License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/OASIcs.ATMOS.2018.15
URN: urn:nbn:de:0030-drops-97204
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9720/
van Lieshout, Rolf N. ;
Bouman, Paul C.
Vehicle Scheduling Based on a Line Plan
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}
}
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Keywords: |
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Vehicle scheduling, integrated railway planning, (fractional) matching, treewidth |
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Collection: |
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18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018) |
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Issue Date: |
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2018 |
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Date of publication: |
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28.08.2018 |
