear programming (the Simplex method) to maximize multi-commodity flow through the network with a separator. The hybrid method was called the Simplex Mass Balancing Method (SMB). In this paper, the SMB is extended to work with a multi-commodity network with multiple separators. Such commodity flow networks with multiple separators have significant practical applications; examples of the latter are pipe networks in oil and gas development infrastructure.