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Documents authored by Karbstein, Marika


Document
A Simple Way to Compute the Number of Vehicles That Are Required to Operate a Periodic Timetable

Authors: Ralf Borndörfer, Marika Karbstein, Christian Liebchen, and Niels Lindner

Published in: OASIcs, Volume 65, 18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018)


Abstract
We consider the following planning problem in public transportation: Given a periodic timetable, how many vehicles are required to operate it? In [Julius Paetzold et al., 2017], for this sequential approach, it is proposed to first expand the periodic timetable over time, and then answer the above question by solving a flow-based aperiodic optimization problem. In this contribution we propose to keep the compact periodic representation of the timetable and simply solve a particular perfect matching problem. For practical networks, it is very much likely that the matching problem decomposes into several connected components. Our key observation is that there is no need to change any turnaround decision for the vehicles of a line during the day, as long as the timetable stays exactly the same.

Cite as

Ralf Borndörfer, Marika Karbstein, Christian Liebchen, and Niels Lindner. A Simple Way to Compute the Number of Vehicles That Are Required to Operate a Periodic Timetable. In 18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018). Open Access Series in Informatics (OASIcs), Volume 65, pp. 16:1-16:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


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@InProceedings{borndorfer_et_al:OASIcs.ATMOS.2018.16,
  author =	{Bornd\"{o}rfer, Ralf and Karbstein, Marika and Liebchen, Christian and Lindner, Niels},
  title =	{{A Simple Way to Compute the Number of Vehicles That Are Required to Operate a Periodic Timetable}},
  booktitle =	{18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018)},
  pages =	{16:1--16:15},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-096-5},
  ISSN =	{2190-6807},
  year =	{2018},
  volume =	{65},
  editor =	{Bornd\"{o}rfer, Ralf and Storandt, Sabine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2018.16},
  URN =		{urn:nbn:de:0030-drops-97214},
  doi =		{10.4230/OASIcs.ATMOS.2018.16},
  annote =	{Keywords: Vehicle Scheduling, Periodic Timetabling, Bipartite Matching}
}
Document
Separation of Cycle Inequalities for the Periodic Timetabling Problem

Authors: Ralf Borndörfer, Heide Hoppmann, and Marika Karbstein

Published in: LIPIcs, Volume 57, 24th Annual European Symposium on Algorithms (ESA 2016)


Abstract
Cycle inequalities play an important role in the polyhedral study of the periodic timetabling problem. We give the first pseudo-polynomial time separation algorithm for cycle inequalities, and we give a rigorous proof for the pseudo-polynomial time separability of the change-cycle inequalities. The efficiency of these cutting planes is demonstrated on real-world instances of the periodic timetabling problem.

Cite as

Ralf Borndörfer, Heide Hoppmann, and Marika Karbstein. Separation of Cycle Inequalities for the Periodic Timetabling Problem. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 21:1-21:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)


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@InProceedings{borndorfer_et_al:LIPIcs.ESA.2016.21,
  author =	{Bornd\"{o}rfer, Ralf and Hoppmann, Heide and Karbstein, Marika},
  title =	{{Separation of Cycle Inequalities for the Periodic Timetabling Problem}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{21:1--21:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Sankowski, Piotr and Zaroliagis, Christos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2016.21},
  URN =		{urn:nbn:de:0030-drops-63722},
  doi =		{10.4230/LIPIcs.ESA.2016.21},
  annote =	{Keywords: periodic timetabling, cycle inequalities, separation algorithm}
}
Document
A Configuration Model for the Line Planning Problem

Authors: Ralf Borndörfer, Heide Hoppmann, and Marika Karbstein

Published in: OASIcs, Volume 33, 13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (2013)


Abstract
We propose a novel extended formulation for the line planning problem in public transport. It is based on a new concept of frequency configurations that account for all possible options to provide a required transportation capacity on an infrastructure edge. We show that this model yields a strong LP relaxation. It implies, in particular, general classes of facet defining inequalities for the standard model.

Cite as

Ralf Borndörfer, Heide Hoppmann, and Marika Karbstein. A Configuration Model for the Line Planning Problem. In 13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 33, pp. 68-79, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)


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@InProceedings{borndorfer_et_al:OASIcs.ATMOS.2013.68,
  author =	{Bornd\"{o}rfer, Ralf and Hoppmann, Heide and Karbstein, Marika},
  title =	{{A Configuration Model for the Line Planning Problem}},
  booktitle =	{13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems},
  pages =	{68--79},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-58-3},
  ISSN =	{2190-6807},
  year =	{2013},
  volume =	{33},
  editor =	{Frigioni, Daniele and Stiller, Sebastian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2013.68},
  URN =		{urn:nbn:de:0030-drops-42451},
  doi =		{10.4230/OASIcs.ATMOS.2013.68},
  annote =	{Keywords: Combinatorial optimization, polyhedral combinatorics, line planning}
}
Document
A Direct Connection Approach to Integrated Line Planning and Passenger Routing

Authors: Ralf Borndörfer and Marika Karbstein

Published in: OASIcs, Volume 25, 12th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (2012)


Abstract
The treatment of transfers is a major challenge in line planning. Existing models either route passengers and lines sequentially, and hence disregard essential degrees of freedom, or they are of extremely large scale, and seem to be computationally intractable. We propose a novel direct connection approach that allows an integrated optimization of line and passenger routing, including accurate estimates of the number of direct travelers, for large-scale real-world instances.

Cite as

Ralf Borndörfer and Marika Karbstein. A Direct Connection Approach to Integrated Line Planning and Passenger Routing. In 12th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 25, pp. 47-57, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2012)


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@InProceedings{borndorfer_et_al:OASIcs.ATMOS.2012.47,
  author =	{Bornd\"{o}rfer, Ralf and Karbstein, Marika},
  title =	{{A Direct Connection Approach to Integrated Line Planning and Passenger Routing}},
  booktitle =	{12th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems},
  pages =	{47--57},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-45-3},
  ISSN =	{2190-6807},
  year =	{2012},
  volume =	{25},
  editor =	{Delling, Daniel and Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2012.47},
  URN =		{urn:nbn:de:0030-drops-37027},
  doi =		{10.4230/OASIcs.ATMOS.2012.47},
  annote =	{Keywords: combinatorial optimization, line planning, transfers, passenger routing}
}
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