Introduction to stochastic programming

In this chapter, you will see how the simplex method simplifies when it is applied to a class of optimization problems that are known as “network flow models.” You will also see that if a network flow model has “integer-valued data,” the simplex method finds an optimal solution that is integer-valued.

Flows in Networks

Transportation research. part c, emerging technologies

The transport system is critical to the welfare of modern societies. This article provides an overview of recent research on vulnerability and resilience of transport systems. Definitions of vulnerability and resilience are formulated and discussed together with related concepts. In the increasing and extensive literature of transport vulnerability studies, two distinct traditions are identified. One tradition with roots in graph theory studies the vulnerability of transport networks based on their topological properties. The other tradition also represents the demand and supply side of the transport systems to allow for a more complete assessment of the consequences of disruptions or disasters for the users and society. The merits and drawbacks of the approaches are discussed. The concept of resilience offers a broader socio-technical perspective on the transport system’s capacity to maintain or quickly recover its function after a disruption or a disaster. The transport resilience literature is less abundant, especially concerning the post-disaster phases of response and recovery. The research on transport system vulnerability and resilience is now a mature field with a developed methodology and a large amount of research findings with large potential practical usefulness. The authors argue that more cross-disciplinary collaborations between authorities, operators and researchers would be desirable to transform this knowledge into practical strategies to strengthen the resilience of the transport system.

Vulnerability and resilience of transport systems : A discussion of recent research

This paper presents an overview of recovery models and algorithms for real-time railway disturbance and disruption management. This area is currently an active research area in Operations Research, including real-time timetable rescheduling and real-time rescheduling of the rolling stock and crew duties. These topics are addressed in this paper. Also research dealing with the integration of more than one rescheduling phase is discussed. Currently, the developed methods have been tested mainly in an experimental setting, thereby showing promising results, both in terms of their solution quality and in terms of their computation times. The application of these models and algorithms in real-life railway systems will be instrumental for increasing the quality of the provided railway services, leading to an increased utilization of the involved railway systems.

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An overview of recovery models and algorithms for real-time railway rescheduling

In December 2006, Netherlands Railways introduced a completely new timetable. Its objective was to facilitate the growth of passenger and freight transport on a highly utilized railway network and improve the robustness of the timetable, thus resulting in fewer operational train delays. Modifications to the existing timetable, which was constructed in 1970, were not an option; additional growth would require significant investments in the rail infrastructure.

Constructing a railway timetable from scratch for about 5,500 daily trains was a complex problem. To support this process, we generated several timetables using sophisticated operations research techniques. Furthermore, because rolling-stock and crew costs are principal components of the costs of a passenger railway operator, we used innovative operations research tools to devise efficient schedules for these two resources.

The new resource schedules and the increased number of passengers resulted in an additional annual profit of €40 million ($60 million); the additional revenues generated approximately €10 million of this profit. We expect this profit to increase to €70 million ($105 million) annually in the coming years. However, the benefits of the new timetable for the Dutch society as a whole are much greater: more trains are transporting more passengers on the same railway infrastructure, and these trains are arriving and departing on schedule more than they ever have in the past. In addition, the rail transport system will be able to handle future transportation demand growth and thus allow cities to remain accessible to more people. Therefore, we expect that many will switch from car transport to rail transport, thus reducing the emission of greenhouse gases.

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The New Dutch Timetable: The OR Revolution

Real-time railway operations are subject to stochastic disturbances. Thus a timetable should be designed in such a way that it can cope with these disturbances as well as possible. For that purpose, a timetable usually contains time supplements in several process times and buffer times between pairs of consecutive trains. This paper describes a Stochastic Optimization Model that can be used to allocate the time supplements and the buffer times in a given timetable in such a way that the timetable becomes maximally robust against stochastic disturbances. The Stochastic Optimization Model was tested on several instances of NS Reizigers, the main operator of passenger trains in the Netherlands. Moreover, a timetable that was computed by the model was operated in practice in a timetable experiment on the so-called “Zaanlijn”. The results show that the average delays of trains can often be reduced significantly by applying relatively small modifications to a given timetable.

/pdf/stochastic-improvement-of-cyclic-railway-timetables-1kyjvctyyq.pdf

Stochastic improvement of cyclic railway timetables

This paper studies the disruption management problem of rapid transit rail networks. Besides optimizing the timetable and the rolling stock schedules, we explicitly deal with the effects of the disruption on the passenger demand. We propose a two-step approach that combines an integrated optimization model (for the timetable and rolling stock) with a model for the passengers’ behavior. We report our computational tests on realistic problem instances of the Spanish rail operator RENFE. The proposed approach is able to find solutions with a very good balance between various managerial goals within a few minutes.

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Recovery of disruptions in rapid transit networks

This paper deals with disruption management in passenger
railway transportation. In the disruption management process, many
actors belonging to different organizations play a role. In this paper
we therefore describe the process itself and the roles of the
different actors.
Furthermore, we discuss the three main subproblems in railway
disruption management: timetable adjustment, and rolling stock and
crew re-scheduling. Next to a general description of these problems,
we give an overview of the existing literature and we present some
details of the specific situations at DSB S-tog and NS. These are
the railway operators in the suburban area of Copenhagen, Denmark,
and on the main railway lines in the Netherlands, respectively.
Since not much research has been carried out yet on Operations
Research models for disruption management in the railway context,
models and techniques that have been developed for related problems
in the airline world are discussed as well.
Finally, we address the integration of the re-scheduling processes
of the timetable, and the resources rolling stock and crew.

/pdf/disruption-management-in-passenger-railway-transportation-3f4d7592yp.pdf

Disruption management in passenger railway transportation.

This paper addresses the railway rolling stock circulation problem. Given the departure and arrival times as well as the expected numbers of passengers, we have to assign the rolling stock to the timetable services. We consider several objective criteria that are related to operational costs, service quality and reliability of the railway system. Our model is an extension of an existing rolling stock model for routing train units along a number of connected train lines. The extended model can also handle underway combining and splitting of trains. We illustrate our model by computational experiments based on instances of NS Reizigers, the main Dutch operator of passenger trains

Gábor Maróti

Papers

The New Dutch Timetable: The OR Revolution

Stochastic improvement of cyclic railway timetables

Recovery of disruptions in rapid transit networks

Disruption management in passenger railway transportation.

A rolling stock circulation model for combining and splitting of passenger trains.