Resolving Infeasibilities in Railway Timetabling Instances

29 Pages Posted: 23 Jan 2018

See all articles by Gert-Jaap Polinder

Gert-Jaap Polinder

Erasmus University Rotterdam (EUR) - Rotterdam School of Management (RSM)

Leo Kroon

Erasmus Research Institute of Management (ERIM)

Karen Aardal

Eindhoven University of Technology (TUE)

Marie Schmidt

Erasmus Research Institute of Management (ERIM)

Marco Molinaro

Pontifical Catholic University of Rio de Janeiro (PUC-Rio)

Date Written: January 22, 2018

Abstract

One of the key assumptions of timetabling algorithms is that a solution exists that meets the pre-specified constraints, like driving times, transfer constraints and headway constraints. If this assumption is satisfied, in most cases a timetable can be found rapidly. Nowadays, railways are being used more intensively, which leads to a higher utilization of the network. Due to this increased utilisation, capacity conflicts occur, so that no feasible solution to the timetabling models can be found, without making subtle but non-trivial changes to the initial input. Resolving these conflicts is essential for railway companies with high utilization of infrastructure. In this paper, we consider infeasible timetabling instances together with a list of allowed modifications of the constraints. We iteratively identify local conflicts in these instances and resolve them by adapting some of the constraints, until there are no more conflicts. The adaptations of the constraints are changes in the right-hand sides that we try to make as small as possible but that resolve the infeasibility. We empirically show that our method can be improved by enriching the initial minimal conflicts found with more constraints. In order to keep the problems tractable, an iterative procedure is used to find solutions to subproblems corresponding to conflicts in the complete timetabling instance. In a case study on instances from the Dutch railway network, we show that these instances can be made feasible within a few minutes.

Keywords: railway timetabling

Suggested Citation

Polinder, Gert-Jaap and Kroon, Leo and Aardal, Karen and Schmidt, Marie and Molinaro, Marco, Resolving Infeasibilities in Railway Timetabling Instances (January 22, 2018). Available at SSRN: https://ssrn.com/abstract=3106739 or http://dx.doi.org/10.2139/ssrn.3106739

Gert-Jaap Polinder (Contact Author)

Erasmus University Rotterdam (EUR) - Rotterdam School of Management (RSM) ( email )

P.O. Box 1738
Room T08-21
3000 DR Rotterdam, 3000 DR
Netherlands

Leo Kroon

Erasmus Research Institute of Management (ERIM) ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands

Karen Aardal

Eindhoven University of Technology (TUE) ( email )

PO Box 513
Eindhoven, 5600 MB
Netherlands

Marie Schmidt

Erasmus Research Institute of Management (ERIM) ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands

Marco Molinaro

Pontifical Catholic University of Rio de Janeiro (PUC-Rio) ( email )

Rua Marquas de Sao Vicente, 225
Rio De Janeiro, RJ 22453-900
Brazil

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