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DOI: 10.4230/OASIcs.ATMOS.2010.24

Robust Train Routing and Online Re-scheduling

Authors: Alberto Caprara, Laura Galli, Leo Kroon, Gábor Maróti, and Paolo Toth

Published in: OASIcs, Volume 14, 10th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'10) (2010)

Abstract

Train Routing is a problem that arises in the early phase of the passenger railway planning process, usually several months before operating the trains. The main goal is to assign each train a stopping platform and the corresponding arrival/departure paths through a railway station. It is also called Train Platforming when referring to the platform assignment task. Railway stations often represent bottlenecks and train delays can easily disrupt the routing schedule. Thereby railway stations are responsible for a large part of the delay propagation in the whole network. In this research we present different models to compute robust routing schedules and we study their power in an online context together with different re-scheduling strategies. We also design a simulation framework and use it to evaluate and compare the effectiveness of the proposed robust models and re-scheduling algorithms using real-world data from Rete Ferroviaria Italiana, the main Italian Railway Infrastructure Manager.

Cite as

Alberto Caprara, Laura Galli, Leo Kroon, Gábor Maróti, and Paolo Toth. Robust Train Routing and Online Re-scheduling. In 10th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'10). Open Access Series in Informatics (OASIcs), Volume 14, pp. 24-33, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{caprara_et_al:OASIcs.ATMOS.2010.24,
  author =	{Caprara, Alberto and Galli, Laura and Kroon, Leo and Mar\'{o}ti, G\'{a}bor and Toth, Paolo},
  title =	{{Robust Train Routing and Online Re-scheduling}},
  booktitle =	{10th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'10)},
  pages =	{24--33},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-20-0},
  ISSN =	{2190-6807},
  year =	{2010},
  volume =	{14},
  editor =	{Erlebach, Thomas and L\"{u}bbecke, Marco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2010.24},
  URN =		{urn:nbn:de:0030-drops-27470},
  doi =		{10.4230/OASIcs.ATMOS.2010.24},
  annote =	{Keywords: Railway optimisation, Train platforming, Robust planning, Online re-scheduling, Simulation}
}

Document

DOI: 10.4230/OASIcs.ATMOS.2008.1590

Recoverable Robustness for Railway Rolling Stock Planning

Authors: Valentina Cacchiani, Alberto Caprara, Laura Galli, Leo Kroon, and Gábor Maróti

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

Abstract

In this paper we explore the possibility of applying the notions of Recoverable Robustness and Price of Recoverability (introduced by [5]) to railway rolling stock planning, being interested in recoverability measures that can be computed in practice, thereby evaluating the robustness of rolling stock schedules. In order to lower bound the Price of Recoverability for any set of recovery algorithms, we consider an "optimal" recovery algorithm and propose a Benders decomposition approach to assess the Price of Recoverability for this "optimal" algorithm. We evaluate the approach on real-life rolling stock planning problems of NS, the main operator of passenger trains in the Netherlands. The preliminary results show that, thanks to Benders decomposition, our lower bound can be computed within relatively short time for our case study.

Cite as

Valentina Cacchiani, Alberto Caprara, Laura Galli, Leo Kroon, and Gábor Maróti. Recoverable Robustness for Railway Rolling Stock Planning. 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{cacchiani_et_al:OASIcs.ATMOS.2008.1590,
  author =	{Cacchiani, Valentina and Caprara, Alberto and Galli, Laura and Kroon, Leo and Mar\'{o}ti, G\'{a}bor},
  title =	{{Recoverable Robustness for Railway Rolling Stock Planning}},
  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.2008.1590},
  URN =		{urn:nbn:de:0030-drops-15902},
  doi =		{10.4230/OASIcs.ATMOS.2008.1590},
  annote =	{Keywords: Recoverable robustness, Railway rolling stock scheduling, Benders decomposition}
}

Document

DOI: 10.4230/OASIcs.ATMOS.2007.1174

04. Solution of the Train Platforming Problem

Authors: Alberto Caprara, Laura Galli, and Paolo Toth

Published in: OASIcs, Volume 7, 7th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'07) (2007)

Abstract

In this paper we study a general formulation of the train platforming problem, which contains as special cases all the versions previously considered in the literature as well as a case study from the Italian Infrastructure manager that we addressed. In particular, motivated by our case study, we consider a general quadratic objective function, and propose a new way to linearize it by using a small number of new variables along with a set of constraints that can be separated efficiently by solving an appropriate linear program. The resulting integer linear programming formulation has a continuous relaxation that leads to strong bounds on the optimal value. For the instances in our case study, we show that a simple diving heuristic based on this relaxation produces solutions that are much better than those produced by a simple heuristic currently in use, and that often turn out to be (nearly-) optimal.

Cite as

Alberto Caprara, Laura Galli, and Paolo Toth. 04. Solution of the Train Platforming Problem. In 7th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'07). Open Access Series in Informatics (OASIcs), Volume 7, pp. 49-61, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{caprara_et_al:OASIcs.ATMOS.2007.1174,
  author =	{Caprara, Alberto and Galli, Laura and Toth, Paolo},
  title =	{{04. Solution of the Train Platforming Problem}},
  booktitle =	{7th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'07)},
  pages =	{49--61},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-04-0},
  ISSN =	{2190-6807},
  year =	{2007},
  volume =	{7},
  editor =	{Ahuja, Ravindra K. and Liebchen, Christian and Mesa, Juan A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2007.1174},
  URN =		{urn:nbn:de:0030-drops-11741},
  doi =		{10.4230/OASIcs.ATMOS.2007.1174},
  annote =	{Keywords: Train Platforming, Train Routing, Branch-and-Cut-and-Price, Quadratic Objective Function, Linearization}
}

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Robust Train Routing and Online Re-scheduling

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Recoverable Robustness for Railway Rolling Stock Planning

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04. Solution of the Train Platforming Problem

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