Minimum cost multicommodity network flow problem in time-varying networks: by decomposition principle

Time-varying network flows (also called dynamic network flows) generalize standard network flows by introducing an element of time. In this paper, we consider the dynamic version of the minimum cost multicommodity flow problem with storage at intermediate nodes. This problem is known to be NP-hard. By using of the flow decomposition theorem in network flows, we propose an efficient model based on dynamic path flows for this problem. For some special structures of the path-flow formulation, we provide an algorithm based on decomposition principle, for solving the proposed model. In the end, the efficiency of the proposed approach is evaluated through a number of experimental tests.