Strong duality for the maximum Borel flow problem

Abstract

Research on flows over time has been conducted mainly in two separate and independent approaches, namely discrete and continuous models, depending on whether a discrete or continuous representation of time is used. Recently, Borel flows have been introduced to build a bridge between these two models. In this paper, we consider the maximum Borel flow problem formulated in a network where capacities on arcs are given as Borel measures and storage might be allowed at the nodes of the network. This problem is formulated as a linear program in a space of measures. We define a dual problem and prove a strong duality result. We show that strong duality is closely related to a MaxFlow-MinCut Theorem. © 2011 Springer-Verlag.