Network simplex algorithm for the bi-criteria minimum cost flow over time problem

Abstract

The article formulates and studies the generalization of the bi-criteria minimum cost flow problem for the case of dynamic flows. The approach is based on reducing the dynamic problem to a static bi-criteria problem on a time-expanded network with constant capacities, fixed transit times on arcs and for a flow leaving the source node only at time θ = 0 and solving the problem via a network-simplex-based algorithm.