@article{BorndoerferGrimmReutheretal.2019, author = {Bornd{\"o}rfer, Ralf and Grimm, Boris and Reuther, Markus and Schlechte, Thomas}, title = {Optimization of handouts for rolling stock rotations}, journal = {Journal of Rail Transport Planning \& Management}, number = {10}, doi = {10.1016/j.jrtpm.2019.02.001}, pages = {1 -- 8}, year = {2019}, abstract = {A railway operator creates (rolling stock) rotations in order to have a precise master plan for the operation of a timetable by railway vehicles. A rotation is considered as a cycle that multiply traverses a set of operational days while covering trips of the timetable. As it is well known, the proper creation of rolling stock rotations by, e.g., optimization algorithms is challenging and still a topical research subject. Nevertheless, we study a completely different but strongly related question in this paper, i.e.: How to visualize a rotation? For this purpose, we introduce a basic handout concept, which directly leads to the visualization, i.e., handout of a rotation. In our industrial application at DB Fernverkehr AG, the handout is exactly as important as the rotation itself. Moreover, it turns out that also other European railway operators use exactly the same methodology (but not terminology). Since a rotation can have many handouts of different quality, we show how to compute optimal ones through an integer program (IP) by standard software. In addition, a construction as well as an improvement heuristic are presented. Our computational results show that the heuristics are a very reliable standalone approach to quickly find near-optimal and even optimal handouts. The efficiency of the heuristics is shown via a computational comparison to the IP approach.}, language = {en} } @article{BeckenbachBorndoerfer2018, author = {Beckenbach, Isabel and Bornd{\"o}rfer, Ralf}, title = {Hall's and Kőnig's theorem in graphs and hypergraphs}, volume = {341}, journal = {Discrete Mathematics}, number = {10}, doi = {10.1016/j.disc.2018.06.013}, pages = {2753 -- 2761}, year = {2018}, abstract = {We investigate the relation between Hall's theorem and Kőnig's theorem in graphs and hypergraphs. In particular, we characterize the graphs satisfying a deficiency version of Hall's theorem, thereby showing that this class strictly contains all Kőnig-Egerv{\´a}ry graphs. Furthermore, we give a generalization of Hall's theorem to normal hypergraphs.}, language = {en} } @article{GrimmHoogervorstBorndoerfer2025, author = {Grimm, Boris and Hoogervorst, Rowan and Bornd{\"o}rfer, Ralf}, title = {A Comparison of Two Models for Rolling Stock Scheduling}, volume = {59}, journal = {Transportation Science}, number = {5}, arxiv = {http://arxiv.org/abs/2312.09697}, doi = {10.1287/trsc.2024.0505}, year = {2025}, abstract = {A major step in the planning process of passenger railway operators is the assignment of rolling stock, that is, train units, to the trips of the timetable. A wide variety of mathematical optimization models have been proposed to support this task, which we discuss and argue to be justified in order to deal with operational differences between railway operators, and hence different planning requirements, in the best possible way. Our investigation focuses on two commonly used models, the composition model and the hypergraph model, that were developed for Netherlands Railways (NS) and DB Fernverkehr AG (DB), respectively. We compare these models in two distinct problem settings, an NS setting and DB-light setting and consider different model variants to tune the models to these settings. We prove that in both of these settings, the linear programming bounds of the two models are equally strong as long as a number of reasonable assumptions are met. However, through a numerical evaluation on NS and DB-light instances, we show that the numerical performance of the models strongly depends on the instances. Although the composition model is the most compact and fastest model for the NS instances, an adjusted version of this model grows quickly for the DB-light instances and is then outperformed by the considered hypergraph model variants. Moreover, we show that a depot-extended version of the hypergraph model is able to combine strengths of both models and show good performance on both the NS and DB-light instances.}, language = {en} } @article{BorndoerferReutherSchlechteetal.2012, author = {Bornd{\"o}rfer, Ralf and Reuther, Markus and Schlechte, Thomas and Weider, Steffen}, title = {Vehicle Rotation Planning for Intercity Railways}, journal = {Proceedings of Conference on Advanced Systems for Public Transport 2012 (CASPT12)}, editor = {Mu{\~n}oz, J. C. and Voß, S.}, year = {2012}, abstract = {This paper provides a generic formulation for rolling stock planning problems in the context of intercity passenger traffic. The main contributions are a graph theoretical model and a Mixed-Integer-Programming formulation that integrate all main requirements of the considered Vehicle-Rotation-Planning problem (VRPP). We show that it is possible to solve this model for real-world instances provided by our industrial partner DB Fernverkehr AG using modern algorithms and computers.}, language = {en} } @article{BorndoerferLoebelReutheretal.2013, author = {Bornd{\"o}rfer, Ralf and L{\"o}bel, Andreas and Reuther, Markus and Schlechte, Thomas and Weider, Steffen}, title = {Rapid Branching}, volume = {5}, journal = {Public Transport}, number = {1}, editor = {Mu{\~n}oz, J. C. and Voß, S.}, publisher = {Springer Berlin Heidelberg}, pages = {3 -- 23}, year = {2013}, abstract = {We propose rapid branching (RB) as a general branch-and-bound heuristic for solving large scale optimization problems in traffic and transport. The key idea is to combine a special branching rule and a greedy node selection strategy in order to produce solutions of controlled quality rapidly and efficiently. We report on three successful applications of the method for integrated vehicle and crew scheduling, railway track allocation, and railway vehicle rotation planning.}, language = {en} } @article{BorndoerferReutherSchlechteetal.2011, author = {Bornd{\"o}rfer, Ralf and Reuther, Markus and Schlechte, Thomas and Weider, Steffen}, title = {A Hypergraph Model for Railway Vehicle Rotation Planning}, volume = {OpenAccess Series in Informatics (OASIcs)}, journal = {11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems}, number = {20}, doi = {10.4230/OASIcs.ATMOS.2011.146}, pages = {146 -- 155}, year = {2011}, abstract = {We propose a model for the integrated optimization of vehicle rotations and vehicle compositions in long distance railway passenger transport. The main contribution of the paper is a hypergraph model that is able to handle the challenging technical requirements as well as very general stipulations with respect to the ``regularity'' of a schedule. The hypergraph model directly generalizes network flow models, replacing arcs with hyperarcs. Although NP-hard in general, the model is computationally well-behaved in practice. High quality solutions can be produced in reasonable time using high performance Integer Programming techniques, in particular, column generation and rapid branching. We show that, in this way, large-scale real world instances of our cooperation partner DB Fernverkehr can be solved.}, language = {en} } @article{BorndoerferFuegenschuhKlugetal.2016, author = {Bornd{\"o}rfer, Ralf and F{\"u}genschuh, Armin and Klug, Torsten and Schang, Thilo and Schlechte, Thomas and Sch{\"u}lldorf, Hanno}, title = {The Freight Train Routing Problem for Congested Railway Networks with Mixed Traffic}, volume = {50}, journal = {Transportation Science}, number = {2}, doi = {10.1287/trsc.2015.0656}, pages = {408 -- 423}, year = {2016}, abstract = {We consider the following freight train routing problem (FTRP). Given is a transportation network with fixed routes for passenger trains and a set of freight trains (requests), each defined by an origin and destination station pair. The objective is to calculate a feasible route for each freight train such that the sum of all expected delays and all running times is minimal. Previous research concentrated on microscopic train routings for junctions or inside major stations. Only recently approaches were developed to tackle larger corridors or even networks. We investigate the routing problem from a strategic perspective, calculating the routes in a macroscopic transportation network of Deutsche Bahn AG. In this context, macroscopic refers to an aggregation of complex and large real-world structures into fewer network elements. Moreover, the departure and arrival times of freight trains are approximated. The problem has a strategic character since it asks only for a coarse routing through the network without the precise timings. We provide a mixed-integer nonlinear programming (MINLP) formulation for the FTRP, which is a multicommodity flow model on a time-expanded graph with additional routing constraints. The model's nonlinearities originate from an algebraic approximation of the delays of the trains on the arcs of the network by capacity restraint functions. The MINLP is reduced to a mixed-integer linear model (MILP) by piecewise linear approximation. The latter is solved by a state-of-the art MILP solver for various real-world test instances.}, language = {en} } @article{GilgKlugMartienssenetal.2018, author = {Gilg, Brady and Klug, Torsten and Martienssen, Rosemarie and Paat, Joseph and Schlechte, Thomas and Schulz, Christof and Seymen, Senan and Tesch, Alexander}, title = {Conflict-free railway track assignment at depots}, journal = {Journal of Rail Transport Planning \& Management}, doi = {10.1016/j.jrtpm.2017.12.004}, year = {2018}, abstract = {Managing rolling stock with no passengers aboard is a critical component of railway operations. One aspect of managing rolling stock is to park the rolling stock on a given set of tracks at the end of a day or service. Depending on the parking assignment, shunting may be required in order for a parked train to depart or for an incoming train to park. Given a collection of tracks M and a collection of trains T with a fixed arrival-departure timetable, the train assignment problem (TAP) is to determine the maximum number of trains from T that can be parked on M according to the timetable and without the use of shunting. Hence, efficiently solving the TAP allows to quickly compute feasible parking schedules that do not require further shunting adjustments. In this paper, we show that the TAP is NP-hard and present two integer programming models for solving the TAP. We compare both models on a theoretical level. Moreover, to our knowledge, we consider the first approach that integrates track lengths along with the three most common types of parking tracks FIFO, LIFO and FREE tracks in a common model. Furthermore, to optimize against uncertainty in the arrival times of the trains we extend our models by stochastic and robust modeling techniques. We conclude by giving computational results for both models, observing that they perform well on real timetables.}, language = {en} } @article{BorndoerferKlugLamorgeseetal.2017, author = {Bornd{\"o}rfer, Ralf and Klug, Torsten and Lamorgese, Leonardo and Mannino, Carlo and Reuther, Markus and Schlechte, Thomas}, title = {Recent success stories on integrated optimization of railway systems}, volume = {74}, journal = {Transportation Research Part C: Emerging Technologies}, number = {1}, doi = {10.1016/j.trc.2016.11.015}, pages = {196 -- 211}, year = {2017}, abstract = {Planning and operating railway transportation systems is an extremely hard task due to the combinatorial complexity of the underlying discrete optimization problems, the technical intricacies, and the immense size of the problem instances. Because of that, however, mathematical models and optimization techniques can result in large gains for both railway customers and operators, e.g., in terms of cost reductions or service quality improvements. In the last years a large and growing group of researchers in the OR community have devoted their attention to this domain developing mathematical models and optimization approaches to tackle many of the relevant problems in the railway planning process. However, there is still a gap to bridge between theory and practice (e.g. Cacchiani et al., 2014; Bornd{\"o}rfer et al., 2010), with a few notable exceptions. In this paper we address three individual success stories, namely, long-term freight train routing (part I), mid-term rolling stock rotation planning (part II), and real-time train dispatching (part III). In each case, we describe real-life, successful implementations. We will discuss the individual problem setting, survey the optimization literature, and focus on particular aspects addressed by the mathematical models. We demonstrate on concrete applications how mathematical optimization can support railway planning and operations. This gives proof that mathematical optimization can support the planning of railway resources. Thus, mathematical models and optimization can lead to a greater efficiency of railway operations and will serve as a powerful and innovative tool to meet recent challenges of the railway industry.}, language = {en} } @article{WitzigBeckenbachEifleretal.2018, author = {Witzig, Jakob and Beckenbach, Isabel and Eifler, Leon and Fackeldey, Konstantin and Gleixner, Ambros and Grever, Andreas and Weber, Marcus}, title = {Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes}, volume = {16}, journal = {Multiscale Modeling and Simulation}, number = {1}, issn = {1438-0064}, doi = {10.1137/16M1091162}, pages = {248 -- 265}, year = {2018}, abstract = {In this paper, we present a new, optimization-based method to exhibit cyclic behavior in non-reversible stochastic processes. While our method is general, it is strongly motivated by discrete simulations of ordinary differential equations representing non-reversible biological processes, in particular molecular simulations. Here, the discrete time steps of the simulation are often very small compared to the time scale of interest, i.e., of the whole process. In this setting, the detection of a global cyclic behavior of the process becomes difficult because transitions between individual states may appear almost reversible on the small time scale of the simulation. We address this difficulty using a mixed-integer programming model that allows us to compute a cycle of clusters with maximum net flow, i.e., large forward and small backward probability. For a synthetic genetic regulatory network consisting of a ring-oscillator with three genes, we show that this approach can detect the most productive overall cycle, outperforming classical spectral analysis methods. Our method applies to general non-equilibrium steady state systems such as catalytic reactions, for which the objective value computes the effectiveness of the catalyst.}, language = {en} } @article{BeckenbachScheidweiler2017, author = {Beckenbach, Isabel and Scheidweiler, Robert}, title = {Perfect f-Matchings and f-Factors in Hypergraphs - A Combinatorial Approach}, volume = {340}, journal = {Discrete Mathematics}, number = {10}, doi = {10.1016/j.disc.2017.05.005}, pages = {2499 -- 2506}, year = {2017}, abstract = {We prove characterizations of the existence of perfect f-matchings in uniform mengerian and perfect hypergraphs. Moreover, we investigate the f-factor problem in balanced hypergraphs. For uniform balanced hypergraphs we prove two existence theorems with purely combinatorial arguments, whereas for non-uniform balanced hypergraphs we show that the f-factor problem is NP-hard.}, language = {de} } @article{BorndoerferHeismann2015, author = {Bornd{\"o}rfer, Ralf and Heismann, Olga}, title = {The hypergraph assignment problem}, volume = {15}, journal = {Discrete Optimization}, doi = {10.1016/j.disopt.2014.11.002}, pages = {15 -- 25}, year = {2015}, language = {en} } @article{BorndoerferReutherSchlechteetal.2016, author = {Bornd{\"o}rfer, Ralf and Reuther, Markus and Schlechte, Thomas and Waas, Kerstin and Weider, Steffen}, title = {Integrated Optimization of Rolling Stock Rotations for Intercity Railways}, volume = {50}, journal = {Transportation Science}, number = {3}, doi = {10.1287/trsc.2015.0633}, pages = {863 -- 877}, year = {2016}, abstract = {This paper proposes a highly integrated solution approach for rolling stock planning problems in the context of long distance passenger traffic between cities. The main contributions are a generic hypergraph-based mixed-integer programming model for the considered rolling stock rotation problem and an integrated algorithm for its solution. The newly developed algorithm is able to handle a large spectrum of industrial railway requirements, such as vehicle composition, maintenance constraints, infrastructure capacities, and regularity aspects. We show that our approach has the power to produce rolling stock rotations that can be implemented in practice. In this way, the rolling stock rotations at the largest German long distance operator Deutsche Bahn Fernverkehr AG could be optimized by an automated system utilizing advanced mathematical programming techniques.}, language = {en} } @article{BorndoerferGrimmReutheretal.2017, author = {Bornd{\"o}rfer, Ralf and Grimm, Boris and Reuther, Markus and Schlechte, Thomas}, title = {Template-based Re-optimization of Rolling Stock Rotations}, journal = {Public Transport}, publisher = {Springer}, doi = {10.1007/s12469-017-0152-4}, pages = {1 -- 19}, year = {2017}, abstract = {Rolling stock, i.e., the set of railway vehicles, is among the most expensive and limited assets of a railway company and must be used efficiently. We consider in this paper the re-optimization problem to recover from unforeseen disruptions. We propose a template concept that allows to recover cost minimal rolling stock rotations from reference rotations under a large variety of operational requirements. To this end, connection templates as well as rotation templates are introduced and their application within a rolling stock rotation planning model is discussed. We present an implementation within the rolling stock rotation optimization framework rotor and computational results for scenarios provided by DB Fernverkehr AG, one of the leading railway operators in Europe.}, language = {en} } @article{BorndoerferEsserFrankenbergeretal.2021, author = {Bornd{\"o}rfer, Ralf and Eßer, Thomas and Frankenberger, Patrick and Huck, Andreas and Jobmann, Christoph and Krostitz, Boris and Kuchenbecker, Karsten and Moorhagen, Kai and Nagl, Philipp and Peterson, Michael and Reuther, Markus and Schang, Thilo and Schoch, Michael and Sch{\"u}lldorf, Hanno and Sch{\"u}tz, Peter and Therolf, Tobias and Waas, Kerstin and Weider, Steffen}, title = {Deutsche Bahn Schedules Train Rotations Using Hypergraph Optimization}, volume = {51}, journal = {Informs Journal on Applied Analytics}, number = {1}, doi = {10.1287/inte.2020.1069}, pages = {42 -- 62}, year = {2021}, abstract = {Deutsche Bahn (DB) operates a large fleet of rolling stock (locomotives, wagons, and train sets) that must be combined into trains to perform rolling stock rotations. This train composition is a special characteristic of railway operations that distinguishes rolling stock rotation planning from the vehicle scheduling problems prevalent in other industries. DB models train compositions using hyperarcs. The resulting hypergraph models are ad-dressed using a novel coarse-to-fine method that implements a hierarchical column genera-tion over three levels of detail. This algorithm is the mathematical core of DB's fleet em-ployment optimization (FEO) system for rolling stock rotation planning. FEO's impact within DB's planning departments has been revolutionary. DB has used it to support the company's procurements of its newest high-speed passenger train fleet and its intermodal cargo locomotive fleet for cross-border operations. FEO is the key to successful tendering in regional transport and to construction site management in daily operations. DB's plan-ning departments appreciate FEO's high-quality results, ability to reoptimize (quickly), and ease of use. Both employees and customers benefit from the increased regularity of operations. DB attributes annual savings of 74 million euro, an annual reduction of 34,000 tons of CO2 emissions, and the elimination of 600 coupling operations in cross-border operations to the implementation of FEO.}, language = {en} } @article{SahinAhmadiBorndoerferetal.2020, author = {Sahin, Guvenc and Ahmadi, Amin and Bornd{\"o}rfer, Ralf and Schlechte, Thomas}, title = {Multi-period line planning with resource transfers}, volume = {119}, journal = {Transportation Research Part C: Emerging Technologies}, doi = {10.1016/j.trc.2020.102726}, pages = {102726}, year = {2020}, abstract = {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.}, language = {en} } @article{Beckenbach2020, author = {Beckenbach, Isabel}, title = {Von Graphen zu Hypergraphen}, journal = {OR News}, number = {70}, issn = {1437-2045}, year = {2020}, language = {en} }