Minimum cost time-varying network flow problems

This paper deals with a general minimum cost dynamic flow problem in a discrete time model with time-varying transit times, transit costs, transit capacities, storage costs, and storage capacities. For this problem, an algorithm of time complexity O(V nT(n+T)) is presented, where V is an upper bound on the total supply, n is the number of nodes, and T denotes the given time horizon of the dynamic flow problem. The algorithm is a discrete-time version of the successive shortest path algorithm.

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