@inproceedings{GrimmBorndoerferSchulzetal.2018, author = {Grimm, Boris and Bornd{\"o}rfer, Ralf and Schulz, Christof and Weider, Steffen}, title = {The Rolling Stock Rotation Planning Problem under Revenue Considerations}, booktitle = {Proceedings of the Rail Transport Demand Management Conference}, year = {2018}, abstract = {In many railway undertakings a railway timetable is offered that is valid for a longer period of time. At DB Fernverkehr AG, one of our industrial partners, this results in a summer and a winter timetable. For both of these timetables rotation plans, i.e., a detailed plan of railway vehicle movements is constructed as a template for this period. Sometimes there are be periods where you know for sure that vehicle capacities are not sufficient to cover all trips of the timetable or to transport all passenger of the trips. Reasons for that could be a heavy increase of passenger flow, a heavy decrease of vehicle availability, impacts from nature, or even strikes of some employees. In such events the rolling stock rotations have to be adapted. Optimization methods are particularly valuable in such situations in order to maintain a best possible level of service or to maximize the expected revenue using the resources that are still available. In most cases found in the literature, a rescheduling based on a timetable update is done, followed by the construction of new rotations that reward the recovery of parts of the obsolete rotations. We consider a different, novel, and more integrated approach. The idea is to guide the cancellation of the trips or reconfiguration of the vehicle composition used to operate a trip of the timetable by the rotation planning process, which is based on the mixed integer programming approach presented in Reuther (2017). The goal is to minimize the operating costs while cancelling or operating a trip with an insufficient vehicle configuration in sense of passenger capacities inflicts opportunity costs and loss of revenue, which are based on an estimation of the expected number of passengers. The performance of the algorithms presented in two case studies, including real world scenarios from DB Fernverkehr AG and a railway operator in North America.}, language = {en} } @article{LangenhanBorndoerferLoebeletal.2012, author = {Langenhan, Andreas and Bornd{\"o}rfer, Ralf and L{\"o}bel, Andreas and Schulz, Christof and Weider, Steffen}, title = {Duty Scheduling Templates}, journal = {Proceedings of Conference on Advanced Systems for Public Transport 2012 (CASPT12)}, editor = {Mu{\~n}oz, J. C. and Voß, S.}, year = {2012}, abstract = {We propose duty templates as a novel concept to produce similar duty schedules for similar days of operation in public transit. Duty templates can conveniently handle various types of similarity requirements, and they can be implemented with ease using standard algorithmic techniques. They have produced good results in practice.}, 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} } @inproceedings{LoebelBorndoerferWeider2025, author = {L{\"o}bel, Fabian and Bornd{\"o}rfer, Ralf and Weider, Steffen}, title = {Non-linear Battery Behavior in Electric Vehicle Scheduling Problems}, booktitle = {Operations Research Proceedings 2023. OR 2023.}, editor = {Voigt, Guido and Fliedner, Malte and Haase, Knut and Br{\"u}ggermann, Wolfgang and Hoberg, Kai and Meissner, Joern}, publisher = {Springer Nature Switzerland}, address = {Cham}, isbn = {9783031584046}, issn = {2731-040X}, doi = {10.1007/978-3-031-58405-3_53}, pages = {415 -- 421}, year = {2025}, abstract = {The currently most popular approach to handle non-linear battery behavior for electric vehicle scheduling is to use a linear spline interpolation of the charge curve. We show that this can lead to approximate models that underestimate the charge duration and overestimate the state of charge, which is not desirable. While the error is of second order with respect to the interpolation step size, the associated mixed-integer linear programs do not scale well with the number of spline segments. It is therefore recommendable to use coarse interpolation grids adapted to the curvature of the charge curve, and to include sufficient safety margins to ensure solutions of approximate models remain feasible subjected to the exact charge curve.}, language = {en} } @article{BorndoerferDittbrennerLangenhanetal.2014, author = {Bornd{\"o}rfer, Ralf and Dittbrenner, Bastian and Langenhan, Andreas and Seidl, Stephan and Weider, Steffen}, title = {Integrierte Dienst- und Dienstreihenfolgeplanung zur Erh{\"o}hung der Fahrerzufriedenheit}, journal = {Straßenverkehrstechnik}, number = {9}, pages = {583 -- 591}, year = {2014}, language = {de} } @inproceedings{BorndoerferGroetschelLoebeletal.2001, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and L{\"o}bel, Andreas and Weider, Steffen}, title = {Integrierte Umlauf- und Dienstplanung im {\"o}ffentlichen Nahverkehr}, booktitle = {Neue Mathematische Verfahren in Industrie und Dienstleistungen}, year = {2001}, language = {en} } @inproceedings{BorndoerferSchlechteWeider2010, author = {Bornd{\"o}rfer, Ralf and Schlechte, Thomas and Weider, Steffen}, title = {Railway Track Allocation by Rapid Branching}, volume = {14}, booktitle = {Proceedings of the 10th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems}, editor = {Erlebach, Thomas and L{\"u}bbecke, Marco}, publisher = {Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik}, address = {Dagstuhl, Germany}, doi = {http://dx.doi.org/10.4230/OASIcs.ATMOS.2010.13}, pages = {13 -- 23}, year = {2010}, language = {en} } @inproceedings{BorndoerferLoebelWeider2008, author = {Bornd{\"o}rfer, Ralf and L{\"o}bel, Andreas and Weider, Steffen}, title = {A Bundle Method for Integrated Multi-Depot Vehicle and Duty Scheduling in Public Transit}, volume = {600}, booktitle = {Computer-aided Systems in Public Transport}, editor = {Hickman, Mark and Mirchandani, Pitu and Voß, Stefan}, publisher = {Springer-Verlag}, pages = {3 -- 24}, year = {2008}, language = {en} } @inproceedings{BorndoerferScheltenSchlechteetal.2006, author = {Bornd{\"o}rfer, Ralf and Schelten, Uwe and Schlechte, Thomas and Weider, Steffen}, title = {A Column Generation Approach to Airline Crew Scheduling}, booktitle = {Operations Research Proceedings 2005}, editor = {Haasis, Hans-Dietrich}, publisher = {Springer-Verlag}, pages = {343 -- 348}, year = {2006}, language = {en} } @inproceedings{BorndoerferLoebelWeider2002, author = {Bornd{\"o}rfer, Ralf and L{\"o}bel, Andreas and Weider, Steffen}, title = {Integrierte Umlauf- und Dienstplanung im {\"O}ffentlichen Verkehr}, booktitle = {Heureka '02}, publisher = {Forschungsgesellschaft f{\"u}r Straßen- und Verkehrswesen}, address = {K{\"o}ln}, pages = {77 -- 98}, year = {2002}, language = {en} } @inproceedings{BorndoerferReutherSchlechteetal.2015, author = {Bornd{\"o}rfer, Ralf and Reuther, Markus and Schlechte, Thomas and Schulz, Christof and Swarat, Elmar and Weider, Steffen}, title = {Duty Rostering in Public Transport - Facing Preferences, Fairness, and Fatigue}, booktitle = {Proceedings of Conference on Advanced Systems in Public Transport 2015 (CASPT2015)}, year = {2015}, abstract = {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.}, 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} } @misc{LoebelBorndoerferWeider2024, author = {L{\"o}bel, Fabian and Bornd{\"o}rfer, Ralf and Weider, Steffen}, title = {Electric Bus Scheduling with Non-Linear Charging, Power Grid Bottlenecks, and Dynamic Recharge Rates}, arxiv = {http://arxiv.org/abs/2407.14446}, year = {2024}, abstract = {Public transport operators are gradually electrifying their bus fleets, predominantly with battery-powered drive trains. These buses commonly have to be scheduled to recharge in-service, which gives rise to a number of challenges. A major problem is that the relationship between charging time and replenished driving range is non-linear, which is often approximately modeled. We examine the associated approximation error and show how it can result in a gross over- or underestimation of the fleet size. Moreover, we demonstrate that commonly used piecewise linear underestimations of the charge curve do not result in an underestimation of the predicted charge states in electric vehicle scheduling and routing models. Furthermore, since power grid upgrades are currently not keeping up with an ever growing electricity demand, operators are introducing active charge management tools to dynamically adjust the charging speed depending on the amount of available energy. It is therefore imperative to extend electric bus scheduling models to account for these developments. We propose a novel mixed-integer programming formulation for the electric bus scheduling problem featuring an improved approximation of the non-linear battery charging behavior as well as dynamic recharge speeds to accommodate grid load limits. The idea is to linearly interpolate what we call the charge increment function, which is closely related to the derivative of the commonly used charge curve. This provides very good error control and integrates easily into integer programming models. We demonstrate the practical usefulness of our model on a diverse library of real-life instances.}, language = {en} } @inproceedings{BorndoerferLoebelLoebeletal.2024, author = {Bornd{\"o}rfer, Ralf and L{\"o}bel, Andreas and L{\"o}bel, Fabian and Weider, Steffen}, title = {Solving the Electric Bus Scheduling Problem by an Integrated Flow and Set Partitioning Approach}, volume = {123}, booktitle = {24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, doi = {10.4230/OASIcs.ATMOS.2024.11}, url = {http://nbn-resolving.de/urn:nbn:de:0030-drops-211992}, pages = {11:1 -- 11:16}, year = {2024}, abstract = {Attractive and cost-efficient public transport requires solving computationally difficult optimization problems from network design to crew rostering. While great progress has been made in many areas, new requirements to handle increasingly complex constraints are constantly coming up. One such challenge is a new type of resource constraints that are used to deal with the state-of-charge of battery-electric vehicles, which have limited driving ranges and need to be recharged in-service. Resource constrained vehicle scheduling problems can classically be modelled in terms of either a resource constrained (multi-commodity) flow problem or in terms of a path-based set partition problem. We demonstrate how a novel integrated version of both formulations can be leveraged to solve resource constrained vehicle scheduling with replenishment in general and the electric bus scheduling problem in particular by Lagrangian relaxation and the proximal bundle method.}, 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} } @inproceedings{LoebelBorndoerferWeider2023, author = {L{\"o}bel, Fabian and Bornd{\"o}rfer, Ralf and Weider, Steffen}, title = {Non-Linear Charge Functions for Electric Vehicle Scheduling with Dynamic Recharge Rates}, volume = {115}, booktitle = {23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)}, doi = {10.4230/OASIcs.ATMOS.2023.15}, url = {http://nbn-resolving.de/urn:nbn:de:0030-drops-187765}, pages = {15:1 -- 15:6}, year = {2023}, abstract = {The ongoing electrification of logistics systems and vehicle fleets increases the complexity of associated vehicle routing or scheduling problems. Battery-powered vehicles have to be scheduled to recharge in-service, and the relationship between charging time and replenished driving range is non-linear. In order to access the powerful toolkit offered by mixed-integer and linear programming techniques, this battery behavior has to be linearized. Moreover, as electric fleets grow, power draw peaks have to be avoided to save on electricity costs or to adhere to hard grid capacity limits, such that it becomes desirable to keep recharge rates dynamic. We suggest a novel linearization approach of battery charging behavior for vehicle scheduling problems, in which the recharge rates are optimization variables and not model parameters.}, language = {en} }