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Research articles

The optimal flow in dynamic networks with nonlinear cost functions on edges

M. Fonoberova^a, D. Lozovanu<sup>b

a</sup> Moldova State University, Chişinău, Moldova
^b Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Chişinău, Moldova

Abstract: In this paper 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 edges that depend on time and flow. Moreover, we assume that the demand function and capacities of 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.

Keywords and phrases: Dynamic networks, network flow, dynamic flows, flows over time, minimum cost flows.

MSC: 90B10, 90C35, 90C27

Received: 08.07.2004

Language: English

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