Iterative mass balance method for the multi-commodity flow maximisation problem

There are many multi-commodity maximisation problems present in the literature. The problem addressed in this article deals with the number of sources producing a mixture of multiple commodities with different proportions. There are also separators which separate the commodity flows. However, component failures often occur after the separation of commodities, resulting in a limited flow capacity to carry these commodities. As a result, production from certain number of sources has to be reduced to adjust for the capacity reduction caused by component failures. The objective is to maximise the flow with respect to one particular commodity, while satisfying the capacity constraints and the flow conservation law. This problem can be solved as a linear programming problem. In this article, a new algorithm is proposed for a three-commodity problem, which performs much faster than the simplex method. The three-commodity problem has a close relation to oil and gas production, where three different commodities, namely oil, gas and water are dealt with. This method can be used in a discrete-event simulator for long-term production planning while designing a piped network for the oil field.