Railway Track Allocation: Models and
vorgelegt vonDipl.-Math. oec. Thomas Schlechte
aus Halle an der Saale
Von der Fakultat II Mathematik und Naturwissenschaftender Technischen Universitat Berlin
zur Erlangung des akademischen Grades
Doktor der Naturwissenschaften Dr. rer. nat.
PromotionsausschussBerichter: Prof. Dr. Dr. h. c. mult. Martin Grotschel
PD Dr. habil. Ralf BorndorferVorsitzender: Prof. Dr. Fredi Troltzsch
Tag der wissenschaftlichen Aussprache: 21.12.2011
Berlin 2012D 83
Railway Track Allocation: Modelsand Algorithms
The heart of a railway system is the timetable. Each railway opera-tor has to decide on the timetable to offer and on the rolling stock tooperate the trips of the trains. For the railway infrastructure managerthe picture is slightly different trains have to be allocated to rail-way tracks and times, called slots such that all passenger and freighttransport operators are satisfied and all train movements can be car-ried out safely. This problem is called the track allocation problem. Mythesis deals with integer programming models and algorithmic solutionmethods for the track allocation problem in real world railway systems.
My work on this topic has been initiated and motivated by the in-terdisciplinary research project railway slot allocation or in GermanTrassenborse.1 This project investigated the question whether a com-petitive marketing of a railway infrastructure can be achieved using anauction-based allocation of railway slots. The idea is that competingtrain operating companies (TOCs) can bid for any imaginable use ofthe infrastructure. Possible conflicts will be resolved in favor of theparty with the higher willingness to pay, which leads directly to thequestion of finding revenue maximal track allocations. Moreover afair and transparent mechanism cries out for exact optimization ap-proaches, because otherwise the resulting allocation is hardly accept-able and applicable in practice. This leads to challenging questionsin economics, railway engineering, and mathematical optimization. Inparticular, developing models that build a bridge between the abstractworld of mathematics and the technical world of railway operationswas an exciting task.
I worked on the Trassenborse project with partners from different ar-eas, namely, on economic problems with the Workgroup for Economicand Infrastructure Policy (WIP) at the Technical University of Berlin(TU Berlin), on railway aspects with the Chair of Track and Rail-way Operations (SFWBB) at TU Berlin, the Institute of Transport,Railway Construction and Operation (IVE) at the Leibniz UniversitatHannover, and the Management Consultants Ilgmann Miethner Part-ner (IMP).
1This project was funded by the Federal Ministry of Education and Research(BMBF), Grant number 19M2019 and the Federal Ministry of Economics and Tech-nology (BMWi), Grant number 19M4031A and Grant number 19M7015B.
This thesis is written from the common perspective of all persons Iworked closely with, especially the project heads Ralf Borndorfer andMartin Grotschel, project partners Gottfried Ilgmann and KlemensPolatschek, and the ZIB colleagues Berkan Erol, Elmar Swarat, andSteffen Weider.
The highlight of the project was a cooperation with the SchweizerischeBundesbahnen (SBB) on optimizing the cargo traffic through the Sim-plon tunnel, one of the major transit routes in the Alps. This real worldapplication was challenging in many ways. It provides the opportunityto verify the usefulness of our methods and algorithms by computinghigh quality solutions in a fully automatic way.
The material covered in this thesis has been presented at several in-ternational conferences, e.g., European Conference on Operational Re-search (EURO 2009, 2010), Conference on Transportation Schedulingand Disruption Handling, Workshop on Algorithmic Approaches forTransportation Modeling, Optimization, and System (ATMOS 2007,2010), International Seminar on Railway Operations Modeling andAnalysis (ISROR 2007, 2009, 2011), Symposium on Operations Re-search (OR 2005, 2006, 2007, 2008), International Conference on Com-puter System Design and Operation in the Railway and other TransitSystems (COMPRAIL), International Conference on Multiple CriteriaDecision Making (MCDM), World Conference on Transport Research(WCTR). Significant parts have already been published in various ref-ereed conference proceedings and journals:
. Borndorfer et al. (2006) ,
. Borndorfer et al. (2005) ,
. Borndorfer & Schlechte (2007) ,
. Borndorfer & Schlechte (2007) ,
. Erol et al. (2008) ,
. Schlechte & Borndorfer (2008) ,
. Borndorfer, Mura & Schlechte (2009) ,
. Borndorfer, Erol & Schlechte (2009) ,
. Schlechte & Tanner (2010) 3,
. Borndorfer, Schlechte & Weider (2010) ,
. Schlechte et al. (2011) ,1
. and Borndorfer et al. (2010) 2.
1accepted by Journal of Rail Transport Planning & Management.2accepted by Annals of Operations Research.3submitted to Research in Transportation Economics.
Research Goals and Contributions
The goal of the thesis is to solve real world track allocation problemsby exact integer programming methods. In order to establish a fair andtransparent railway slot allocation, exact optimization approaches arerequired, as well as accurate and reliable railway models. Integer pro-gramming based methods can provide excellent guarantees in practice.We successfully identified and tackled several tasks to achieve theseambitious goals:
1. applying a novel modeling approach to the track allocation prob-lem called configuration models and providing a mathematicalanalysis of the associated polyhedron,
2. developing a sophisticated integer programming approach calledrapid branching that highly utilizes the column generation tech-nique and the bundle method to tackle large scale track allocationinstances,
3. developing a Micro-Macro Transformation, i.e., a bottom-up ag-gregation, approach to railway models of different scale to pro-duce a reliable macroscopic problem formulation of the track al-location problem,
4. providing a study comparing the proposed methodology to formerapproaches, and,
5. carrying out a comprehensive real world data study for the Sim-plon corridor in Switzerland of the entire optimal railway trackallocation framework.
In addition, we present extensions to incorporate aspects of robustnessand we provide an integration and empirical analysis of railway slotallocation in an auction based framework.
A rough outline of the thesis is shown in Figure 1. It follows thesolution cycle of applied mathematics. In a first step the real worldproblem is analyzed, then the track allocation problem is translatedinto a suitable mathematical model, then a method to solve the models
in an efficient way is developed, followed by applying the developedmethodology in practice to evaluate its performance. Finally, the loopis closed by re-translating the results back to the real world applicationand analyze them together with experts and practitioners.
Main concepts on planning problems in railway transportation are pre-sented in Chapter I. Railway modeling and infrastructure capacity isthe main topic of Chapter II. Chapter III focuses on the mathematicalmodeling and the solution of the track allocation problem. Finally,Chapter IV presents results for real world data as well as for ambitioushypothetical auctioning instances.
Planning in RailwayTransportation
1 Introduction2 Planning Process3 Network Design4 Freight Service Network Design5 Line Planning6 Timetabling7 Rolling Stock Planning8 Crew Scheduling
1 Microscopic Railway Modeling2 Macroscopic Railway Modeling3 Final Remarks and Outlook
1 The Track Allocation Problem2 Integer Programming Models3 Branch and Price
1 Model Comparison2 Algorithmic Ingredients3 Auction Experiments4 The Simplon Corridor
Figure 1: Structure of the thesis.
This thesis is about mathematical optimization for the efficient useof railway infrastructure. We address the optimal allocation of theavailable railway track capacity the track allocation problem. Thistrack allocation problem is a major challenge for a railway company,independent of whether a free market, a private monopoly, or a pub-lic monopoly is given. Planning and operating railway transportationsystems is extremely hard due to the combinatorial complexity of theunderlying discrete optimization problems, the technical intricacies,and the immense sizes of the problem instances. Mathematical modelsand optimization techniques can result in huge gains for both railwaycustomers and operators, e.g., in terms of cost reductions or servicequality improvements. We tackle this challenge by developing novelmathematical models and associated innovative algorithmic solutionmethods for large scale instances. This allows us to produce for thefirst time reliable solutions for a real world instance, i.e., the Simploncorridor in Switzerland.
The opening chapter gives a comprehensive overview on railway plan-ning problems. This provides insights into the regulatory and technicalframework, it discusses the interaction of several planning steps, andidentifies optimization potentials in railway transportation. The re-mainder of the thesis is comprised of two major parts.
The first part (Chapter II) is concer