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Line Planning and Connectivity

Authors: Ralf Borndörfer, Marika Neumann, and Marc E. Pfetsch

Published in: Dagstuhl Seminar Proceedings, Volume 9261, Models and Algorithms for Optimization in Logistics (2009)

Abstract

The line planning problem in public transport deals with the construction of a system of lines that is both attractive for the passengers and of low costs for the operator. In general, the computed line system should be connected, i.e., for each two stations there have to be a path that is covered by the lines. This subproblem is a generalization of the well-known Steiner tree problem; we call it the Steiner connectivity Problem. We discuss complexity of this problem, generalize the so-called Steiner partition inequalities and give a transformation to the directed Steiner tree problem. We show that directed models provide tight formulations for the Steiner connectivity problem, similar as for the Steiner tree problem.

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Ralf Borndörfer, Marika Neumann, and Marc E. Pfetsch. Line Planning and Connectivity. In Models and Algorithms for Optimization in Logistics. Dagstuhl Seminar Proceedings, Volume 9261, pp. 1-3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{borndorfer_et_al:DagSemProc.09261.15,
  author =	{Bornd\"{o}rfer, Ralf and Neumann, Marika and Pfetsch, Marc E.},
  title =	{{Line Planning and Connectivity}},
  booktitle =	{Models and Algorithms for Optimization in Logistics},
  pages =	{1--3},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9261},
  editor =	{Cynthia Barnhart and Uwe Clausen and Ulrich Lauther and Rolf H. M\"{o}hring},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.09261.15},
  URN =		{urn:nbn:de:0030-drops-21661},
  doi =		{10.4230/DagSemProc.09261.15},
  annote =	{Keywords: Steiner tree, generalization, paths}
}

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DOI: 10.4230/OASIcs.ATMOS.2008.1583

Line Planning on Paths and Tree Networks with Applications to the Quito TrolebÃƒÂºs System

Authors: Luis M. Torres, Ramiro Torres, Ralf Borndörfer, and Marc E. Pfetsch

Published in: OASIcs, Volume 9, 8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'08) (2008)

Abstract

Line planning is an important step in the strategic planning process of a public transportation system. In this paper, we discuss an optimization model for this problem in order to minimize operation costs while guaranteeing a certain level of quality of service, in terms of available transport capacity. We analyze the problem for path and tree network topologies as well as several categories of line operation that are important for the Quito TrolebÃƒÂºs system. It turns out that, from a computational complexity worst case point of view, the problem is hard in all but the most simple variants. In practice, however, instances based on real data from the TrolebÃƒÂºs System in Quito can be solved quite well, and significant optimization potentials can be demonstrated.

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Luis M. Torres, Ramiro Torres, Ralf Borndörfer, and Marc E. Pfetsch. Line Planning on Paths and Tree Networks with Applications to the Quito TrolebÃƒÂºs System. In 8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'08). Open Access Series in Informatics (OASIcs), Volume 9, pp. 1-13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{torres_et_al:OASIcs.ATMOS.2008.1583,
  author =	{Torres, Luis M. and Torres, Ramiro and Bornd\"{o}rfer, Ralf and Pfetsch, Marc E.},
  title =	{{Line Planning on Paths and Tree Networks with Applications to the Quito Troleb\~{A}ƒ\^{A}ºs System}},
  booktitle =	{8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'08)},
  pages =	{1--13},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-07-1},
  ISSN =	{2190-6807},
  year =	{2008},
  volume =	{9},
  editor =	{Fischetti, Matteo and Widmayer, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2008.1583},
  URN =		{urn:nbn:de:0030-drops-15838},
  doi =		{10.4230/OASIcs.ATMOS.2008.1583},
  annote =	{Keywords: Line planning, computational complexity, public transport, combinatorial optimization}
}

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Documents authored by Pfetsch, Marc E.

Line Planning and Connectivity

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Line Planning on Paths and Tree Networks with Applications to the Quito TrolebÃƒÂºs System

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