Optimal multicommodity flows in dynamic networks and algorithms for their finding

In this paper we study two basic problems related to dynamic flows: maximum multicommodity flow and the minimum cost multicommodity flow problems. We consider these problems on dynamic networks with time-varying capacities of edges. For minimum cost multicommodity flow problem we assume that cost functions, defined on edges, are nonlinear and depending on time and flow, and the demand function also depends on time. We propose algorithms for solving these dynamic problems, which are based on their reducing to static ones on a time-expanded network.