TY - GEN A1 - Schlechte, Thomas T1 - Railway Track Allocation N2 - This article gives an overview of the results of the author's PhD thesis. The thesis deals with the 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. 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. This allows us to produce for the first time reliable solutions for a real world instance, i.e., the Simplon corridor in Switzerland. T3 - ZIB-Report - 12-38 KW - large-scale integer programming KW - network aggregation KW - configuration models KW - rapid branching Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-16402 SN - 1438-0064 ER - TY - GEN A1 - Harrod, Steven A1 - Schlechte, Thomas T1 - A Direct Comparison of Physical Block Occupancy Versus Timed Block Occupancy in Train Timetabling Formulations N2 - Two fundamental mathematical formulations for railway timetabling are compared on a common set of sample problems, representing both multiple track high density services in Europe and single track bidirectional operations in North America. One formulation, ACP, enforces against conflicts by constraining time intervals between trains, while the other formulation, HGF, monitors physical occupation of controlled track segments. The results demonstrate that both ACP and HGF return comparable solutions in the aggregate, with some significant differences in select instances, and a pattern of significant differences in performance and constraint enforcement overall. T3 - ZIB-Report - 13-18 KW - Railway Scheduling KW - Train Timetabling KW - Track Allocation Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17946 SN - 1438-0064 ER - TY - GEN A1 - Raack, Christian A1 - Raymond, Annie A1 - Werner, Axel A1 - Schlechte, Thomas T1 - Integer Programming and Sports Rankings N2 - Sports rankings are obtained by applying a system of rules to evaluate the performance of the participants in a competition. We consider rankings that result from assigning an ordinal rank to each competitor according to their performance. We develop an integer programming model for rankings that allows us to calculate the number of points needed to guarantee a team the ith position, as well as the minimum number of points that could yield the ith place. The model is very general and can thus be applied to many types of sports. We discuss examples coming from football (soccer), ice hockey, and Formula~1. We answer various questions and debunk a few myths along the way. Are 40 points enough to avoid relegation in the Bundesliga? Do 95 points guarantee the participation of a team in the NHL playoffs? Moreover, in the season restructuration currently under consideration in the NHL, will it be easier or harder to access the playoffs? Is it possible to win the Formula~1 World Championship without winning at least one race or without even climbing once on the podium? Finally, we observe that the optimal solutions of the aforementioned model are associated to extreme situations which are unlikely to happen. Thus, to get closer to realistic scenarios, we enhance the model by adding some constraints inferred from the results of the previous years. T3 - ZIB-Report - 13-19 KW - sport ranking KW - integer programming Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-18068 SN - 1438-0064 ER - TY - CHAP A1 - Klug, Torsten A1 - Reuther, Markus A1 - Schlechte, Thomas T1 - Does Laziness Pay Off? - A Lazy-Constraint Approach to Timetabling T2 - 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022) N2 - Timetabling is a classical and complex task for public transport operators as well as for railway undertakings. The general question is: Which vehicle is taking which route through the transportation network in which order? In this paper, we consider the special setting to find optimal timetables for railway systems under a moving block regime. We directly set up on our work of [8 ], i.e., we consider the same model formulation and real-world instances of a moving block headway system. In this paper, we present a repair heuristic and a lazy-constraint approach utilizing the callback features of Gurobi, see [3]. We provide an experimental study of the different algorithmic approaches for a railway network with 100 and up to 300 train requests. The computational results show that the lazy-constraint approach together with the repair heuristic significantly improves our previous approaches. Y1 - 2022 U6 - https://doi.org/10.4230/OASIcs.ATMOS.2022.11 VL - 106 SP - 11:1 EP - 11:8 PB - Schloss Dagstuhl -- Leibniz-Zentrum für Informatik ER - TY - JOUR A1 - Sahin, Guvenc A1 - Ahmadi, Amin A1 - Borndörfer, Ralf A1 - Schlechte, Thomas T1 - Multi-period line planning with resource transfers JF - Transportation Research Part C: Emerging Technologies N2 - Urban transportation systems are subject to a high level of variation and fluctuation in demand over the day. When this variation and fluctuation are observed in both time and space, it is crucial to develop line plans that are responsive to demand. A multi-period line planning approach that considers a changing demand during the planning horizon is proposed. If such systems are also subject to limitations of resources, a dynamic transfer of resources from one line to another throughout the planning horizon should also be considered. A mathematical modelling framework is developed to solve the line planning problem with a cost-oriented approach considering transfer of resources during a finite length planning horizon of multiple periods. We use real-life public transportation network data for our computational results. We analyze whether or not multi-period solutions outperform single period solutions in terms of feasibility and relevant costs. The importance of demand variation on multi-period solutions is investigated. We evaluate the impact of resource transfer constraints on the effectiveness of solutions. We also study the effect of period lengths along with the problem parameters that are significant for and sensitive to the optimality of solutions. Y1 - 2020 U6 - https://doi.org/10.1016/j.trc.2020.102726 VL - 119 SP - 102726 ER - TY - GEN A1 - Schade, Stanley A1 - Schlechte, Thomas A1 - Witzig, Jakob T1 - Structure-based Decomposition for Pattern-Detection for Railway Timetables N2 - We consider the problem of pattern detection in large scale railway timetables. This problem arises in rolling stock optimization planning in order to identify invariant sections of the timetable for which a cyclic rotation plan is adequate. We propose a dual reduction technique which leads to an decomposition and enumeration method. Computational results for real world instances demonstrate that the method is able to produce optimal solutions as fast as standard MIP solvers. T3 - ZIB-Report - 17-40 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64525 SN - 1438-0064 ER - TY - CHAP A1 - Schade, Stanley A1 - Schlechte, Thomas A1 - Witzig, Jakob T1 - Structure-based Decomposition for Pattern-Detection for Railway Timetables T2 - Operations Research Proceedings 2017 N2 - We consider the problem of pattern detection in large scale railway timetables. This problem arises in rolling stock optimization planning in order to identify invariant sections of the timetable for which a cyclic rotation plan is adequate. We propose a dual reduction technique which leads to an decomposition and enumeration method. Computational results for real world instances demonstrate that the method is able to produce optimal solutions as fast as standard MIP solvers. Y1 - 2018 U6 - https://doi.org/10.1007/978-3-319-89920-6_95 SP - 715 EP - 721 PB - Springer International Publishing ER - TY - CHAP A1 - Şahin, Güvenç A1 - Lindner, Niels A1 - Schlechte, Thomas ED - Pardalos, P. M. ED - Prokopyev, O. A. T1 - Line Planning Problem T2 - Encyclopedia of Optimization Y1 - 2023 SN - 978-3-030-54621-2 U6 - https://doi.org/10.1007/978-3-030-54621-2_782-1 SP - 1 EP - 6 PB - Springer International Publishing CY - Cham ER - TY - GEN A1 - Schlechte, Thomas A1 - Blome, Christian A1 - Gerber, Stefan A1 - Hauser, Stefan A1 - Kasten, Jens A1 - Müller, Gilbert A1 - Schulz, Christof A1 - Thüring, Michel A1 - Weider, Steffen T1 - The Bouquet of Features in Rolling Stock Rotation Planning T2 - Conference Proceedings RailBelgrade 2023 N2 - Rolling stock is one of the major assets for a railway transportation company. Hence, their utilization should be as efficiently and effectively as possible. Railway undertakings are facing rolling stock scheduling challenges in different forms - from rather idealized weekly strategic problems to very concrete operational ones. Thus, a vast of optimization models with different features and objectives exist. Thorlacius et al. (2015) provides a comprehensive and valuable collection on technical requirements, models, and methods considered in the scientific literature. We contribute with an update including recent works. The main focus of the paper is to present a classification and elaboration of the major features which our solver R-OPT is able to handle. Moreover, the basic optimization model and algorithmic ingredients of R-OPT are discussed. Finally, we present computational results for a cargo application at SBB CARGO AG and other railway undertakings for passenger traffic in Europe to show the capabilities of R-OPT. Y1 - 2023 UR - https://easychair.org/publications/preprint/Nms6 ER -