TY - BOOK A1 - Abbink, Erwin A1 - Bärmann, Andreas A1 - Bešinovic, Nikola A1 - Bohlin, Markus A1 - Cacchiani, Valentina A1 - Caimi, Gabrio A1 - de Fabris, Stefano A1 - Dollevoet, Twan A1 - Fischer, Frank A1 - Fügenschuh, Armin A1 - Galli, Laura A1 - Goverde, Rob M.P. A1 - Hansmann, Ronny A1 - Homfeld, Henning A1 - Huisman, Dennis A1 - Johann, Marc A1 - Klug, Torsten A1 - Törnquist Krasemann, Johanna A1 - Kroon, Leo A1 - Lamorgese, Leonardo A1 - Liers, Frauke A1 - Mannino, Carlo A1 - Medeossi, Giorgio A1 - Pacciarelli, Dario A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Schmidt, Marie A1 - Schöbel, Anita A1 - Schülldorf, Hanno A1 - Stieber, Anke A1 - Stiller, Sebastian A1 - Toth, Paolo A1 - Zimmermann, Uwe ED - Borndörfer, Ralf ED - Klug, Torsten ED - Lamorgese, Leonardo ED - Mannino, Carlo ED - Reuther, Markus ED - Schlechte, Thomas T1 - Handbook of Optimization in the Railway Industry N2 - This book promotes the use of mathematical optimization and operations research methods in rail transportation. The editors assembled thirteen contributions from leading scholars to present a unified voice, standardize terminology, and assess the state-of-the-art. There are three main clusters of articles, corresponding to the classical stages of the planning process: strategic, tactical, and operational. These three clusters are further subdivided into five parts which correspond to the main phases of the railway network planning process: network assessment, capacity planning, timetabling, resource planning, and operational planning. Individual chapters cover: Simulation Capacity Assessment Network Design Train Routing Robust Timetabling Event Scheduling Track Allocation Blocking Shunting Rolling Stock Crew Scheduling Dispatching Delay Propagation Y1 - 2018 SN - 978-3-319-72152-1 U6 - https://doi.org/10.1007/978-3-319-72153-8 VL - 268 PB - Springer Verlag ER - TY - GEN A1 - Borndörfer, Ralf A1 - Löbel, Andreas A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Weider, Steffen T1 - Rapid Branching N2 - 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. T3 - ZIB-Report - 12-10 KW - large scale optimization KW - rapid branching KW - column generation Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14728 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Weider, Steffen T1 - Vehicle Rotation Planning for Intercity Railways N2 - 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. T3 - ZIB-Report - 12-11 KW - rolling-stock-planning KW - mixed-integer-programming KW - hypergraphs KW - column generation KW - rapid branching Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14731 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Weider, Steffen T1 - A Hypergraph Model for Railway Vehicle Rotation Planning N2 - 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. T3 - ZIB-Report - 11-36 KW - Rolling Stock Planning, Hypergraph Modeling, Integer Programming, Column Generation, Rapid Branching Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0030-drops-32746 SN - 1438-0064 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Mehrgardt, Julika A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Waas, Kerstin T1 - Re-Optimization of Rolling Stock Rotations N2 - The Rolling Stock Rotation Problem is to schedule rail vehicles in order to cover timetabled trips by a cost optimal set of vehicle rotations. The problem integrates several facets of railway optimization, such as vehicle composition, maintenance constraints, and regularity aspects. In industrial applications existing vehicle rotations often have to be re-optimized to deal with timetable changes or construction sites. We present an integrated modeling and algorithmic approach to this task as well as computational results for industrial problem instances of DB Fernverkehr AG. Y1 - 2014 U6 - https://doi.org/10.1007/978-3-319-07001-8_8 SP - 49 EP - 55 PB - Springer International Publishing ET - Operations Research Proceedings 2013 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Reuther, Markus T1 - Regional Search for the Resource Constrained Assignment Problem T2 - 15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015) N2 - The resource constrained assignment problem (RCAP) is to find a minimal cost partition of the nodes of a directed graph into cycles such that a resource constraint is fulfilled. The RCAP has its roots in rolling stock rotation optimization where a railway timetable has to be covered by rotations, i.e., cycles. In that context, the resource constraint corresponds to maintenance constraints for rail vehicles. Moreover, the RCAP generalizes variants of the vehicle routing problem (VRP). The paper contributes an exact branch and bound algorithm for the RCAP and, primarily, a straightforward algorithmic concept that we call regional search (RS). As a symbiosis of a local and a global search algorithm, the result of an RS is a local optimum for a combinatorial optimization problem. In addition, the local optimum must be globally optimal as well if an instance of a problem relaxation is computed. In order to present the idea for a standardized setup we introduce an RS for binary programs. But the proper contribution of the paper is an RS that turns the Hungarian method into a powerful heuristic for the resource constrained assignment problem by utilizing the exact branch and bound. We present computational results for RCAP instances from an industrial cooperation with Deutsche Bahn Fernverkehr AG as well as for VRP instances from the literature. The results show that our RS provides a solution quality of 1.4 % average gap w.r.t. the best known solutions of a large test set. In addition, our branch and bound algorithm can solve many RCAP instances to proven optimality, e.g., almost all asymmetric traveling salesman and capacitated vehicle routing problems that we consider. Y1 - 2015 U6 - https://doi.org/10.4230/OASIcs.ATMOS.2015.111 VL - 48 SP - 111 EP - 129 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Lamorgese, Leonardo A1 - Klug, Torsten A1 - Mannino, Carlo A1 - Reuther, Markus A1 - Schlechte, Thomas T1 - Recent Success Stories on Optimization of Railway Systems T2 - Proceedings of the IAROR conference RailTokyo N2 - 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 cus- tomers 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 devel- oping 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, with a few notable exceptions. In this paper we address three 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 dis- cuss 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 math- ematical optimization can support the planning of rolling stock resources. Thus, mathematical models and optimization can lead to a greater effi- ciency of railway operations and will serve as a powerful and innovative tool to meet recent challenges of the railway industry. Y1 - 2015 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Schulz, Christof A1 - Swarat, Elmar A1 - Weider, Steffen T1 - Duty Rostering in Public Transport - Facing Preferences, Fairness, and Fatigue T2 - Proceedings of Conference on Advanced Systems in Public Transport 2015 (CASPT2015) N2 - Duty rostering problems occur in different application contexts and come in different flavors. They give rise to very large scale integer programs which ypically have lots of solutions and extremely fractional LP relaxations. In such a situation, heuristics can be a viable algorithmic choice. We propose an mprovement method of the Lin-Kernighan type for the solution of duty rostering problems. We illustrate its versatility and solution quality on three different applications in public transit, vehicle routing, and airline rostering with a focus on the management of preferences, fairness, and fatigue, respectively. Y1 - 2015 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Waas, Kerstin A1 - Weider, Steffen T1 - Integrated Optimization of Rolling Stock Rotations for Intercity Railways JF - Transportation Science N2 - 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. Y1 - 2016 U6 - https://doi.org/10.1287/trsc.2015.0633 VL - 50 IS - 3 SP - 863 EP - 877 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Grimm, Boris A1 - Reuther, Markus A1 - Schlechte, Thomas T1 - Template based re-optimization of rolling stock rotations T2 - Proceedings of Conference on Advanced Systems in Public Transport 2015 (CASPT2015) N2 - Rolling stock, i.e., rail vehicles, are among the most expensive and limited assets of a railway company. They must be used efficiently applying optimization techniques. One important aspect is re-optimization, which is the topic that we consider in this paper. We propose a template concept that allows to compute cost minimal rolling stock rotations under a large variety of re-optimization requirements. Two examples, involving a connection template and a rotation template, are discussed. An implementation within the rolling stock rotation optimizer rotor and computational results for scenarios provided by DB Fernverkehr AG, one of the leading railway operators in Europe, are presented. Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-57539 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Karbstein, Marika A1 - Mehrgahrdt, Julika A1 - Reuther, Markus A1 - Schlechte, Thomas T1 - The Cycle Embedding Problem T2 - Operations Research Proceedings 2014 N2 - Given two hypergraphs, representing a fine and a coarse "layer", and a cycle cover of the nodes of the coarse layer, the cycle embedding problem (CEP) asks for an embedding of the coarse cycles into the fine layer. The CEP is NP-hard for general hypergraphs, but it can be solved in polynomial time for graphs. We propose an integer rogramming formulation for the CEP that provides a complete escription of the CEP polytope for the graphical case. The CEP comes up in railway vehicle rotation scheduling. We present computational results for problem instances of DB Fernverkehr AG that justify a sequential coarse-first-fine-second planning approach. Y1 - 2016 U6 - https://doi.org/10.1007/978-3-319-28697-6_65 SP - 465 EP - 472 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Klug, Torsten A1 - Lamorgese, Leonardo A1 - Mannino, Carlo A1 - Reuther, Markus A1 - Schlechte, Thomas T1 - Recent success stories on integrated optimization of railway systems JF - Transportation Research Part C: Emerging Technologies N2 - 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; Borndörfer 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. Y1 - 2017 U6 - https://doi.org/10.1016/j.trc.2016.11.015 VL - 74 IS - 1 SP - 196 EP - 211 ER - TY - CHAP A1 - Grimm, Boris A1 - Borndörfer, Ralf A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Schade, Stanley T1 - Regularity patterns for rolling stock rotation optimization T2 - 8th International Conference on Applied Operational Research, Proceedings N2 - The operation of railways gives rise to many fundamental optimization problems. One of these problems is to cover a given set of timetabled trips by a set of rolling stock rotations. This is well known as the Rolling Stock Rotation Problem (RSRP). Most approaches in the literature focus primarily on modeling and minimizing the operational costs. However, an essential aspect for the industrial application is mostly neglected. As the RSRP follows timetabling and line planning, where periodicity is a highly desired property, it is also desired to carry over periodic structures to rolling stock rotations and following operations. We call this complex requirement regularity. Regularity turns out to be of essential interest, especially in the industrial scenarios that we tackle in cooperation with DB Fernverkehr AG. Moreover, regularity in the context of the RSRP has not been investigated thoroughly in the literature so far. We introduce three regularity patterns to tackle this requirement, namely regular trips, regular turns, and regular handouts. We present a two-stage approach in order to optimize all three regularity patterns. At first, we integrate regularity patterns into an integer programming approach for the minimization of the operational cost of rolling stock rotations. Afterwards regular handouts are computed. These handouts present the rotations of the first stage in the most regular way. Our computational results (i.e., rolling stock rotations evaluated by planners of DB Fernverkehr AG) show that the three regularity patterns and our concept are a valuable and, moreover, an essential contribution to rolling stock rotation optimization. Y1 - 2016 VL - 8 SP - 28 EP - 32 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Mehrgardt, Julika A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Waas, Kerstin T1 - Re-optimization of Rolling Stock Rotations N2 - The Rolling Stock Rotation Problem is to schedule rail vehicles in order to cover timetabled trips by a cost optimal set of vehicle rotations. The problem integrates several facets of railway optimization, i.e., vehicle composition, maintenance constraints, and regularity aspects. In industrial applications existing schedules often have to be re-optimized to integrate timetable changes or construction sites. We present an integrated modeling and algorithmic approach for this task as well as computational results for industrial problem instances of DB Fernverkehr AG. T3 - ZIB-Report - 13-60 Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42569 SN - 1438-0064 ER - TY - CHAP A1 - Schade, Stanley A1 - Borndörfer, Ralf A1 - Breuer, Matthias A1 - Grimm, Boris A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Siebeneicher, Patrick T1 - Pattern Detection For Large-Scale Railway Timetables T2 - Proceedings of the IAROR conference RailLille N2 - We consider railway timetables of our industrial partner DB Fernverkehr AG that operates the ICE high speed trains in the long-distance passenger railway network of Germany. Such a timetable covers a whole year with 364 days and, typically, includes more than 45,000 trips. A rolling stock rotation plan is not created for the whole timetable at once. Instead the timetable is divided into regular invariant sections and irregular deviations (e.g. for public holidays). A separate rotation plan with a weekly period can then be provided for each of the different sections of the timetable. We present an algorithmic approach to automatically recognize these sections. Together with the supplementing visualisation of the timetable this method has shown to be very relevant for our industrial partner. Y1 - 2017 ER - TY - CHAP A1 - Grimm, Boris A1 - Borndörfer, Ralf A1 - Reuther, Markus A1 - Schade, Stanley A1 - Schlechte, Thomas T1 - A Propagation Approach to Acyclic Rolling Stock Rotation Optimization T2 - Proceedings of the IAROR conference RailLille N2 - The rolling stock, i.e., railway vehicles, are one of the key ingredients of a running railway system. As it is well known, the offer of a railway company to their customers, i.e., the railway timetable, changes from time to time. Typical reasons for that are different timetables associated with different seasons, maintenance periods or holidays. Therefore, the regular lifetime of a timetable is split into (more or less) irregular periods where parts of the timetable are changed. In order to operate a railway timetable most railway companies set up sequences that define the operation of timetabled trips by a single physical railway vehicle called (rolling stock) rotations. Not surprisingly, the individual parts of a timetable also affect the rotations. More precisely, each of the parts brings up an acyclic rolling stock rotation problem with start and end conditions associated with the beginning and ending of the corresponding period. In this paper, we propose a propagation approach to deal with large planning horizons that are composed of many timetables with shorter individual lifetimes. The approach is based on an integer linear programming formulation that propagates rolling stock rotations through the irregular parts of the timetable while taking a large variety of operational requirements into account. This approach is implemented within the rolling stock rotation optimization framework ROTOR used by DB Fernverkehr AG, one of the leading railway operators in Europe. Computational results for real world scenarios are presented to evaluate the approach. Y1 - 2017 ER - TY - GEN A1 - Grimm, Boris A1 - Borndörfer, Ralf A1 - Reuther, Markus A1 - Schade, Stanley A1 - Schlechte, Thomas T1 - A Propagation Approach to Acyclic Rolling Stock Rotation Optimization N2 - The rolling stock, i.e., railway vehicles, are one of the key ingredients of a running railway system. As it is well known, the offer of a railway company to their customers, i.e., the railway timetable, changes from time to time. Typical reasons for that are different timetables associated with different seasons, maintenance periods or holidays. Therefore, the regular lifetime of a timetable is split into (more or less) irregular periods where parts of the timetable are changed. In order to operate a railway timetable most railway companies set up sequences that define the operation of timetabled trips by a single physical railway vehicle called (rolling stock) rotations. Not surprisingly, the individual parts of a timetable also affect the rotations. More precisely, each of the parts brings up an acyclic rolling stock rotation problem with start and end conditions associated with the beginning and ending of the corresponding period. In this paper, we propose a propagation approach to deal with large planning horizons that are composed of many timetables with shorter individual lifetimes. The approach is based on an integer linear programming formulation that propagates rolling stock rotations through the irregular parts of the timetable while taking a large variety of operational requirements into account. This approach is implemented within the rolling stock rotation optimization framework ROTOR used by DB Fernverkehr AG, one of the leading railway operators in Europe. Computational results for real world scenarios are presented to evaluate the approach. T3 - ZIB-Report - 17-24 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-63930 SN - 1438-0064 ER - TY - GEN A1 - Schade, Stanley A1 - Borndörfer, Ralf A1 - Breuer, Matthias A1 - Grimm, Boris A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Siebeneicher, Patrick T1 - Pattern Detection For Large-Scale Railway Timetables N2 - We consider railway timetables of our industrial partner DB Fernverkehr AG that operates the ICE high speed trains in the long-distance passenger railway network of Germany. Such a timetable covers a whole year with 364 days and, typically, includes more than 45,000 trips. A rolling stock rotation plan is not created for the whole timetable at once. Instead the timetable is divided into regular invariant sections and irregular deviations (e.g. for public holidays). A separate rotation plan with a weekly period can then be provided for each of the different sections of the timetable. We present an algorithmic approach to automatically recognize these sections. Together with the supplementing visualisation of the timetable this method has shown to be very relevant for our industrial partner. T3 - ZIB-Report - 17-17 KW - railway timetables KW - visualization KW - pattern detection Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-63390 SN - 1438-0064 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Weider, Steffen T1 - A Hypergraph Model for Railway Vehicle Rotation Planning JF - 11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems N2 - 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. Y1 - 2011 U6 - https://doi.org/10.4230/OASIcs.ATMOS.2011.146 VL - OpenAccess Series in Informatics (OASIcs) IS - 20 SP - 146 EP - 155 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Löbel, Andreas A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Weider, Steffen ED - Muñoz, J. C. ED - Voß, S. T1 - Rapid Branching JF - Public Transport N2 - 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. Y1 - 2013 VL - 5 IS - 1 SP - 3 EP - 23 PB - Springer Berlin Heidelberg ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Weider, Steffen ED - Muñoz, J. C. ED - Voß, S. T1 - Vehicle Rotation Planning for Intercity Railways JF - Proceedings of Conference on Advanced Systems for Public Transport 2012 (CASPT12) N2 - 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. Y1 - 2012 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Breuer, Matthias A1 - Grimm, Boris A1 - Reuther, Markus A1 - Schade, Stanley A1 - Schlechte, Thomas T1 - Timetable Sparsification by Rolling Stock Rotation Optimization N2 - Rolling stock optimization is a task that naturally arises by operating a railway system. It could be seen with different level of details. From a strategic perspective to have a rough plan which types of fleets to be bought to a more operational perspective to decide which coaches have to be maintained first. This paper presents a new approach to deal with rolling stock optimisation in case of a (long term) strike. Instead of constructing a completely new timetable for the strike period, we propose a mixed integer programming model that is able to choose appropriate trips from a given timetable to construct efficient tours of railway vehicles covering an optimized subset of trips, in terms of deadhead kilometers and importance of the trips. The decision which trip is preferred over the other is made by a simple evaluation method that is deduced from the network and trip defining data. T3 - ZIB-Report - 17-63 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-65948 SN - 1438-0064 ER - TY - CHAP A1 - Reuther, Markus A1 - Schlechte, Thomas T1 - Optimization of Rolling Stock Rotations T2 - Handbook of Optimization in the Railway Industry N2 - This chapter shows a successful approach how to model and optimize rolling stock rotations that are required for the operation of a passenger timetable. The underlying mathematical optimization problem is described in detail and solved by RotOR, i.e., a complex optimization algorithm based on linear programming and combinatorial methods. RotOR is used by DB Fernverkehr AG (DBF) in order to optimize intercity express (ICE) rotations for the European high-speed network. We focus on main modeling and solving components, i.e. a hypergraph model and a coarse-to-fine column generation approach. Finally, the chapter concludes with a complex industrial re-optimization application showing the effectiveness of the approach for real world challenges. Y1 - 2018 SN - 978-3-319-72152-1 U6 - https://doi.org/https://doi.org/10.1007/978-3-319-72153-8 VL - 268 SP - 213 EP - 241 PB - Springer International Publishing ER - TY - GEN A1 - Borndörfer, Ralf A1 - Grimm, Boris A1 - Reuther, Markus A1 - Schlechte, Thomas T1 - Optimization of Handouts for Rolling Stock Rotations Visualization N2 - 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. T3 - ZIB-Report - ZR-16-73 Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-61430 SN - 1438-0064 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Grimm, Boris A1 - Reuther, Markus A1 - Schlechte, Thomas T1 - Template-based Re-optimization of Rolling Stock Rotations JF - Public Transport N2 - 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. Y1 - 2017 U6 - https://doi.org/10.1007/s12469-017-0152-4 SP - 1 EP - 19 PB - Springer ER - TY - GEN A1 - Borndörfer, Ralf A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Schulz, Christof A1 - Swarat, Elmar A1 - Weider, Steffen T1 - Duty Rostering in Public Transport - Facing Preferences, Fairness, and Fatigue N2 - Duty rostering problems occur in different application contexts and come in different flavors. They give rise to very large scale integer programs which ypically have lots of solutions and extremely fractional LP relaxations. In such a situation, heuristics can be a viable algorithmic choice. We propose an mprovement method of the Lin-Kernighan type for the solution of duty rostering problems. We illustrate its versatility and solution quality on three different applications in public transit, vehicle routing, and airline rostering with a focus on the management of preferences, fairness, and fatigue, respectively. T3 - ZIB-Report - 15-44 Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-56070 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Karbstein, Marika A1 - Mehrgardt, Julika A1 - Reuther, Markus A1 - Schlechte, Thomas T1 - The Cycle Embedding Problem N2 - Given two hypergraphs, representing a fine and a coarse "layer", and a cycle cover of the nodes of the coarse layer, the cycle embedding problem (CEP) asks for an embedding of the coarse cycles into the fine layer. The CEP is NP-hard for general hypergraphs, but it can be solved in polynomial time for graphs. We propose an integer rogramming formulation for the CEP that provides a complete escription of the CEP polytope for the graphical case. The CEP comes up in railway vehicle rotation scheduling. We present computational results for problem instances of DB Fernverkehr AG that justify a sequential coarse-first-fine-second planning approach. T3 - ZIB-Report - 14-37 KW - cycle embedding problem KW - railway vehicle rotation scheduling KW - sequential coarse-first-fine-second planning approach Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-52788 SN - 1438-0064 ER - TY - CHAP A1 - Reuther, Markus T1 - Local Search for the Resource Constrained Assignment Problem T2 - 14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems N2 - The resource constrained assignment problem (RCAP) is to find a minimal cost cycle partition in a directed graph such that a resource constraint is fulfilled. The RCAP has its roots in an application that deals with the covering of a railway timetable by rolling stock vehicles. Here, the resource constraint corresponds to maintenance constraints for rail vehicles. Moreover, the RCAP generalizes several variants of vehicle routing problems. We contribute a local search algorithm for this problem that is derived from an exact algorithm which is similar to the Hungarian method for the standard assignment problem. Our algorithm can be summarized as a k-OPT heuristic, exchanging k arcs of an alternating cycle of the incumbent solution in each improvement step. The alternating cycles are found by dual arguments from linear programming. We present computational results for instances from our railway application at Deutsche Bahn Fernverkehr AG as well as for instances of the vehicle routing problem from the literature. Y1 - 2014 U6 - https://doi.org/10.4230/OASIcs.ATMOS.2014.62 VL - 42 SP - 62 EP - 78 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Reuther, Markus A1 - Schlechte, Thomas T1 - A Coarse-To-Fine Approach to the Railway Rolling Stock Rotation Problem T2 - 14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems N2 - We propose a new coarse-to-fine approach to solve certain linear programs by column generation. The problems that we address contain layers corresponding to different levels of detail, i.e., coarse layers as well as fine layers. These layers are utilized to design efficient pricing rules. In a nutshell, the method shifts the pricing of a fine linear program to a coarse counterpart. In this way, major decisions are taken in the coarse layer, while minor details are tackled within the fine layer. We elucidate our methodology by an application to a complex railway rolling stock rotation problem. We provide comprehensive computational results that demonstrate the benefit of this new technique for the solution of large scale problems. Y1 - 2014 U6 - https://doi.org/10.4230/OASIcs.ATMOS.2014.79 VL - 42 SP - 79 EP - 91 ER - TY - GEN A1 - Brett, Charles A1 - Hoberg, Rebecca A1 - Pacheco, Meritxell A1 - Smith, Kyle A1 - Borndörfer, Ralf A1 - Euler, Ricardo A1 - Gamrath, Gerwin A1 - Grimm, Boris A1 - Heismann, Olga A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Tesch, Alexander T1 - G-RIPS 2014 RailLab - Towards robust rolling stock rotations N2 - The Graduate-Level Research in Industrial Projects (G-RIPS) Program provides an opportunity for high-achieving graduate-level students to work in teams on a real-world research project proposed by a sponsor from industry or the public sector. Each G-RIPS team consists of four international students (two from the US and two from European universities), an academic mentor, and an industrial sponsor. This is the report of the Rail-Lab project on the definition and integration of robustness aspects into optimizing rolling stock schedules. In general, there is a trade-off for complex systems between robustness and efficiency. The ambitious goal was to explore this trade-off by implementing numerical simulations and developing analytic models. In rolling stock planning a very large set of industrial railway requirements, such as vehicle composition, maintenance constraints, infrastructure capacity, and regularity aspects, have to be considered in an integrated model. General hypergraphs provide the modeling power to tackle those requirements. Furthermore, integer programming approaches are able to produce high quality solutions for the deterministic problem. When stochastic time delays are considered, the mathematical programming problem is much more complex and presents additional challenges. Thus, we started with a basic variant of the deterministic case, i.e., we are only considering hypergraphs representing vehicle composition and regularity. We transfered solution approaches for robust optimization from the airline industry to the setting of railways and attained a reasonable measure of robustness. Finally, we present and discuss different methods to optimize this robustness measure. T3 - ZIB-Report - 14-34 KW - robust optimization, rolling stock planning Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-53475 SN - 1438-0064 N1 - ZIB-Report 14-34 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Klug, Torsten A1 - Lamorgese, Leonardo A1 - Mannino, Carlo A1 - Reuther, Markus A1 - Schlechte, Thomas T1 - Recent Success Stories on Optimization of Railway Systems N2 - 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 cus- tomers 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 devel- oping 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, with a few notable exceptions. In this paper we address three 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 dis- cuss 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 math- ematical optimization can support the planning of rolling stock resources. Thus, mathematical models and optimization can lead to a greater effi- ciency of railway operations and will serve as a powerful and innovative tool to meet recent challenges of the railway industry. T3 - ZIB-Report - 14-47 KW - railway planning KW - railway operations KW - capacity optimization Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-53726 SN - 1438-0064 ER - TY - THES A1 - Reuther, Markus T1 - Mathematical Optimization of Rolling Stock Rotations N2 - We show how to optimize rolling stock rotations that are required for the operation of a passenger timetable. The underlying mathematical ptimization problem is called rolling stock rotation problem (RSRP) and the leitmotiv of the thesis is RotOR, i.e., a highly integrated optimization algorithm for the RSRP. RotOR is used by DB Fernverkehr AG (DBF) in order to optimize intercity express (ICE) rotations for the European high-speed network. In this application, RSRPs have to be solved which (A) require many different aspects to be simultaneously considered, (B) are typically of large scale, and (C) include constraints that have a difficult combinatorial structure. This thesis suggests answers to these issues via the following concepts. (A) The main model, which RotOR uses, relies on a hypergraph. The hypergraph provides an easy way to model manifold industrial railway requirements in great detail. This includes well known vehicle composition requirements as well as relatively unexplored regularity stipulations. At the same time, the hypergraph directly leads to a mixed-integer programming (MIP) model for the RSRP. (B) The main algorithmic ingredient to solve industrial instances of the RSRP is a coarse-to-fine (C2F) column generation procedure. In this approach, the hypergraph is layered into coarse and fine layers that distinguish different levels of detail of the RSRP. The coarse layers are algorithmically utilized while pricing fine columns until proven optimality. Initially, the C2F approach is presented in terms of pure linear programming in order to provide an interface for other applications. (C) Rolling stock rotations have to comply to resource constraints in order to ensure, e.g., enough maintenance inspections along the rotations. These constraints are computationally hard, but are well known in the literature on the vehicle routing problem (VRP). We define an interface problem in order to bridge between the RSRP and the VRP and derive a straightforward algorithmic concept, namely regional search (RS), from their common features and, moreover, differences. Our RS algorithms show promising results for classical VRPs and RSRPs. In the first part of the thesis we present these concepts, which encompass its main mathematical contribution. The second part explains all modeling and solving components of RotOR that turn out to be essential in its industrial application. The thesis concludes with a solution to a complex re-optimization RSRP that RotOR has computed successfully for DBF. In this application all ICE vehicles of the ICE-W fleets of DBF had to be redirected past a construction site on a high-speed line in the heart of Germany. Y1 - 2017 UR - https://depositonce.tu-berlin.de/handle/11303/6309 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Grimm, Boris A1 - Reuther, Markus A1 - Schlechte, Thomas T1 - Optimization of handouts for rolling stock rotations JF - Journal of Rail Transport Planning & Management N2 - 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. Y1 - 2019 U6 - https://doi.org/10.1016/j.jrtpm.2019.02.001 IS - 10 SP - 1 EP - 8 ER - TY - CHAP A1 - Grimm, Boris A1 - Borndörfer, Ralf A1 - Reuther, Markus A1 - Schlechte, Thomas ED - Cacchiani, Valentina ED - Marchetti-Spaccamela, Alberto T1 - A Cut Separation Approach for the Rolling Stock Rotation Problem with Vehicle Maintenance T2 - 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019) N2 - For providing railway services the company's railway rolling stock is one if not the most important ingredient. It decides about the number of passenger or cargo trips the company can offer, about the quality a passenger experiences the train ride and it is often related to the image of the company itself. Thus, it is highly desired to have the available rolling stock in the best shape possible. Moreover, in many countries, as Germany where our industrial partner DB Fernverkehr AG (DBF) is located, laws enforce regular vehicle inspections to ensure the safety of the passengers. This leads to rolling stock optimization problems with complex rules for vehicle maintenance. This problem is well studied in the literature for example see [Maróti and Kroon, 2005; Gábor Maróti and Leo G. Kroon, 2007], or [Cordeau et al., 2001] for applications including vehicle maintenance. The contribution of this paper is a new algorithmic approach to solve the Rolling Stock Rotation Problem for the ICE high speed train fleet of DBF with included vehicle maintenance. It is based on a relaxation of a mixed integer linear programming model with an iterative cut generation to enforce the feasibility of a solution of the relaxation in the solution space of the original problem. The resulting mixed integer linear programming model is based on a hypergraph approach presented in [Ralf Borndörfer et al., 2015]. The new approach is tested on real world instances modeling different scenarios for the ICE high speed train network in Germany and compared to the approaches of [Reuther, 2017] that are in operation at DB Fernverkehr AG. The approach shows a significant reduction of the run time to produce solutions with comparable or even better objective function values. Y1 - 2019 UR - https://drops.dagstuhl.de/opus/volltexte/2019/11413/ U6 - https://doi.org/10.4230/OASIcs.ATMOS.2019.1 VL - 75 SP - 1:1 EP - 1:12 PB - Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik CY - Dagstuhl, Germany ER - TY - GEN A1 - Grimm, Boris A1 - Borndörfer, Ralf A1 - Reuther, Markus A1 - Schlechte, Thomas T1 - A Cut Separation Approach for the Rolling Stock Rotation Problem with Vehicle Maintenance T2 - 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019) N2 - For providing railway services the company’s railway rolling stock is one if not the most important ingredient. It decides about the number of passenger or cargo trips the company can offer, about the quality a passenger experiences the train ride and it is often related to the image of the company itself. Thus, it is highly desired to have the available rolling stock in the best shape possible. Moreover, in many countries, as Germany where our industrial partner DB Fernverkehr AG (DBF) is located, laws enforce regular vehicle inspections to ensure the safety of the passengers. This leads to rolling stock optimization problems with complex rules for vehicle maintenance. This problem is well studied in the literature for example see Maroti and Kroon 2005, or Cordeau et. al. 2001 for applications including vehicle maintenance. The contribution of this paper is a new algorithmic approach to solve the Rolling Stock Rotation Problem for the ICE high speed train fleet of DBF with included vehicle maintenance. It is based on a relaxation of a mixed integer linear programming model with an iterative cut generation to enforce the feasibility of a solution of the relaxation in the solution space of the original problem. The resulting mixed integer linear programming model is based on a hypergraph approach presented in Borndörfer et. al. 2015. The new approach is tested on real world instances modeling different scenarios for the ICE high speed train network in Germany and compared to the approaches of Reuther 2017 that are in operation at DB Fernverkehr AG. The approach shows a significant reduction of the run time to produce solutions with comparable or even better objective function values. T3 - ZIB-Report - 19-61 Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-75501 SN - 1438-0064 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Eßer, Thomas A1 - Frankenberger, Patrick A1 - Huck, Andreas A1 - Jobmann, Christoph A1 - Krostitz, Boris A1 - Kuchenbecker, Karsten A1 - Moorhagen, Kai A1 - Nagl, Philipp A1 - Peterson, Michael A1 - Reuther, Markus A1 - Schang, Thilo A1 - Schoch, Michael A1 - Schülldorf, Hanno A1 - Schütz, Peter A1 - Therolf, Tobias A1 - Waas, Kerstin A1 - Weider, Steffen T1 - Deutsche Bahn Schedules Train Rotations Using Hypergraph Optimization JF - Informs Journal on Applied Analytics N2 - 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. Y1 - 2021 U6 - https://doi.org/10.1287/inte.2020.1069 VL - 51 IS - 1 SP - 42 EP - 62 ER - TY - CHAP A1 - Berthold, Timo A1 - Grimm, Boris A1 - Reuther, Markus A1 - Schade, Stanley A1 - Schlechte, Thomas T1 - Strategic Planning of Rolling Stock Rotations for Public Tenders T2 - Proceedings of the 8th International Conference on Railway Operations Modelling and Analysis - RailNorrköping 2019 N2 - Since railway companies have to apply for long-term public contracts to operate railway lines in public tenders, the question how they can estimate the operating cost for long-term periods adequately arises naturally. We consider a rolling stock rotation problem for a time period of ten years, which is based on a real world instance provided by an industry partner. We use a two stage approach for the cost estimation of the required rolling stock. In the first stage, we determine a weekly rotation plan. In the second stage, we roll out this weekly rotation plan for a longer time period and incorporate scheduled maintenance treatments. We present a heuristic approach and a mixed integer programming model to implement the process of the second stage. Finally, we discuss computational results for a real world tendering scenario. Y1 - 2019 UR - http://www.ep.liu.se/ecp/article.asp?issue=069&article=009&volume= SN - 978-91-7929-992-7 SN - 1650-3686 VL - Linköping Electronic Conference Proceedings IS - 069 SP - 148 EP - 159 PB - Linköping University Electronic Press, Linköpings universitet ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Breuer, Matthias A1 - Grimm, Boris A1 - Reuther, Markus A1 - Schade, Stanley A1 - Schlechte, Thomas T1 - Timetable Sparsification by Rolling Stock Rotation Optimization T2 - Operations Research 2017 N2 - Rolling stock optimization is a task that naturally arises by operating a railway system. It could be seen with different level of details. From a strategic perspective to have a rough plan which types of fleets to be bought to a more operational perspective to decide which coaches have to be maintained first. This paper presents a new approach to deal with rolling stock optimisation in case of a (long term) strike. Instead of constructing a completely new timetable for the strike period, we propose a mixed integer programming model that is able to choose appropriate trips from a given timetable to construct efficient tours of railway vehicles covering an optimized subset of trips, in terms of deadhead kilometers and importance of the trips. The decision which trip is preferred over the other is made by a simple evaluation method that is deduced from the network and trip defining data. Y1 - 2018 U6 - https://doi.org/10.1007/978-3-319-89920-6_96 SP - 723 EP - 728 PB - Springer International Publishing ER - TY - CHAP A1 - Gamrath, Gerwin A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Swarat, Elmar T1 - An LP-based heuristic for Inspector Scheduling T2 - Proceedings of the 13th International Conference on the Practice and Theory of Automated Timetabling - PATAT 2021: Volume I N2 - We present a heuristic based on linear programming (LP) for the integrated tour and crew roster planning of toll enforcement inspectors. Their task is to enforce the proper paying of a distance-based toll on German motorways. This leads to an integrated tour planning and duty rostering problem; it is called Toll Enforcement Problem (TEP). We tackle the TEP by a standard multi-commodity flow model with some extensions in order to incorporate the control tours. The heuristic consists of two variants. The first, called Price & Branch, is a column generation approach to solve the model’s LP relaxation by pricing tour and roster arc variables. Then, we compute an integer feasible solution by restricting to all variables that were priced. The second is a coarse-to-fine approach. Its basic idea is projecting variables to an aggregated variable space, which is much smaller. The aim is to spend as much algorithmic effort in this coarse model as possible. For both heuristic procedures we will show that feasible solutions of high quality can be computed even for large scale industrial instances. Y1 - 2021 UR - https://patatconference.org/patat2020/proceedings/ VL - 1 SP - 77 EP - 86 ER - TY - JOUR A1 - Schlechte, Thomas A1 - Borndörfer, Ralf A1 - Denißen, Jonas A1 - Heller, Simon A1 - Klug, Torsten A1 - Küpper, Michael A1 - Lindner, Niels A1 - Reuther, Markus A1 - Söhlke, Andreas A1 - Steadman, William T1 - Timetable Optimization for a Moving Block System JF - Journal of Rail Transport Planning & Management N2 - We present an optimization model which is capable of routing and ordering trains on a microscopic level under a moving block regime. Based on a general timetabling definition (GTTP) that allows the plug in of arbitrarily detailed methods to compute running and headway times, we describe a layered graph approach using velocity expansion, and develop a mixed integer linear programming formulation. Finally, we present promising results for a German corridor scenario with mixed traffic, indicating that applying branch-and-cut to our model is able to solve reasonably sized instances with up to hundred trains to optimality. Y1 - 2022 U6 - https://doi.org/10.1016/j.jrtpm.2022.100315 SN - 2210-9706 VL - 22 SP - 100315 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Denißen, Jonas A1 - Heller, Simon A1 - Klug, Torsten A1 - Küpper, Michael A1 - Lindner, Niels A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Söhlke, Andreas A1 - Steadman, William T1 - Microscopic Timetable Optimization for a Moving Block System N2 - We present an optimization model which is capable of routing and ordering trains on a microscopic level under a moving block regime. Based on a general timetabling definition (GTTP) that allows the plug in of arbitrarily detailed methods to compute running and headway times, we describe a layered graph approach using velocity expansion, and develop a mixed integer linear programming formulation. Finally, we present promising results for a German corridor scenario with mixed traffic, indicating that applying branch-and-cut to our model is able to solve reasonably sized instances with up to hundred trains to optimality. T3 - ZIB-Report - 21-13 KW - Moving Block KW - Railway Track Allocation KW - Railway Timetabling KW - Train Routing Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82547 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Reuther, Markus A1 - Schlechte, Thomas T1 - A Coarse-To-Fine Approach to the Railway Rolling Stock Rotation Problem N2 - We propose a new coarse-to-fine approach to solve certain linear programs by column generation. The problems that we address contain layers corresponding to different levels of detail, i.e., coarse layers as well as fine layers. These layers are utilized to design efficient pricing rules. In a nutshell, the method shifts the pricing of a fine linear program to a coarse counterpart. In this way, major decisions are taken in the coarse layer, while minor details are tackled within the fine layer. We elucidate our methodology by an application to a complex railway rolling stock rotation problem. We provide comprehensive computational results that demonstrate the benefit of this new technique for the solution of large scale problems. T3 - ZIB-Report - 14-26 KW - column generation KW - coarse-to-fine approach KW - multi-layer approach KW - rolling stock rotation problem Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-51009 SN - 1438-0064 ER - TY - GEN A1 - Reuther, Markus A1 - Borndörfer, Ralf A1 - Schlechte, Thomas A1 - Weider, Steffen T1 - Integrated Optimization of Rolling Stock Rotations for Intercity Railways N2 - This paper provides a highly integrated solution approach for rolling stock planning problems in the context of intercity passenger traffic. The main contributions are a generic hypergraph based mixed integer programming model and an integrated algorithm for the considered rolling stock rotation planning problem. The new developed approach is able to handle a very large set of industrial railway requirements, such as vehicle composition, maintenance constraints, infrastructure capacity, and regularity aspects. By the integration of this large bundle of technical railway aspects, we show that our approach has the power to produce implementable rolling stock rotations for our industrial cooperation partner DB Fernverkehr. This is the first time that the rolling stock rotations at DB Fernverkehr could be optimized by an automated system utilizing advanced mathematical programming techniques. T3 - ZIB-Report - 12-39 KW - Mixed Integer Programming KW - Railway Optimization KW - Rolling Stock Rostering Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-16424 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 -