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A rolling horizon approach for disruption management of railway rolling stock

https://doi.org/10.1016/j.ejor.2012.01.037Get rights and content

Abstract

This paper deals with real-time disruption management of rolling stock in passenger railway transportation. We describe a generic framework for dealing with disruptions of railway rolling stock schedules. The framework is presented as an online combinatorial decision problem, where the uncertainty of a disruption is modeled by a sequence of information updates. To decompose the problem and to reduce the computation time, we propose a rolling horizon approach: rolling stock decisions are only considered if they are within a certain time horizon from the time of rescheduling. The schedules are then revised as time progresses and new information becomes available. We extend an existing model for rolling stock scheduling to the specific requirements of the real-time situation, and we apply it in the rolling horizon framework. We perform computational tests on instances constructed from real-life cases of Netherlands Railways (NS), the main operator of passenger trains in the Netherlands. We explore the consequences of different settings of the approach for the trade-off between solution quality and computation time.

Highlights

► We consider real-time railway rolling stock rescheduling in case of largescale disruption. ► We describe a rolling horizon approach. ► We propose a heuristic way of taking global criteria into account in the rolling horizon algorithm. ► We demonstrate the power of the method on complex real-life problem instances of Netherlands Railways.

Introduction

The planning and operation of a busy passenger railway network is a complex task. Rolling stock and crew have to be scheduled to serve the timetable with ever growing demand for capacity. This has led to extensive research on optimizing the utilization of railway resources such as the infrastructure, the rolling stock and the crew, see Caprara et al., 2007, Huisman et al., 2005. The developed methods have resulted in resource schedules that are highly efficient when operations run as planned, see Kroon et al. (2009). However, when operating a dense timetable, operations occasionally have to deviate from the plans. Currently, such deviations are handled manually under large time pressure. As a consequence, there is a demand for decision support systems for effectively dealing with the challenges posed by the real-time operations of a passenger railway system. However, to this date only limited research has been conducted on the real-time rescheduling of railway resources.

Irregularities of the railway operations are more or less inevitable and require real-time rescheduling of the system. Practitioners distinguish minor and major incidents; minor incidents are called disturbances, while major incidents are called disruptions. The distinction is not exactly defined, but depends on the impact on the operations. As a rule of thumb, disruptions are incidents that require significant changes of the pre-set resource schedules.

Disruptions may be caused by various internal or external factors such as a faulty switch on a busy track, broken down rolling stock, or damaged overhead wires. In a disrupted situation, the planned resource schedules are no longer feasible and will have to be updated to take the actual situation into account. Disturbances, on the other hand, only need simple recovery measures. An example of a disturbance is a delay caused when the boarding of passengers at a station takes unexpectedly long. Disturbances of such kind are either absorbed by the slack in the system or can be handled by small changes in the timetable.

Disruption management of railway resources often relies on an updated timetable. In fact, the utilization of the railway infrastructure of many European countries is managed by an independent authority, while the operators are responsible for the resource schedules. In the Netherlands, hundreds of so called handling scenarios have been defined, in order to speed up the timetable updating process. A handling scenario is a set of rules telling which timetable services are to be canceled, rerouted or delayed in case of a particular disruption. An example of a handling scenario is described in Appendix A.

The challenges in real-time decision making differ from the static planning tasks in a number of aspects. The most important difference is that real-time rescheduling needs to deal with uncertain information as the environment evolves, see Séguin et al., 1997, Grötschel et al., 2001, Yu and Qi, 2004. In addition, real-time decisions must be made within a tight time frame. Finally, a highly optimized plan already exists, and any changes to that plan will have to be communicated to the involved parties. Decision support methods for real-time rescheduling need to address these aspects adequately.

This paper deals with the real-time rescheduling of rolling stock in case of a disruption of the railway system. We aim at contributing to the central (i.e. network level) rolling stock rescheduling process while taking into account several aspects of the local (i.e. station level) operational details.

We first formulate a generic framework for the Rolling Stock Rescheduling Problem (RSRP) as a static decision making problem, and then we define its online variant in order to be able to deal with uncertain information. We propose a rolling horizon approach to solve the online RSRP. That is, the solution method amounts to rescheduling the rolling stock within a certain rolling horizon of limited length, and then periodically updating the plans as time progresses and more information becomes available. Rolling horizons are often used in various areas of operations management; we refer to Chand et al. (2002) for an extensive overview of such applications. Also, we note that our proposed framework and solution approach are generic in that they can be applied to any rolling stock rescheduling model.

The rolling horizon approach is a heuristic problem decomposition in order to pursue the overall goals of the online RSRP. The problem specification of online RSRP involves global criteria that cannot be taken into account directly when considering a single rolling horizon iteration. In this paper we propose a novel heuristic way to deal with such a criterion: to guide the rolling horizon solution process towards the desirable end-of-day rolling stock distribution.

An essential contribution of this paper is that we apply the generic framework to the specific realistic rolling stock rescheduling problems of Netherlands Railways (NS), the major passenger railway operator in the Netherlands. The method is based on an extension of the existing rolling stock scheduling model of Fioole et al. (2006) for the special needs of real-time rescheduling. The model of Fioole et al. (2006) is a well-tested integer linear programming model which has successfully been used by NS for medium-term planning since 2004.

The computational results indicate that the rolling horizon approach is capable to deal with fairly large problem instances. The outcome of the rolling horizon approach in an online setting turns out to be reasonably close to the off-line optimum. This also shows the effectiveness of the heuristic guidance for the desired end-of-day rolling stock distribution.

This paper is structured as follows. In Section 2 we set the terminology we use and we give a literature overview. Section 3 describes the rolling stock rescheduling process from a practical point of view. In Section 4 we describe the generic framework for the Rolling Stock Rescheduling Problem and for its online variant, and we propose the rolling horizon approach. In Section 5 we specialize the generic framework to real-life problems of NS. Section 6 is devoted to the computational results on a particular set of disruptions. Finally, we draw some conclusions in Section 7.

The paper is supplied with two appendices. In Appendix A we give a detailed example of a disruption on a train line of NS. In Appendix B we report further computational results on another set of realistic disruption instances of NS.

Section snippets

Terminology and literature

In this section we briefly describe the notions of the rolling stock operations at NS. The concrete models as well as the computational experiments are based on these assumptions. For more details we refer to Fioole et al. (2006). Having set the terminology, we give a brief literature overview on rolling stock scheduling.

Real time control in passenger railways

In this section we describe the practical aspects of the real-time monitoring and rescheduling of rolling stock. We discuss the options that are open to dispatchers for rescheduling the rolling stock during operations. For a comprehensive overview of the disruption management process in passenger railways we refer to Jespersen-Groth et al. (2007).

The Rolling Stock Rescheduling Problem

The Rolling Stock Rescheduling Problem (RSRP) amounts to adjusting the current circulation of the rolling stock to a changed timetable. RSRP can be considered as an off-line optimization problem for disruption management without uncertainty. Later in this section we use RSRP as a building block of the online variant of RSRP in order to deal with uncertainty.

An instance of RSRP is a 4-tuple T0,C0,τ,T. Here T0 is the original timetable which consists of a set of trips including the rolling

A concrete RSRP application

In Section 4 we described a generic framework for RSRP and online RSRP. In this section we extend an existing rolling stock scheduling model to be able to solve real-life RSRP instances of NS. The computational results reported in Section 6 are all based on this extended model.

Computational results

In this section we present our computational results for online RSRP. In particular, we explore the relationship between the horizon parameters, and the solution quality and characteristics using a set of test instances. We first describe the test instances and then discuss the results.

Conclusions

This paper deals with real-time disruption management of railway rolling stock. We defined the Rolling Stock Rescheduling Problem (RSRP). The main assumption is that timetable updates are explicitly given via the handling scenarios. The goal is to adjust the original rolling stock schedules for the updated timetables, taking various objectives into account.

We also defined the online variant of RSRP where the uncertainty about the duration of the disruption is modeled by a sequence of timetable

Acknowledgments

We would like to thank the dispatchers at the Rolling Stock Managing Center of NS for their input on the practical details of rolling stock operations.

This work was partially supported by the Future and Emerging Technologies Unit of EC (IST priority – 6th FP), under contract No. FP6-021235-2 (project ARRIVAL).

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