Abstract
The minimum flow (MF) problem aims to find a solution that can send the minimum flow from one node (the source) to another node (the sink), under the constraint that the lower bounds and the upper bounds (capacities) of the arcs in the general network are all satisfied. On the other hand, the bipartite network also arises in practical context. In a bipartite network the several minimum flow algorithms can be substantially improved. Most MF models considered in the literature are static, that is, problems that have no underlying temporal dimension. In practical situations, it is easy to see many time-varying MF problems. In these instances, to account properly for the evolution of the underlying system over time, we need to use dynamic network flow models. When the time is considered as a variable discrete values, these problems can be solved by constructing an equivalent, static time expanded network. This is a static approach. In this paper we study the minimum flows in bipartite dynamic networks with static approach.
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