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The optimal flow in dynamic networks with nonlinear cost functions on edges. (English) Zbl 1068.90020
Summary: We study the dynamic version of the nonlinear minimum-cost flow problem on networks. We consider the problem on dynamic networks with nonlinear cost functions on their edges that depend on time and flow. Moreover, we assume that the demand function and capacities of the edges also depend on time. To solve the problem we propose an algorithm, which is based on reducing the dynamic problem to the classical minimum-cost problem on a time-expanded network. We also study some generalization of the proposed problem.

90B10 Deterministic network models in operations research
90C35 Programming involving graphs or networks
90C27 Combinatorial optimization
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