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The continuous stop location problem in public transportation networks

  • In this paper we consider the location of stops along the edges of an already existing public transportation network. This can be the introduction of bus stops along some given bus routes, or of railway stations along the tracks in a railway network. The positive effect of new stops is given by the better access of the potential customers to their closest station, while the increasement of travel time caused by the additional stopping activities of the trains leads to a negative effect. The goal is to cover all given demand points with a minimal amount of additional traveling time, where covering may be defined with respect to an arbitrary norm (or even a gauge). Unfortunately, this problem is NP-hard, even if only the Euclidean distance is used. In this paper, we give a reduction to a finite candidate set leading to a discrete set covering problem. Moreover, we identify network structures in which the coefficient matrix of the resulting set covering problem is totally unimodular, and use this result to derive efficient solution approaches. Various extensions of the problem are also discussed.

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Author:A. Schöbel, H. W. Hamacher, A. Liebers, D. Wagner
URN (permanent link):urn:nbn:de:hbz:386-kluedo-11930
Serie (Series number):Report in Wirtschaftsmathematik (WIMA Report) (81)
Document Type:Preprint
Language of publication:English
Year of Completion:2002
Year of Publication:2002
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2002/05/21
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011