Online Train Shunting

Authors Vianney Boeuf, Frédéric Meunier

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Vianney Boeuf
Frédéric Meunier

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Vianney Boeuf and Frédéric Meunier. Online Train Shunting. In 14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 42, pp. 34-45, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)


At the occasion of ATMOS 2012, Tim Nonner and Alexander Souza defined a new train shunting problem that can roughly be described as follows. We are given a train visiting stations in a given order and cars located at some source stations. Each car has a target station. During the trip of the train, the cars are added to the train at their source stations and removed from it at their target stations. An addition or a removal of a car in the strict interior of the train incurs a cost higher than when the operation is performed at the end of the train. The problem consists in minimizing the total cost, and thus, at each source station of a car, the position the car takes in the train must be carefully decided. Among other results, Nonner and Souza showed that this problem is polynomially solvable by reducing the problem to the computation of a minimum independent set in a bipartite graph. They worked in the offline setting, i.e. the sources and the targets of all cars are known before the trip of the train starts. We study the online version of the problem, in which cars become known at their source stations. We derive a 2-competitive algorithm and prove than no better ratios are achievable. Other related questions are also addressed.
  • Bipartite graph
  • competitive analysis
  • online algorithm
  • train shunting problem
  • vertex cover


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  1. Katharina Beygang, Florian Dahms, and Sven O. Krumke. Train marshalling problem: Algorithms and bounds. Technical report, 2010. Google Scholar
  2. Markus Bohlin, Florian Dahms, Holger Flier, and Sara Gestrelius. Optimal freight train classification using column generation. In Proceedings of the 12th workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'12), volume 25, pages 10-22, 2012. Google Scholar
  3. Nils Boysen, Malte Fliedner, Florian Jaehn, and Erwin Pesch. Shunting yard operations: Theoretical aspects and applications. European Journal of Operational Research, 220:1-14, 2012. Google Scholar
  4. Alberto Ceselli, Michael Gatto, Marco E. Lübbecke, Marc Nunkesser, and Heiko Schilling. Optimizing the cargo express service of Swiss federal railways. Transportation Science, 42:450-465, 2008. Google Scholar
  5. Elias Dahlhaus, Peter Horák, Mirka Miller, and Joseph F. Ryan. The train marshalling problem. Discrete Applied Mathematics, 103:41-54, 2000. Google Scholar
  6. Marc Demange and Vangelis T. Paschos. On-line vertex-covering. Theoretical Computer Science, 332:83-108, 2005. Google Scholar
  7. Gabriele Di Stefano and Magnus Love Koci. A graph theoretical approach to the shunting problem. Electronic Notes in Theoretical Computer Science, 92:16-33, 2004. Google Scholar
  8. Andrew L. Dulmage and Nathan S. Mendelsohn. Coverings of bipartite graphs. Canadian Journal of Mathematics, 10:517-534, 1958. Google Scholar
  9. Michael Gatto, Jens Maue, Matús Mihalák, and Peter Widmayer. Robust and Online Large-Scale Optimization, chapter Shunting for dummies: An introductory algorithmic survey, pages 310-337. Springer, 2009. Google Scholar
  10. Riko Jacob, Peter Marton, Jens Maue, and Marc Nunkesser. Multistage methods for freight train classification. Networks, 57:87-105, 2011. Google Scholar
  11. Tim Nonner and Alexander Souza. Optimal algorithms for train shunting and relaxed list update problems. In Proceedings of the 12th workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'12), volume 25, pages 97-107, 2012. Google Scholar
  12. Marc Nunkesser, Michael Gatto, and Riko Jacob. Optimization of a railway hub-and-spoke system: routing and shunting. In Proceedings of WEA 2005, 2005. Google Scholar
  13. Alexandrer Schrijver. Combinatorial Optimization. Springer, 2003. Google Scholar
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