@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} } @misc{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}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-56070}, 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} } @misc{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}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-50270}, year = {2014}, abstract = {Wir stellen einen mathematischen Optimierungsansatz zur integrierten Dienst- und Dienstreihenfolgeplanung im {\"o}ffentlichen Nahverkehr vor, mit dem sich bei konstanten Personalkosten die Fahrerzufriedenheit deutlich steigern l{\"a}sst.}, language = {de} } @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{BorndoerferSchulzSeidletal.2015, author = {Bornd{\"o}rfer, Ralf and Schulz, Christof and Seidl, Stephan and Weider, Steffen}, title = {Integration of Duty Scheduling and Rostering to Increase Driver Satisfaction}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-56299}, year = {2015}, abstract = {Integrated treatment of hitherto individual steps in the planning process of public transit companies discloses opportunities to reduce costs and to improve the quality of service. The arising integrated planning problems are complex and their solution requires the development of novel mathematical methods. This article proposes a mathematical optimization approach to integrate duty scheduling and rostering in public transit, which allows to significantly increase driver satisfaction at almost zero cost. This is important in order to to increase the attractiveness of the driver profession. The integration is based on coupling the subproblems by duty templates, which, compared to a coupling by duties, drastically reduces the problem complexity.}, language = {en} } @misc{BorndoerferLoebelReutheretal.2012, author = {Bornd{\"o}rfer, Ralf and L{\"o}bel, Andreas and Reuther, Markus and Schlechte, Thomas and Weider, Steffen}, title = {Rapid Branching}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14728}, number = {12-10}, year = {2012}, 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} } @misc{BorndoerferReutherSchlechteetal.2012, author = {Bornd{\"o}rfer, Ralf and Reuther, Markus and Schlechte, Thomas and Weider, Steffen}, title = {Vehicle Rotation Planning for Intercity Railways}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14731}, number = {12-11}, 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} } @misc{BorndoerferLangenhanLoebeletal.2012, author = {Bornd{\"o}rfer, Ralf and Langenhan, Andreas and L{\"o}bel, Andreas and Schulz, Christof and Weider, Steffen}, title = {Duty Scheduling Templates}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14699}, number = {12-09}, 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} } @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} } @misc{LoebelBorndoerferWeider2023, author = {L{\"o}bel, Fabian and Bornd{\"o}rfer, Ralf and Weider, Steffen}, title = {Non-Linear Battery Behavior in Electric Vehicle Scheduling Problems}, issn = {1438-0064}, doi = {10.1007/978-3-031-58405-3_53}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-92441}, year = {2023}, 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{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} } @misc{SchlechteBlomeGerberetal.2023, author = {Schlechte, Thomas and Blome, Christian and Gerber, Stefan and Hauser, Stefan and Kasten, Jens and M{\"u}ller, Gilbert and Schulz, Christof and Th{\"u}ring, Michel and Weider, Steffen}, title = {The Bouquet of Features in Rolling Stock Rotation Planning}, journal = {Conference Proceedings RailBelgrade 2023}, year = {2023}, abstract = {Rolling stock is one of the major assets for a railway transportation company. Hence, their utilization should be as efficiently and effectively as possible. Railway undertakings are facing rolling stock scheduling challenges in different forms - from rather idealized weekly strategic problems to very concrete operational ones. Thus, a vast of optimization models with different features and objectives exist. Thorlacius et al. (2015) provides a comprehensive and valuable collection on technical requirements, models, and methods considered in the scientific literature. We contribute with an update including recent works. The main focus of the paper is to present a classification and elaboration of the major features which our solver R-OPT is able to handle. Moreover, the basic optimization model and algorithmic ingredients of R-OPT are discussed. Finally, we present computational results for a cargo application at SBB CARGO AG and other railway undertakings for passenger traffic in Europe to show the capabilities of R-OPT.}, language = {en} }