An Overview and Categorization of Approaches for Train Timetable Generation

A train timetable is a crucial component of railway transportation systems as it directly impacts the system’s performance and the customer satisfaction. Various approaches can be found in the literature that deal with timetable generation. However, the approaches proposed in the literature differ significantly in terms of the use case for which they are in tended. Differences in objective function, timetable periodicity, and solution methods have led to a confusing number of works on this topic. Therefore, this paper presents a com pact literature review of approaches to train timetable generation. The reviewed papers are briefly summarized and categorized by objective function and periodicity. Special emphasis is given to approaches that have been applied to real-world railway data

Almost 20 Years of Combinatorial Optimization for Railway Planning: from Lagrangian Relaxation to Column Generation

We summarize our experience in solving combinatorial optimization problems arising in railway planning, illustrating all of these problems as integer multicommodity flow ones and discussing the main features of the mathematical programming models that were successfully used in the 1990s and in recent years to solve them

Optimization in railway timetabling for regional and intercity trains in Zealand: A case of study of DSB

The Train Timetabling Problem is one of the main tactical problems in the railway planning process. Depending on the size of the network, the problem can be hard to solve directly and alternative methods should be studied. In this thesis, the Train Timetabling Problem is formulated using a graph formu-lation that takes advantage of the symmetric timetabling strategy and assumed fixed running times between station. The problem is formulated for the morning rush hour period of the Regional and InterCity train network of Zealand. The solution method implemented is based on a Large Neighborhood Search model that iteratively applies a dive-and-cut-and-price procedure. An LP relax version of the problem is solved using Column Generation considering only a subset of columns and constraints. Each column corresponds to the train paths of a line that are found by shortest paths in the graphs. Then, violated constraints are added by separation and an heuristic process is applied to help finding integer solutions. Last, the passengers are routed on the network based on the found timetable and the passenger travel time calculated. The process is repeated taking into account the best transfers from the solution found. A parameter tuning is conducted to find the best algorithm setting. Then, the model is solved for different scenarios where the robustness and quality of the solution is analyzed. The model shows good performance in most of the scenarios being able to find good quality solutions relatively fast. The way the best transfers are considered between timetable solutions does not add significant value in terms of solution quality but could be useful from a planning perspective. In addition, most of the real-life conflicts are taken into account in the model but not all of them. As a result, the model can still be improved in order to provide completely conflict-free timetables. In general, the model appears to be useful for the timetabling planning process of DSB. It allows to test different network requirements and preferences easily. The model not only generates a timetable but also estimates the passenger travel time and the occupancy of the trains quite accurately. Also, any modification in the line plan can easily be included without affecting the core model.Outgoin

Railway Rolling Stock Planning: Robustness Against Large Disruptions

In this paper we describe a two-stage optimization model for determining robust rolling stock circulations for passenger trains. Here robustness means that the rolling stock circulations can better deal with large disruptions of the railway system. The two-stage optimization model is formulated as a large mixed-integer linear programming (MILP) model. We first use Benders decomposition to determine optimal solutions for the LP-relaxation of this model. Then we use the cuts that were generated by the Benders decomposition for computing heuristic robust solutions for the two-stage optimization model. We call our method Benders heuristic. We evaluate our approach on the real-life rolling stock-planning problem of Netherlands Railways, the main operator of passenger trains in the Netherlands. The computational results show that, thanks to Benders decomposition, the LP-relaxation of the two-stage optimization problem can be solved in a short time for a representative number of disruption scenarios. In addition, they demonstrate that the robust rolling stoc

Freight and passenger railway optimization

Das Ziel dieser Arbeit war es, einen Überblick über die aktuellen Beiträge der Literatur in den Bereichen der Eisenbahnlogistik sowohl im Güter- als auch im Personenverkehr zu geben. Während sich der Güterverkehr mit Problemen der Zusammenstellung der Züge und Waggons beziehungsweise der Verteilung der Leerfahrzeuge auseinander setzte, beschäftigte sich die Eisenbahnlogistik im Bereich des Personenverkehrs mit Optimierungsmodellen bezüglich Eisenbahnlinienplanung, Erstellung eines Fahrplanes, Inbetriebnahme von Fahrzeugen und Besatzungs- und Einsatzplanung. Die Bereiche der Eisenbahnlogistik haben in der Literatur eindeutig an Aufmerksamkeit gewonnen. In der Folge war es schwierig eine Auswahl aus dieser Vielfalt an Beiträgen zu treffen. Deshalb versucht diese Arbeit nur einen kurzen Einblick über einige wichtige Beiträge der letzten Jahre im Bereich der Eisenbahnlogistik zu geben. Aufgrund hochentwickelter mathematischer Techniken und deren Lösungsmöglichkeiten, die in den letzten Jahren aufgekommen sind, war es nun möglich die komplizierten Modelle der Eisenbahnlogistik in einer vernünftigen Zeit zu lösen. Darüber hinaus wurde ein Trend zur Entwicklung effizienterer entscheidungsunterstützender Hilfsprogramme für reale Gegebenheiten der Eisenbahnlogistik beobachtet. Im Großen und Ganzen sollten in Zukunft stärker integrierte Modelle der Eisenbahnplanung und Routenplanung entwickelt werden um robuste Lösungen und Methoden zu fördern.The aim of this work was to provide a survey of recent contributions about freight and passenger transportation. Whereas passenger optimization models considered problems such as line planning, train timetabling, platforming, rolling stock circulation, shunting and crew scheduling, freight transportation dealt with issues concerning car blocking, train makeup, routing, and empty car distribution. The field of rail transportation has clearly received attention resulting in a diversity of literature contribution. As it was difficult to handle the large amount of papers, this work is trying to give a short review of some important contributions made in recent years. Due to the increase in more sophisticated mathematical techniques, constant refinements in development of the models were made that were able to deal with larger problems. In addition, a trend towards more efficient transportation support systems was observed taking robustness into account. In addition, solution approaches that can deal with larger disturbances of the rail environment in a considerable speed and time, have received attention. Thus, future research can be done to develop more integrated models of scheduling and routing problems of train and passenger transportation to provide robust solutions and problem solving methods that handle disturbances of rail environment

A new approach to crew scheduling in rapid transit networks

We propose a new approach for the crew scheduling problem in rapid transit networks. With this approach we try to open a new branch for future research, providing a different way of facing the crew scheduling problem which makes integration with other planning problems easier than the traditional approach based on column generation for solving a set covering/partitioning problem. For solving this new model we develop a Lagrangian relaxation and we take advantage of an ad hoc decomposition based on time personnel clustering. We present some preliminary computational experiments for real case studies drawn from the main Spanish train operator, RENFE

Computer-based decision support for railway traffic scheduling and dispatching: A review of models and algorithms

This paper provides an overview of the research in railway scheduling and dispatching. A distinction is made between tactical scheduling, operational scheduling and re-scheduling. Tactical scheduling refers to master scheduling, whereas operational scheduling concerns scheduling at a later stage. Re-scheduling focuses on the re-planning of an existing timetable when deviations from it have occurred. 48 approaches published between 1973 and 2005 have been reviewed according to a framework that classifies them with respect to problem type, solution mechanism, and type of evaluation. 26 of the approaches support the representation of a railway network rather than a railway line, but the majority has been experimentally evaluated for traffic on a line. 94 % of the approaches have been subject to some kind of experimental evaluation, while approximately 4 % have been implemented. The solutions proposed vary from myopic, priority-based algorithms, to traditional operations research techniques and the application of agent technology.This paper provides an overview of the research in railway scheduling and dispatching. A distinction is made between tactical scheduling, operational scheduling and re-scheduling. Tactical scheduling refers to master scheduling, whereas operational scheduling concerns scheduling at a later stage. Re-scheduling focuses on the re-planning of an existing timetable when deviations from it have occurred. 48 approaches published between 1973 and 2005 have been reviewed according to a framework that classifies them with respect to problem type, solution mechanism, and type of evaluation. 26 of the approaches support the representation of a railway network rather than a railway line, but the majority has been experimentally evaluated for traffic on a line. 94 % of the approaches have been subject to some kind of experimental evaluation, while approximately 4 % have been implemented. The solutions proposed vary from myopic, priority-based algorithms, to traditional operations research techniques and the application of agent technology