Integer programming based solution approaches for the train dispatching problem

Railroads face the challenge of competing with the trucking industry in a fastpaced environment. In this respect, they are working toward running freight trains on schedule and reducing travel times. The planned train schedules consist of departure and arrival times at main stations on the rail network. A detailed timetable, on the other hand, consists of the departure and arrival times of each train in each track section of its route. The train dispatching problem aims to determine detailed timetables over a rail network in order to minimize deviations from the planned schedule. We provide a new integer programming formulation for this problem based on a spacetime network; we propose heuristic algorithms to solve it and present computational results of these algorithms. Our approach includes some realistic constraints that have not been previously considered as well as all the assumptions and practical issues considered by the earlier works

Modelling single line train operations

Scheduling of trains on a single line involves using train priorities for the resolution of conflicts. The mathematical programming model described in the first part of this paper schedules trains over a single line track when the priority of each train in a conflict depends on an estimate of the remaining crossing and overtaking delay. This priority is used in a branch and bound procedure to allow the determination of optimal solutions quickly. This is demonstrated with the use of an example. Rail operations over a single line track require the existence of a set of sidings at which trains can cross and/ or overtake each other. Investment decisions on upgrading the number and location of these sidings can have a significant impact on both customer service and rail profitability. Sidings located at insufficient positions may lead to high operating costs and congestion. The second part of this paper puts forward a model to determine the optimal position of a set of sidings on a single track rail corridor. The sidings are positioned to minimise the total delay and train operating costs of a given cyclic train schedule. The key feature of the model is the allowance of non-constant train velocities and non-uniform departure times

Optimal Scheduling of Trains on a Single Line Track

This paper describes the development and use of a model designed to optimise train schedules on single line rail corridors. The model has been developed with two major applications in mind, namely: as a decision support tool for train dispatchers to schedule trains in real time in an optimal way; and as a planning tool to evaluate the impact of timetable changes, as well as railroad infrastructure changes. The mathematical programming model described here schedules trains over a single line track. The priority of each train in a conflict depends on an estimate of the remaining crossing and overtaking delay, as well as the current delay. This priority is used in a branch and bound procedure to allow and optimal solution to reasonable size train scheduling problems to be determined efficiently. The use of the model in an application to a 'real life' problem is discussed. The impacts of changing demand by increasing the number of trains, and reducing the number of sidings for a 150 kilometre section of single line track are discussed. It is concluded that the model is able to produce useful results in terms of optimal schedules in a reasonable time for the test applications shown here

Shunting of Passenger Train Units in a Railway Station

In this paper we introduce the problem of shunting passenger trainunits in a railway station. Shunting occurs whenever train units aretemporarily not necessary to operate a given timetable. We discussseveral aspects of this problem and focus on two subproblems. Wepropose mathematical models for these subproblems together with asolution method based on column generation. Furthermore, a newefficient and speedy solution technique for pricing problems in columngeneration algorithms is introduced. Finally, we present computationalresults based on real life instances from Netherlands Railways.logistics;column generation;railway optimization;real world application

Operations research in passenger railway transportation

In this paper, we give an overview of state-of-the-art OperationsResearch models and techniques used in passenger railwaytransportation. For each planning phase (strategic, tactical andoperational), we describe the planning problems arising there anddiscuss some models and algorithms to solve them. We do not onlyconsider classical, well-known topics such as timetabling, rollingstock scheduling and crew scheduling, but we also discuss somerecently developed topics as shunting and reliability oftimetables.Finally, we focus on several practical aspects for each of theseproblems at the largest Dutch railway operator, NS Reizigers.passenger railway transportation;operation research;planning problems

Shunting of Passenger Train Units: an Integrated Approach

In this paper, we describe a new model for the Train Unit Shunting Problem. This model is capable of solving the matching and parking subproblems in an integrated manner, usually requiring a reasonable amount of computation time for generating acceptable solutions. Furthermore, the model incorporates complicating details from practice, such as trains composed of several train units and tracks that can be approached from two sides. Computation times are reduced by introducing the concept of virtual shunt tracks. Computational results are presented for real-life cases of NS Reizigers, the main Dutch passenger railway operator.Optimization;Passenger Railways;Shunting

The Maraca: a tool for minimizing resource conflicts in a non-periodic railway timetable

While mathematical optimization and operations research receive growing attention in the railway sector, computerized timetabling tools that actually make significant use of optimization remain relatively rare. SICS has developed a prototype tool for non-periodic timetabling that minimizes resource conflicts, enabling the user to focus on the strategic decisions. The prototype is called the Maraca and has been used and evaluated during the railway timetabling construction phase at the Swedish Transport Administration between April and September 2010

An exact decomposition approach for the real-time Train Dispatching problem (v.2)

-Trains movements on a railway network are regulated by official timetables. Deviations and delays occur quite often in practice, demanding fast re-scheduling and re-routing decisions in order to avoid conflicts and minimize overall delay. This is the real-time train dispatching problem. In contrast with the classic ""holistic"" approach, we show how to decompose the problem into smaller subproblems associated with the line and the stations. The decomposition is the basis for a master-slave solution algorithm, in which the master problem is associated with the line and the slave problem is associated with the stations. The two subproblems are modeled as mixed integer linear programs, with their specific sets of variables and constraints. Similarly to the classical Bender's decomposition approach, the slave and the master communicate through suitable feasibility cuts in the variables of the master. By applying our approach to a number of real-life instances from single and double-track lines in Italy, we were able to (quickly) find optimal or near-optimal solutions, with impressive improvements over the performances of the current operating control systems. The new approach will be put in operation in such lines for an extensive on-field test-campaign as of April 2013. Follows SINTEF Technical Report A2327

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

Applying Operations Research techniques to planning of train shunting

In this paper, we discuss a model-based algorithmic approach for supporting planners in the creation of shunt plans for passenger trains. The approach provides an example of a mathematical model and a corresponding solution approach for model based support. We introduce a four-step solution approach and we discuss how the planners are supported by this approach. Finally, we present computational results for these steps and give some suggestions for further research.A* search;railway optimization;real world application;routing