On a multicommodity flow network reliability model and its application to a container-loading transportation problem

This paper is mainly to extend the MMCF (multi-commodity minimum cost flow) problem from deterministic flow networks to stochastic cases. Under the transportation budget constraint, this paper proposes an approach to calculate the probability that the required amount of multi-commodity can be transmitted successfully through a stochastic flow network. Such a probability is called transportation reliability. An algorithm is proposed first to find out all lower boundary points for the requirement in terms of minimal paths. The transportation reliability can then be calculated in terms of such lower boundary points. A numerical example, in which two types of commodities are shipped in container under two container-loading policies, is presented to illustrate the application of such a reliability model.