License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC BY-NC-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/OASIcs.ATMOS.2008.1588
URN: urn:nbn:de:0030-drops-15884
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2008/1588/
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Nachtigall, Karl ; Opitz, Jens

Solving Periodic Timetable Optimisation Problems by Modulo Simplex Calculations

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08002.Nachtigall.1588.pdf (0.3 MB)

Abstract

In the last 15 years periodic timetable problems have found
much interest in the combinatorial optimization community. We will focus on the optimisation task to minimise a weighted sum of undesirable slack times. This problem can be formulated as a mixed integer linear problem, which for real world instances is hard to solve. This is mainly caused by the integer variables, the so-called modulo parameter. At first we will discuss some results on the polyhedral structure of the periodic timetable problem. These ideas allow to define a modulo simplex basic solution by calculating the basic variables from modulo equations. This leads to a modulo network simplex method, which iteratively improves the solution by changing the simplex basis.

BibTeX - Entry

@InProceedings{nachtigall_et_al:OASIcs:2008:1588,
  author =	{Karl Nachtigall and Jens Opitz},
  title =	{{Solving Periodic Timetable Optimisation Problems by Modulo Simplex Calculations}},
  booktitle =	{8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'08) },
  series =	{OpenAccess Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-07-1},
  ISSN =	{2190-6807},
  year =	{2008},
  volume =	{9},
  editor =	{Matteo Fischetti and Peter Widmayer},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2008/1588},
  URN =		{urn:nbn:de:0030-drops-15884},
  doi =		{10.4230/OASIcs.ATMOS.2008.1588},
  annote =	{Keywords: Periodic event scheduling problem, integer programming, modulo network simplex}
}

Keywords: Periodic event scheduling problem, integer programming, modulo network simplex
Collection: 8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'08)
Issue Date: 2008
Date of publication: 24.09.2008

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