Railway Track Allocation: Models and Algorithms vorgelegt von Dipl.-Math. oec. Thomas Schlechte aus Halle an der Saale Von der Fakult¨atII { Mathematik und Naturwissenschaften der Technischen Universit¨atBerlin zur Erlangung des akademischen Grades Doktor der Naturwissenschaften { Dr. rer. nat. { genehmigte Dissertation Promotionsausschuss Berichter: Prof. Dr. Dr. h. c. mult. Martin Gr¨otschel PD Dr. habil. Ralf Bornd¨orfer Vorsitzender: Prof. Dr. Fredi Tr¨oltzsch Tag der wissenschaftlichen Aussprache: 23.12.2011 Berlin 2012 D 83 Railway Track Allocation: Models and Algorithms Thomas Schlechte Preface 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 to operate the trips of the trains. For the railway infrastructure manager the picture is slightly different { trains have to be allocated to rail- way tracks and times, called slots such that all passenger and freight transport operators are satisfied and all train movements can be car- ried out safely. This problem is called the track allocation problem. My thesis deals with integer programming models and algorithmic solution methods 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 German \Trassenb¨orse".1 This project investigated the question whether a com- petitive marketing of a railway infrastructure can be achieved using an auction-based allocation of railway slots. The idea is that competing train operating companies (TOCs) can bid for any imaginable use of the infrastructure. Possible conflicts will be resolved in favor of the party with the higher willingness to pay, which leads directly to the question of finding revenue maximal track allocations. Moreover a fair 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 questions in economics, railway engineering, and mathematical optimization. In particular, developing models that build a bridge between the abstract world of mathematics and the technical world of railway operations was an exciting task. I worked on the \Trassenb¨orse"project with partners from different ar- eas, namely, on economic problems with the Workgroup for Economic and 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 Universit¨at Hannover, 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 I worked closely with, especially the project heads Ralf Bornd¨orferand Martin Gr¨otschel, project partners Gottfried Ilgmann and Klemens Polatschek, and the ZIB colleagues Berkan Erol, Elmar Swarat, and Steffen Weider. The highlight of the project was a cooperation with the Schweizerische Bundesbahnen (SBB) on optimizing the cargo traffic through the Sim- plon tunnel, one of the major transit routes in the Alps. This real world application was challenging in many ways. It provides the opportunity to verify the usefulness of our methods and algorithms by computing high 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 Scheduling and Disruption Handling, Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and System (ATMOS 2007, 2010), International Seminar on Railway Operations Modeling and Analysis (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 Transit Systems (COMPRAIL), International Conference on Multiple Criteria Decision Making (MCDM), World Conference on Transport Research (WCTR). Significant parts have already been published in various ref- ereed conference proceedings and journals: . Bornd¨orferet al. (2006) [34], . Bornd¨orferet al. (2005) [33], . Bornd¨orfer& Schlechte (2007) [31], . Bornd¨orfer& Schlechte (2007) [30], . Erol et al. (2008) [85], . Schlechte & Bornd¨orfer(2008) [188], . Bornd¨orfer,Mura & Schlechte (2009) [40], . Bornd¨orfer,Erol & Schlechte (2009) [38], . Schlechte & Tanner (2010) [189]3, . Bornd¨orfer,Schlechte & Weider (2010) [43], . Schlechte et al. (2011) [190],1 . and Bornd¨orferet al. (2010) [42]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 problems by exact integer programming methods. In order to establish a fair and transparent railway slot allocation, exact optimization approaches are required, 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 these ambitious goals: 1. applying a novel modeling approach to the track allocation prob- lem called “configuration” models and providing a mathematical analysis of the associated polyhedron, 2. developing a sophisticated integer programming approach called \rapid branching" that highly utilizes the column generation tech- nique and the bundle method to tackle large scale track allocation instances, 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 former approaches, and, 5. carrying out a comprehensive real world data study for the Sim- plon corridor in Switzerland of the \entire" optimal railway track allocation framework. In addition, we present extensions to incorporate aspects of robustness and we provide an integration and empirical analysis of railway slot allocation in an auction based framework. Thesis Structure A rough outline of the thesis is shown in Figure1. It follows the \solution cycle of applied mathematics". In a first step the real world problem is analyzed, then the track allocation problem is translated into a suitable mathematical model, then a method to solve the models in an efficient way is developed, followed by applying the developed methodology in practice to evaluate its performance. Finally, the loop is closed by re-translating the results back to the real world application and analyze them together with experts and practitioners. Main concepts on planning problems in railway transportation are pre- sented in ChapterI. Railway modeling and infrastructure capacity is the main topic of ChapterII. Chapter III focuses on the mathematical modeling and the solution of the track allocation problem. Finally, ChapterIV presents results for real world data as well as for ambitious hypothetical auctioning instances. 1 Introduction 2 Planning Process Chapter I 3 Network Design - 4 Freight Service Network Design Planning in Railway 5 Line Planning Transportation 6 Timetabling 7 Rolling Stock Planning 8 Crew Scheduling Chapter II 1 Microscopic Railway Modeling - 2 Macroscopic Railway Modeling Railway Modeling 3 Final Remarks and Outlook Chapter III 1 The Track Allocation Problem - 2 Integer Programming Models Railway Track 3 Branch and Price Allocation 1 Model Comparison Chapter IV 2 Algorithmic Ingredients - 3 Auction Experiments Case Studies 4 The Simplon Corridor Figure 1: Structure of the thesis. Abstract This thesis is about mathematical optimization for the efficient use of railway infrastructure. We address the optimal allocation of the available railway track capacity { the track allocation problem. This track 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 transportation systems is extremely hard due to the combinatorial complexity of the underlying discrete optimization problems, the technical intricacies, and the immense sizes of the problem instances. Mathematical models and optimization techniques can result in huge gains for both railway customers and operators, e.g., in terms of cost reductions or service quality improvements. We tackle this challenge by developing novel mathematical models and associated innovative algorithmic solution methods for large scale instances. This allows us to produce for the first time reliable solutions for a real world instance, i.e., the Simplon corridor in Switzerland. The opening chapter gives a comprehensive overview on railway plan- ning problems. This provides insights into the regulatory and technical framework, it discusses the interaction of several planning steps, and identifies optimization potentials in railway transportation. The re- mainder of the thesis is comprised of two major parts. The first part (Chapter II) is