The minimum cost multicommodity flow problem in dynamic networks and an algorithm for its solving

The dynamic version of the minimum cost multicommodity flow problem that generalizes the static minimum cost multicommodity flow problem is formulated and studied. This dynamic problem is considered on directed networks with a set of commodities, time-varying capacities, fixed transit times on arcs,...

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Published inComputer science journal of Moldova Vol. 13; no. 1(37); pp. 29 - 36
Main Authors Maria A. Fonoberova, Dmitrii D. Lozovanu
Format Journal Article
LanguageEnglish
Published Vladimir Andrunachievici Institute of Mathematics and Computer Science 01.05.2005
Subjects
dynamic flows
dynamic networks
flows over time
minimum cost flows
multicommodity flows
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ISSN1561-4042

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Summary:The dynamic version of the minimum cost multicommodity flow problem that generalizes the static minimum cost multicommodity flow problem is formulated and studied. This dynamic problem is considered on directed networks with a set of commodities, time-varying capacities, fixed transit times on arcs, and a given time horizon. We assume that cost functions, defined on edges, are nonlinear and depend on time and flow and the demand function also depends on time. The corresponding algorithm, based on reducing the dynamic problem to a static problem on a time-expanded network, to solve the minimum cost dynamic multicommodity flow problem is proposed and some details concerning its complexity are discussed. Mathematics Subject Classification 2000: 90B10, 90C35, 90C27.
ISSN:1561-4042