## Solving Railway Track Allocation Problems

Please always quote using this URN: urn:nbn:de:0297-zib-9631

- The \emph{optimal track allocation problem} (\textsc{OPTRA}), also known as the train routing problem or the train timetabling problem, is to find, in a given railway network, a conflict-free set of train routes of maximum value. We propose a novel integer programming formulation for this problem that is based on additional configuration' variables. Its LP-relaxation can be solved in polynomial time. These results are the theoretical basis for a column generation algorithm to solve large-scale track allocation problems. Computational results for the Hanover-Kassel-Fulda area of the German long distance railway network involving up to 570 trains are reported.

Author: | Ralf Borndörfer, Thomas Schlechte |
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Document Type: | ZIB-Report |

Tag: | column generation; railway track allocation; timetabling |

MSC-Classification: | 90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Bxx Operations research and management science / 90B06 Transportation, logistics |

90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C27 Combinatorial optimization | |

Date of first Publication: | 2007/08/02 |

Series (Serial Number): | ZIB-Report (07-20) |

ISSN: | 1438-0064 |

Published in: | Appeared in: Operations Research Proceedings 2007. J. Kalcsics, S. Nickel (eds.)Springer 2008, pp. 117-122 |