Modeling and Solving of Railway Optimization Problems

The main aim of this work is to provide decision makers suitable approaches for solving two crucial planning problems in the railway industry: the locomotive assignment problem and the crew scheduling problem with attendance rates. On the one hand, the focus is on practical usability and the necessary integration and consideration of real-life requirements in the planning process. On the other hand, solution approaches are to be developed, which can provide solutions of sufficiently good quality within a reasonable time by taking all these requirements into account

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

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

Locomotive assignment problem with heterogeneous vehicle fleet and hiring external locomotives

This paper focuses on solving the problem of how to assign locomotives to assembled trains optimally. To solve the problem, linear programming is applied. The situation we model in the paper occurs in the conditions of a transport operator that provides rail transport in the Czech Republic. In the paper, an extended locomotive assignment problem is modeled; the transport operator can use different classes of the locomotives to serve individual connections, some connections must be served by a predefined locomotive class, and the locomotives can be allocated to several depots at the beginning. The proposed model also takes into consideration the fact that some connections can be served by the locomotives of external transport companies or operators. The presented model is applied to a real example in order to test its functionality.Web of Science2015art. no. 58390

Combinatorial optimization model for railway engine assignment problem

This paper presents an experimental study for the Hungarian State Railway Company (M\'AV). The engine assignment problem was solved at M\'AV by their experts without using any explicit operations research tool. Furthermore, the operations research model was not known at the company. The goal of our project was to introduce and solve an operations research model for the engine assignment problem on real data sets. For the engine assignment problem we are using a combinatorial optimization model. At this stage of research the single type train that is pulled by a single type engine is modeled and solved for real data. There are two regions in Hungary where the methodology described in this paper can be used and M\'AV started to use it regularly. There is a need to generalize the model for multiple type trains and multiple type engines

A rolling horizon approach for the locomotive routing problem at the Canadian National Railway Company

Cette thèse étudie le problème du routage des locomotives qui se pose à la Compagnie des chemins de fer nationaux du Canada (CN) - le plus grand chemin de fer au Canada en termes de revenus et de taille physique de son réseau ferroviaire. Le problème vise à déterminer la séquence des activités de chaque locomotive sur un horizon de planification donné. Dans ce contexte, il faut prendre des décisions liées à l'affectation de locomotives aux trains planifiés en tenant compte des besoins d'entretien des locomotives. D’autres décisions traitant l'envoi de locomotives aux gares par mouvements à vide, les déplacements légers (sans tirer des wagons) et la location de locomotives tierces doivent également être prises en compte. Sur la base d'une formulation de programmation en nombres entiers et d'un réseau espace-temps présentés dans la littérature, nous introduisons une approche par horizon roulant pour trouver des solutions sous-optimales de ce problème dans un temps de calcul acceptable. Une formulation mathématique et un réseau espace-temps issus de la littérature sont adaptés à notre problème. Nous introduisons un nouveau type d'arcs pour le réseau et de nouvelles contraintes pour le modèle pour faire face aux problèmes qui se posent lors de la division de l'horizon de planification en plus petits morceaux. Les expériences numériques sur des instances réelles montrent les avantages et les inconvénients de notre algorithme par rapport à une approche exacte.This thesis addresses the locomotive routing problem arising at the Canadian National Railway Company (CN) - the largest railway in Canada in terms of both revenue and the physical size of its rail network. The problem aims to determine the sequence of activities for each locomotive over the planning horizon. Besides assigning locomotives to scheduled trains and considering scheduled locomotive maintenance requirements, the problem also includes other decisions, such as sending locomotives to stations by deadheading, light traveling, and leasing of third-party locomotives. Based on an Integer Programming formulation and a Time-Expanded Network presented in the literature, we introduce a Rolling Horizon Approach (RHA) as a method to find near-optimal solutions of this problem in acceptable computing time. We adapt a mathematical formulation and a space-time network from the literature. We introduce a new type of arcs for the network and new constraints for the model to cope with issues arising when dividing the planning horizon into smaller ones. Computational experiments on real-life instances show the pros and cons of our algorithm when compared to an exact solution approach

Multi-Column Generation Model for the Locomotive Assignment Problem

We propose a new decomposition model and a multi-column generation algorithm for solving the Locomotive Assignment Problem (LAP). The decomposition scheme relies on consist configurations, where each configuration is made of a set of trains pulled by the same set of locomotives. We use the concept of conflict graphs in order to reduce the number of trains to be considered in each consist configuration generator problem: this contributes to significantly reduce the fraction of the computational times spent in generating new potential consists. In addition, we define a column generation problem for each set of variables, leading to a multi-column generation process, with different types of columns. Numerical results, with different numbers of locomotives, are presented on adapted data sets coming from Canada Pacific Railway (CPR). They show that the newly proposed algorithm is able to solve exactly realistic data instances for a timeline spanning up to 6 weeks, in very reasonable computational times

A branch-and-price approach for solving the train unit scheduling problem

We propose a branch-and-price approach for solving the integer multicommodity flow model for the network-level train unit scheduling problem (TUSP). Given a train operator’s fixed timetable and a fleet of train units of different types, the TUSP aims at determining an assignment plan such that each train trip in the timetable is appropriately covered by a single or coupled train units. The TUSP is challenging due to its complex nature. Our branch-and-price approach includes a branching system with multiple branching rules for satisfying real-world requirements that are difficult to realize by linear constraints, such as unit type coupling compatibility relations and locations banned for coupling/decoupling. The approach also benefits from an adaptive node selection method, a column inheritance strategy and a feature of estimated upper bounds with node reservation functions. The branch-and-price solver designed for TUSP is capable of handling instances of up to about 500 train trips. Computational experiments were conducted based on real-world problem instances from First ScotRail. The results are satisfied by rail practitioners and are generally competitive or better than the manual ones

Mathematical models for planning support

In this paper we describe how computer systems can provide planners with active planning support, when these planners are carrying out their daily planning activities. This means that computer systems actively participate in the planning process by automatically generating plans or partial plans. Active planning support by computer systems requires the application of mathematical models and solution techniques. In this paper we describe the modeling process in general terms, as well as several modeling and solution techniques. We also present some background information on computational complexity theory, since most practical planning problems are hard to solve. We also describe how several objective functions can be handled, since it is rare that solutions can be evaluated by just one single objective. Furthermore, we give an introduction into the use of mathematical modeling systems, which are useful tools in a modeling context, especially during the development phases of a mathematical model. We finish the paper with a real life example related to the planning process of the rolling stock circulation of a railway operator.optimization;mathematical models;modeling process;planning support;Planning