TY - GEN A1 - Borndörfer, Ralf A1 - Erol, Berkan A1 - Graffagnino, Thomas A1 - Schlechte, Thomas A1 - Swarat, Elmar T1 - Optimizing the Simplon Railway Corridor N2 - This paper presents a case study on a railway timetable optimization for the very dense Simplon corridor, a major railway connection in the Alps between Switzerland and Italy. Starting from a detailed microscopic network as it is used in railway simulation, the data is transformed by an automatic procedure to a less detailed macroscopic network, that is sufficient for the purpose of capacity planning and amenable to state-of-the-art integer programming optimization methods. In this way, the macroscopic railway network is saturated with trains. Finally, the corresponding timetable is re-transformed to the microscopic level in such a way that it can be operated without any conflicts among the slots. Using this integer programming based micro-macro aggregation-disaggregation approach, it becomes for the first time possible to generate a profit maximal and conflict free timetable for the complete Simplon corridor over an entire day by a simultaneous optimization of all trains requests. This also allows to to undertake a sensitivity analysis of various problem parameters. T3 - ZIB-Report - 10-24 KW - Trassenallokation KW - Netzwerkaggregation KW - Fallstudie KW - Simplon Korridor KW - railway track allocation KW - network aggregation KW - case study KW - Simplon corridor Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11892 SN - 1438-0064 ER - TY - THES A1 - Schlechte, Thomas T1 - Railway Track Allocation: Models and Algorithms N2 - 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 public 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 planning 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 remainder of the thesis is comprised of two major parts. The first part is concerned with modeling railway systems to allow for resource and capacity analysis. Railway capacity has basically two dimensions, a space dimension which are the physical infrastructure elements as well as a time dimension that refers to the train movements, i.e., occupation or blocking times, on the physical infrastructure. Railway safety systems operate on the same principle all over the world. A train has to reserve infrastructure blocks for some time to pass through. Two trains reserving the same block of the infrastructure within the same point in time is called block conflict. Therefore, models for railway capacity involve the definition and calculation of reasonable running and associated reservation and blocking times to allow for a conflict free allocation. In the second and main part of the thesis, the optimal track allocation problem for macroscopic models of the railway system is considered. The literature for related problems is surveyed. A graph-theoretic model for the track allocation problem is developed. In that model optimal track allocations correspond to conflict-free paths in special time-expanded graphs. Furthermore, we made considerable progress on solving track allocation problems by two main features - a novel modeling approach for the macroscopic track allocation problem and algorithmic improvements based on the utilization of the bundle method. Finally, we go back to practice and present in the last chapter several case studies using the tools netcast and tsopt. We provide a computational comparison of our new models and standard packing models used in the literature. Our computational experience indicates that our approach, i.e., ``configuration models'', outperforms other models. Moreover, the rapid branching heuristic and the bundle method enable us to produce high quality solutions for very large scale instances, which has not been possible before. In addition, we present results for a theoretical and rather visionary auction framework for track allocation. We discuss several auction design questions and analyze experiments of various auction simulations. The highlights are results for the Simplon corridor in Switzerland. We optimized the train traffic through this tunnel using our models and software tools. To the best knowledge of the author and confirmed by several railway practitioners this was the first time that fully automatically produced track allocations on a macroscopic scale fulfill the requirements of the originating microscopic model, withstand the evaluation in the microscopic simulation tool OpenTrack, and exploit the infrastructure capacity. This documents the success of our approach in practice and the usefulness and applicability of mathematical optimization to railway track allocation. KW - railway track allocation KW - large-scale integer programming KW - network aggregation KW - rapid branching Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:83-opus-34272 UR - http://opus.kobv.de/tuberlin/volltexte/2012/3427/pdf/schlechte_thomas.pdf SN - 978-3-8381-3222-8 PB - Südwestdeutscher Verlag für Hochschulschriften CY - Saarbrücken, Germany ER - TY - GEN A1 - Borndörfer, Ralf A1 - Schlechte, Thomas T1 - Solving Railway Track Allocation Problems N2 - The \emph{optimal track allocation problem} (\textsc{OPTRA}), also known as the train routing problem or the train timetabling problem, is to find, in a given railway network, a conflict-free set of train routes of maximum value. We propose a novel integer programming formulation for this problem that is based on additional configuration' variables. Its LP-relaxation can be solved in polynomial time. These results are the theoretical basis for a column generation algorithm to solve large-scale track allocation problems. Computational results for the Hanover-Kassel-Fulda area of the German long distance railway network involving up to 570 trains are reported. T3 - ZIB-Report - 07-20 KW - railway track allocation KW - timetabling KW - column generation Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9631 SN - 1438-0064 ER -