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DOI: 10.4230/OASIcs.ATMOS.2007.1170
URN: urn:nbn:de:0030-drops-11701
URL: http://drops.dagstuhl.de/opus/volltexte/2007/1170/
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Borndörfer, Ralf ; Schlechte, Thomas

05. Models for Railway Track Allocation

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Abstract

The optimal track allocation problem (OPTRA) is to find, in a given railway network, a conflict free set of train routes of maximum value. We study two types of integer programming formulations for this problem: a standard formulation that models block conflicts in terms of packing constraints, and a novel formulation of the `extended' type that is based on additional `configuration' variables. The packing constraints in the standard formulation stem from an interval graph and can therefore be separated in polynomial time. It follows that the LP-relaxation of a strong version of this model, including all clique inequalities from block conflicts, can be solved in polynomial time. We prove that the LP-relaxation of the extended formulation can also be solved in polynomial time, and that it produces the same LP-bound. Albeit the two formulations are in this sense equivalent, the extended formulation has advantages from a computational point of view. It features a constant number of rows and is amenable to standard column generation techniques. Results of an empirical model comparison on mesoscopic data for the Hanover-Fulda-Kassel region of the German long distance railway network are reported.

BibTeX - Entry

@InProceedings{borndrfer_et_al:OASIcs:2007:1170,
  author =	{Ralf Bornd{\"o}rfer and Thomas Schlechte},
  title =	{{05. Models for Railway Track Allocation}},
  booktitle =	{7th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'07)},
  series =	{OpenAccess Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-04-0},
  ISSN =	{2190-6807},
  year =	{2007},
  volume =	{7},
  editor =	{Christian Liebchen and Ravindra K. Ahuja and Juan A. Mesa},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2007/1170},
  URN =		{urn:nbn:de:0030-drops-11701},
  doi =		{http://dx.doi.org/10.4230/OASIcs.ATMOS.2007.1170},
  annote =	{Keywords: Track allocation, train timetabling,integer programming, column generation}
}

Keywords: Track allocation, train timetabling,integer programming, column generation
Seminar: 7th Workshop on Algorithmic Methods and Models for Optimization of Railways (ATMOS'07)
Issue Date: 2007
Date of publication: 06.11.2007


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