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when quoting this document, please refer to the following
URN: urn:nbn:de:0030-drops-11701
URL: http://drops.dagstuhl.de/opus/volltexte/2007/1170/
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:DSP:2007:1170,
  author =	{Ralf Bornd{\"o}rfer and Thomas Schlechte},
  title =	{05. Models for Railway Track Allocation},
  booktitle =	{ATMOS 2007 - 7th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems},
  year =	{2007},
  editor =	{Christian Liebchen and Ravindra K. Ahuja and Juan A. Mesa},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2007/1170},
  annote =	{Keywords: Track allocation, train timetabling,integer programming, column generation},
  ISBN =	{978-3-939897-04-0}
}

Keywords: Track allocation, train timetabling,integer programming, column generation
Seminar: ATMOS 2007 - 7th Workshop on Algorithmic Methods and Models for Optimization of Railways
Documenttype: InProceedings
Issue date: 2007
Date of publication: 06.11.2007

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