Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH scholarly article en van Lieshout, Rolf N.; Bouman, Paul C. http://www.dagstuhl.de/oasics License
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URN: urn:nbn:de:0030-drops-97204
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Vehicle Scheduling Based on a Line Plan

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Abstract

We consider the following problem: given a set of lines in a public transportation network with their round trip times and frequencies, a maximum number of vehicles and a maximum number of lines that can be combined into a vehicle circulation, does there exist a set of vehicle circulations that covers all lines given the constraints. Solving this problem provides an estimate of the costs of operating a certain line plan, without having to compute a timetable first. We show that this problem is NP-hard for any restriction on the number of lines that can be combined into a circulation which is equal to or greater than three. We pay special attention to the case where at most two lines can be combined into a circulation, which is NP-hard if a single line can be covered by multiple circulations. If this is not allowed, a matching algorithm can be used to find the optimal solutions, which we show to be a 16/15-approximation for the case where it is allowed. We also provide an exact algorithm that is able to exploit low tree-width of the so-called circulation graph and small numbers of vehicles required to cover single circulations.

BibTeX - Entry

@InProceedings{vanlieshout_et_al:OASIcs:2018:9720,
  author =	{Rolf N. van Lieshout and Paul C. Bouman},
  title =	{{Vehicle Scheduling Based on a Line Plan}},
  booktitle =	{18th Workshop on Algorithmic Approaches for Transportation  Modelling, Optimization, and Systems (ATMOS 2018)},
  pages =	{15:1--15:14},
  series =	{OpenAccess Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-096-5},
  ISSN =	{2190-6807},
  year =	{2018},
  volume =	{65},
  editor =	{Ralf Bornd{\"o}rfer and Sabine Storandt},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9720},
  URN =		{urn:nbn:de:0030-drops-97204},
  doi =		{10.4230/OASIcs.ATMOS.2018.15},
  annote =	{Keywords: Vehicle scheduling, integrated railway planning, (fractional) matching, treewidth}
}

Keywords: Vehicle scheduling, integrated railway planning, (fractional) matching, treewidth
Seminar: 18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018)
Issue date: 2018
Date of publication: 2018


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