A constraint generation algorithm for the construction of periodic railway timetables

Odijk, Michiel A.

doi:10.1016/0191-2615(96)00005-7

Cited by 183 publications

(92 citation statements)

References 2 publications

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“…Often these draft timetables only include arrival and departure times at major stations on the scale of minutes. PESP enables to schedule trains in a relatively large railway network (such as the Netherlands, see Odijk 1996), but the exact train routing on an aggregated level has to be known a priori and the safety system is only roughly modeled using headway times. However, PESP solutions do not guarantee timetable feasibility on a detailed level.…”

Section: Introductionmentioning

confidence: 99%

Design of a Railway Scheduling Model for Dense Services

et al. 2008

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We address the problem of generating detailed conflict-free railway schedules for given sets of train lines and frequencies. To solve this problem for large railway networks, we propose a network decomposition into condensation and compensation zones. Condensation zones contain main station areas, where capacity is limited and trains are required to travel with maximum speed. They are connected by compensation zones, where traffic is less dense and time reserves can be introduced for increasing stability. In this paper, we focus on the scheduling problem in condensation zones. To gain structure in the schedule we enforce a time discretisation which reduces the problem size considerably and also the cognitive load of the dispatchers. The problem is formulated as an independent set problem in a conflict graph, which is then solved using a fixed-point iteration heuristic. Results show that even large-scale problems with dense timetables and large topologies can be solved quickly.

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Section: Introductionmentioning

confidence: 99%

Design of a Railway Scheduling Model for Dense Services

et al. 2008

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“…Since then, this model has been widely used ( [29,18,24,16,26]). In the Periodic Event Scheduling Problem (PESP), we are given a period time T and a set V of events, where an event models either the arrival or the departure of a directed traffic line at a certain station.…”

Section: The Periodic Event Scheduling Problem (Pesp)mentioning

confidence: 99%

The Modeling Power of the Periodic Event Scheduling Problem: Railway Timetables — and Beyond

Liebchen

Möhring

Lecture Notes in Economics and Mathematical Systems

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Abstract. In the planning process of railway companies, we propose to integrate important decisions of network planning, line planning, and vehicle scheduling into the task of periodic timetabling. From such an integration, we expect to achieve an additional potential for optimization.Models for periodic timetabling are commonly based on the Periodic Event Scheduling Problem (PESP). We show that, for our purpose of this integration, the PESP has to be extended by only two features, namely a linear objective function and a symmetry requirement. These extensions of the PESP do not really impose new types of constraints. Indeed, practitioners have already required them even when only planning timetables autonomously without interaction with other planning steps. Even more important, we only suggest extensions that can be formulated by mixed integer linear programs.Moreover, in a selfcontained presentation we summarize the traditional PESP modeling capabilities for railway timetabling. For the first time, also special practical requirements are considered that we proove not being expressible in terms of the PESP.

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“…First, we remark that there exists a wide literature on capacity allocation issues in railway. For example, several models proposed in the literature aim to solving the scheduling problem focusing on a certain objective function under predefined constraints to optimality, such as periodic time windows constraints [5], or introduce stochastic disturbances [6]; Fischetti et al [7] focused on robustness improvement of a given solution; Ho et al [8], after remarking that multi-objective optimization approaches often end with feasible solutions because of the constraints on computation time, propose a method for designing the scheduling based on Particle Swarm Optimization that considers the negotiations rounds among the IM and the TOs. Another interesting field is that of simulation tools, possibly combined with other instruments and approaches.…”

Section: Previous Approachesmentioning

confidence: 99%

A game theoretic model for re-optimizing a railway timetable

Fragnelli

Sanguineti²

2013

Eur. Transp. Res. Rev.

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The Setting In the Nineties of the last century the European Commission decided to open the railway market to competition, allowing different railway companies to operate on the same network. Under this framework Infrastructure Managers have to allocate capacity in order to define the timetable, dealing with possible slot conflicts between competing Transport Operators. The Problem An efficient train scheduling requires collecting a lot of information from the Transport Operators, but it may not be in their interests to reveal their private information. Therefore, it may be useful for real-world applications to design methods that provide incentives to Transport Operators for cooperating with the aim of increasing their utility; moreover, this may result in an improvement of the efficiency even for the Infrastructure Managers, so they also have incentives for favouring the cooperation. The Proposal In this paper we propose a game theoretical model in which the agents (Transport Operators) exchange information on their needs and are compensated by a possible increasing of their utility. This approach represents the situation as a coalition formation problem. In particular, we refer to the C-Solution proposed by Gerber (Rev Econ Design 5:149-175, 1), which is applied to some examples, each with different features. This model requires that information is revealed to a small number of competitors. This is rather important in a market currently still characterized by operator reluctance to an indiscriminate diffusion of information. Furthermore, the low dimension of the problem allows having a low computational complexity.

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A constraint generation algorithm for the construction of periodic railway timetables

Cited by 183 publications

References 2 publications

Design of a Railway Scheduling Model for Dense Services

Design of a Railway Scheduling Model for Dense Services

The Modeling Power of the Periodic Event Scheduling Problem: Railway Timetables — and Beyond

A game theoretic model for re-optimizing a railway timetable

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