@misc{GrimmBorndoerferSchlechte2019, author = {Grimm, Boris and Bornd{\"o}rfer, Ralf and Schlechte, Thomas}, title = {Re-optimizing ICE Rotations after a Tunnel Breakdown near Rastatt}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-73976}, year = {2019}, abstract = {Planning rolling stock movements in industrial passenger railway applications isa long-term process based on timetables which are also often valid for long periods of time. For these timetables and rotation plans, i.e., plans of railway vehicle movements are constructed as templates for these periods. During operation the rotation plans are affected by all kinds of unplanned events. An unusal example for that is the collapse of a tunnel ceiling near Rastatt in southern Germany due to construction works related to the renewal of the central station in Stuttgart. As a result the main railway connection between Stuttgart and Frankfurt am Main, located on top of the tunnel, had to be closed from August 12th to October 2nd 2017. This had a major impact on the railway network in southern Germany. Hence, all rotation plans and train schedules for both passenger and cargo traffic had to be revised. In this paper we focus on a case study for this situation and compute new rotation plans via mixed integer programming for the ICE high speed fleet of DB Fernverkehr AG one of the largest passenger railway companies in Europe. In our approach we take care of some side constraints to ensure a smooth continuation of the rotation plans after the disruption has ended.}, language = {en} } @inproceedings{BorndoerferGrimmSchlechte2019, author = {Bornd{\"o}rfer, Ralf and Grimm, Boris and Schlechte, Thomas}, title = {Re-optimizing ICE Rotations after a Tunnel Breakdown near Rastatt}, volume = {Link{\"o}ping Electronic Conference Proceedings}, booktitle = {Proceedings of the 8th International Conference on Railway Operations Modelling and Analysis - RailNorrk{\"o}ping 2019}, number = {069}, publisher = {Link{\"o}ping University Electronic Press, Link{\"o}pings universitet}, address = {Link{\"o}ping, Sweden}, isbn = {978-91-7929-992-7}, issn = {1650-3686}, pages = {160 -- 168}, year = {2019}, abstract = {Planning rolling stock movements in industrial passenger railway applications isa long-term process based on timetables which are also often valid for long periods of time. For these timetables and rotation plans, i.e., plans of railway vehicle movements are constructed as templates for these periods. During operation the rotation plans are affected by all kinds of unplanned events. An unusal example for that is the collapse of a tunnel ceiling near Rastatt in southern Germany due to construction works related to the renewal of the central station in Stuttgart. As a result the main railway connection between Stuttgart and Frankfurt am Main, located on top of the tunnel, had to be closed from August 12th to October 2nd 2017. This had a major impact on the railway network in southern Germany. Hence, all rotation plans and train schedules for both passenger and cargo traffic had to be revised. In this paper we focus on a case study for this situation and compute new rotation plans via mixed integer programming for the ICE high speed fleet of DB Fernverkehr AG one of the largest passenger railway companies in Europe. In our approach we take care of some side constraints to ensure a smooth continuation of the rotation plans after the disruption has ended.}, language = {en} } @article{BorndoerferGrimmReutheretal.2019, author = {Bornd{\"o}rfer, Ralf and Grimm, Boris and Reuther, Markus and Schlechte, Thomas}, title = {Optimization of handouts for rolling stock rotations}, journal = {Journal of Rail Transport Planning \& Management}, number = {10}, doi = {10.1016/j.jrtpm.2019.02.001}, pages = {1 -- 8}, year = {2019}, abstract = {A railway operator creates (rolling stock) rotations in order to have a precise master plan for the operation of a timetable by railway vehicles. A rotation is considered as a cycle that multiply traverses a set of operational days while covering trips of the timetable. As it is well known, the proper creation of rolling stock rotations by, e.g., optimization algorithms is challenging and still a topical research subject. Nevertheless, we study a completely different but strongly related question in this paper, i.e.: How to visualize a rotation? For this purpose, we introduce a basic handout concept, which directly leads to the visualization, i.e., handout of a rotation. In our industrial application at DB Fernverkehr AG, the handout is exactly as important as the rotation itself. Moreover, it turns out that also other European railway operators use exactly the same methodology (but not terminology). Since a rotation can have many handouts of different quality, we show how to compute optimal ones through an integer program (IP) by standard software. In addition, a construction as well as an improvement heuristic are presented. Our computational results show that the heuristics are a very reliable standalone approach to quickly find near-optimal and even optimal handouts. The efficiency of the heuristics is shown via a computational comparison to the IP approach.}, language = {en} } @inproceedings{BertholdGrimmReutheretal.2019, author = {Berthold, Timo and Grimm, Boris and Reuther, Markus and Schade, Stanley and Schlechte, Thomas}, title = {Strategic Planning of Rolling Stock Rotations for Public Tenders}, volume = {Link{\"o}ping Electronic Conference Proceedings}, booktitle = {Proceedings of the 8th International Conference on Railway Operations Modelling and Analysis - RailNorrköping 2019}, number = {069}, publisher = {Link{\"o}ping University Electronic Press, Link{\"o}pings universitet}, isbn = {978-91-7929-992-7}, issn = {1650-3686}, pages = {148 -- 159}, year = {2019}, abstract = {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.}, language = {en} } @book{AbbinkBaermannBešinovicetal.2018, author = {Abbink, Erwin and B{\"a}rmann, Andreas and Bešinovic, Nikola and Bohlin, Markus and Cacchiani, Valentina and Caimi, Gabrio and de Fabris, Stefano and Dollevoet, Twan and Fischer, Frank and F{\"u}genschuh, Armin and Galli, Laura and Goverde, Rob M.P. and Hansmann, Ronny and Homfeld, Henning and Huisman, Dennis and Johann, Marc and Klug, Torsten and T{\"o}rnquist Krasemann, Johanna and Kroon, Leo and Lamorgese, Leonardo and Liers, Frauke and Mannino, Carlo and Medeossi, Giorgio and Pacciarelli, Dario and Reuther, Markus and Schlechte, Thomas and Schmidt, Marie and Sch{\"o}bel, Anita and Sch{\"u}lldorf, Hanno and Stieber, Anke and Stiller, Sebastian and Toth, Paolo and Zimmermann, Uwe}, title = {Handbook of Optimization in the Railway Industry}, volume = {268}, editor = {Bornd{\"o}rfer, Ralf and Klug, Torsten and Lamorgese, Leonardo and Mannino, Carlo and Reuther, Markus and Schlechte, Thomas}, publisher = {Springer Verlag}, isbn = {978-3-319-72152-1}, doi = {10.1007/978-3-319-72153-8}, year = {2018}, abstract = {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}, language = {en} } @misc{OPUS4-7166, title = {Proceedings of the 18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems}, editor = {Bornd{\"o}rfer, Ralf and Storandt, Sabine}, publisher = {Dagstuhl Publishing, Saarbr{\"u}cken/Wadern, Germany}, isbn = {ISBN 978-3-95977-096-5}, doi = {10.4230/OASIcs.ATMOS.2018.0}, year = {2018}, abstract = {Running and optimizing transportation systems give rise to very complex and large-scale optimization problems requiring innovative solution techniques and ideas from mathematical optimization, theoretical computer science, and operations research. Since 2000, the series of Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS) workshops brings together researchers and practitioners who are interested in all aspects of algorithmic methods and models for transportation optimization and provides a forum for the exchange and dissemination of new ideas and techniques. The scope of ATMOS comprises all modes of transportation. The 18th ATMOS workshop (ATMOS'18) was held in connection with ALGO'18 and hosted by Aalto University in Helsinki, Finland, on August 23-24, 2018. Topics of interest were all optimization problems for passenger and freight transport, including, but not limited to, demand forecasting, models for user behavior, design of pricing systems, infrastructure planning, multi-modal transport optimization, mobile applications for transport, congestion modelling and reduction, line planning, timetable generation, routing and platform assignment, vehicle scheduling, route planning, crew and duty scheduling, rostering, delay management, routing in road networks, traffic guidance, and electro mobility. Of particular interest were papers applying and advancing techniques like graph and network algorithms, combinatorial optimization, mathematical programming, approximation algorithms, methods for the integration of planning stages, stochastic and robust optimization, online and real-time algorithms, algorithmic game theory, heuristics for real-world instances, and simulation tools. There were twenty-nine submissions from eighteen countries. All of them were reviewed by at least three referees in ninety-one reviews, among them five external ones, and judged on their originality, technical quality, and relevance to the topics of the workshop. Based on the reviews, the program committee selected sixteen submissions to be presented at the workshop (acceptance rate: 55\%), which are collected in this volume in the order in which they were presented. Together, they quite impressively demonstrate the range of applicability of algorithmic optimization to transportation problems in a wide sense. In addition, Dennis Huisman kindly agreed to complement the program with an invited talk on Railway Disruption Management: State-of-the-art in practice and new research directions. Based on the reviews, Ralf Bornd{\"o}rfer, Marika Karbstein, Christian Liebchen, and Niels Lindner won the Best Paper Award of ATMOS'18 with their paper A simple way to compute the number of vehicles that Are required to operate a periodic timetable. In addition, we awarded Tomas Lid{\´e}n the Best VGI Paper Award of ATMOS'18 for his paper Reformulations for railway traffic and maintenance planning. We would like to thank the members of the Steering Committee of ATMOS for giving us the opportunity to serve as Program Chairs of ATMOS'18, all the authors who submitted papers, Dennis Huisman for accepting our invitation to present an invited talk, the members of the Program Committee and the additional reviewers for their valuable work in selecting the papers appearing in this volume, our sponsors MODAL, TomTom, and VGIscience for their support of the prizes, and the local organizers for hosting the workshop as part of ALGO'18. We acknowledge the use of the EasyChair system for the great help in managing the submission and review processes, and Schloss Dagstuhl for publishing the proceedings of ATMOS'18 in its OASIcs series.}, language = {en} } @misc{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}, issn = {1438-0064}, doi = {/10.4230/OASIcs.ATMOS.2011.146}, url = {http://nbn-resolving.de/urn:nbn:de:0030-drops-32746}, number = {11-36}, 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} } @misc{Oleynikova2018, type = {Master Thesis}, author = {Oleynikova, Ekaterina}, title = {Mathematical optimization of joint order batching and picker routing problems}, pages = {60}, year = {2018}, abstract = {In this thesis we study order picking optimization problems for a two-blocks rectangle warehouse layout. We present combinatorial formulations and linear programming models based on the Steiner graph representation for order batching, picker routing, and joint order batching and picker routing problems. A special case of the latter is considered. This case assumes that each order contains exactly one item and each item can be picked from different possible locations in a warehouse. The underlying optimization problem is called joint multi-location order batching and picker routing problem (JMLOBPRP). Since having only one-item orders turns the JMLOBPRP into a special case of a capacitated vehicle routing problem, we suggest to implement algorithmic approaches for those to solve the JMLOBPRP. In particular, we define the JMLOBPRP as a generalization of the resource constrained assignment problem, for which a regional search method exists. The intention of the thesis is to investigate how a relaxation of the JMLOBPRP, a so-called group assignment problem (GrAP), can be solved following the ideas of regional search. We present a mathematical model of the GrAP and prove that it is NP-hard. Furthermore, we propose a novel heuristic algorithm for the GrAP. We call this method a network search algorithm, as it is based on a Lagrangian relaxation of the GrAP, which is solved by the network simplex method. On each its iteration network search examines a solution region suggested by the network simplex algorithm and improves the incumbent solution. Numerical experiments are conducted to assess a performance of the network search method. We create more realistic problem instances. The proposed algorithm is compared to the integer optimal solution of the GrAP and optimal fractional solution of its linear relaxation. Both computed using the commercial linear solver Gurobi. Our experiments show that the developed network search algorithm leads to the hight-quality solution within a short computing time. The results obtained testing large problem instances which cannot be solved by Gurobi within a reasonable computing time, show that the network search method provides a solution approach which can be used in practice.}, language = {en} } @misc{GrimmBorndoerferSchulzetal.2019, author = {Grimm, Boris and Bornd{\"o}rfer, Ralf and Schulz, Christof and Weider, Steffen}, title = {The Rolling Stock Rotation Planning Problem under Revenue Considerations}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-71339}, year = {2019}, 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} } @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} } @misc{BeckenbachHatzelWiederrecht2018, author = {Beckenbach, Isabel and Hatzel, Meike and Wiederrecht, Sebastian}, title = {The Tight Cut Decomposition of Matching Covered Uniformable Hypergraphs}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-71149}, year = {2018}, abstract = {The perfect matching polytope, i.e. the convex hull of (incidence vectors of) perfect matchings of a graph is used in many combinatorial algorithms. Kotzig, Lov{\´a}sz and Plummer developed a decomposition theory for graphs with perfect matchings and their corresponding polytopes known as the tight cut decomposition which breaks down every graph into a number of indecomposable graphs, so called bricks. For many properties that are of interest on graphs with perfect matchings, including the description of the perfect matching polytope, it suffices to consider these bricks. A key result by Lov{\´a}sz on the tight cut decomposition is that the list of bricks obtained is the same independent of the choice of tight cuts made during the tight cut decomposition procedure. This implies that finding a tight cut decomposition is polynomial time equivalent to finding a single tight cut. We generalise the notions of a tight cut, a tight cut contraction and a tight cut decomposition to hypergraphs. By providing an example, we show that the outcome of the tight cut decomposition on general hypergraphs is no longer unique. However, we are able to prove that the uniqueness of the tight cut decomposition is preserved on a slight generalisation of uniform hypergraphs. Moreover, we show how the tight cut decomposition leads to a decomposition of the perfect matching polytope of uniformable hypergraphs and that the recognition problem for tight cuts in uniformable hypergraphs is polynomial time solvable.}, language = {en} } @misc{BorndoerferEgererKarbsteinetal.2018, author = {Bornd{\"o}rfer, Ralf and Egerer, Ascan and Karbstein, Marika and Messerschmidt, Ralf and Perez, Marc and Pfisterer, Steven and Strauß, Petra}, title = {Kombil{\"o}sung: Optimierung des Liniennetzes in Karlsruhe}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-69677}, year = {2018}, abstract = {Wir beschreiben die Optimierung des Nahverkehrsnetzes der Stadt Karlsruhe im Zusammmenhang mit den Baumaßnahmen der sogenannten Kombil{\"o}sung.}, language = {de} } @misc{GrimmBorndoerferOlthoff2020, author = {Grimm, Boris and Bornd{\"o}rfer, Ralf and Olthoff, Mats}, title = {A Solution Approach to the Vehicle Routing Problem with Perishable Goods}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-77020}, year = {2020}, abstract = {This paper focuses on a special case of vehicle routing problem where perishable goods are considered. Deliveries have to be performed until a due date date, which may vary for different products. Storing products is prohibited. Since late deliveries have a direct impact on the revenues for these products, a precise demand prediction is important. In our practical case the product demands and vehicle driving times for the product delivery are dependent on weather conditions, i.e., temperatures, wind, and precipitation. In this paper the definition and a solution approach to the Vehicle Routing Problem with Perishable Goods is presented. The approach includes a procedure how historical weather data is used to predict demands and driving times. Its run time and solution quality is evaluated on different data sets given by the MOPTA Competition 2018.}, language = {en} } @inproceedings{GrimmBorndoerferOlthoff2019, author = {Grimm, Boris and Bornd{\"o}rfer, Ralf and Olthoff, Mats}, title = {A Solution Approach to the Vehicle Routing Problem with Perishable Goods}, booktitle = {Operations Research 2019 Proceedings}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-77020}, year = {2019}, abstract = {This paper focuses on a special case of vehicle routing problem where perishable goods are considered. Deliveries have to be performed until a due date date, which may vary for different products. Storing products is prohibited. Since late deliveries have a direct impact on the revenues for these products, a precise demand prediction is important. In our practical case the product demands and vehicle driving times for the product delivery are dependent on weather conditions, i.e., temperatures, wind, and precipitation. In this paper the definition and a solution approach to the Vehicle Routing Problem with Perishable Goods is presented. The approach includes a procedure how historical weather data is used to predict demands and driving times. Its run time and solution quality is evaluated on different data sets given by the MOPTA Competition 2018.}, language = {en} } @misc{GrimmBorndoerferReutheretal.2020, author = {Grimm, Boris and Bornd{\"o}rfer, Ralf and Reuther, Markus and Schlechte, Thomas}, title = {A Cut Separation Approach for the Rolling Stock Rotation Problem with Vehicle Maintenance}, journal = {19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)}, issn = {1438-0064}, doi = {https://doi.org/10.4230/OASIcs.ATMOS.2019.1}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-75501}, year = {2020}, abstract = {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 Bornd{\"o}rfer 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.}, language = {en} } @inproceedings{GrimmBorndoerferReutheretal.2019, author = {Grimm, Boris and Bornd{\"o}rfer, Ralf and Reuther, Markus and Schlechte, Thomas}, title = {A Cut Separation Approach for the Rolling Stock Rotation Problem with Vehicle Maintenance}, volume = {75}, booktitle = {19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)}, editor = {Cacchiani, Valentina and Marchetti-Spaccamela, Alberto}, publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik}, address = {Dagstuhl, Germany}, doi = {10.4230/OASIcs.ATMOS.2019.1}, pages = {1:1 -- 1:12}, year = {2019}, abstract = {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 [Mar{\´o}ti and Kroon, 2005; G{\´a}bor Mar{\´o}ti 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 Bornd{\"o}rfer 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.}, language = {en} } @inproceedings{BorndoerferKarbsteinMehrgahrdtetal.2016, author = {Bornd{\"o}rfer, Ralf and Karbstein, Marika and Mehrgahrdt, Julika and Reuther, Markus and Schlechte, Thomas}, title = {The Cycle Embedding Problem}, booktitle = {Operations Research Proceedings 2014}, doi = {10.1007/978-3-319-28697-6_65}, pages = {465 -- 472}, year = {2016}, abstract = {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.}, language = {en} } @inproceedings{RenkenAhmadiBorndoerferetal.2018, author = {Renken, Malte and Ahmadi, Amin and Bornd{\"o}rfer, Ralf and Sahin, Guvenc and Schlechte, Thomas}, title = {Demand-Driven Line Planning with Selfish Routing}, booktitle = {Operations Research Proceedings 2017}, publisher = {Springer International Publishing}, doi = {10.1007/978-3-319-89920-6_91}, pages = {687 -- 692}, year = {2018}, abstract = {Bus rapid transit systems in developing and newly industrialized countries are often operated at the limits of passenger capacity. In particular, demand during morning and afternoon peaks is hardly or even not covered with available line plans. In order to develop demand-driven line plans, we use two mathematical models in the form of integer programming problem formulations. While the actual demand data is specified with origin-destination pairs, the arc-based model considers the demand over the arcs derived from the origin-destination demand. In order to test the accuracy of the models in terms of demand satisfaction, we simulate the optimal solutions and compare number of transfers and travel times. We also question the effect of a selfish route choice behavior which in theory results in a Braess-like paradox by increasing the number of transfers when system capacity is increased with additional lines.}, language = {en} } @inproceedings{BorndoerferKarbsteinLiebchenetal.2018, author = {Bornd{\"o}rfer, Ralf and Karbstein, Marika and Liebchen, Christian and Lindner, Niels}, title = {A Simple Way to Compute the Number of Vehicles That Are Required to Operate a Periodic Timetable}, volume = {65}, booktitle = {18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018)}, doi = {10.4230/OASIcs.ATMOS.2018.16}, pages = {16:1 -- 16:15}, year = {2018}, abstract = {We consider the following planning problem in public transportation: Given a periodic timetable, how many vehicles are required to operate it? In [9], for this sequential approach, it is proposed to first expand the periodic timetable over time, and then answer the above question by solving a flow-based aperiodic optimization problem. In this contribution we propose to keep the compact periodic representation of the timetable and simply solve a particular perfect matching problem. For practical networks, it is very much likely that the matching problem decomposes into several connected components. Our key observation is that there is no need to change any turnaround decision for the vehicles of a line during the day, as long as the timetable stays exactly the same.}, language = {en} } @article{BeckenbachBorndoerfer2018, author = {Beckenbach, Isabel and Bornd{\"o}rfer, Ralf}, title = {Hall's and Kőnig's theorem in graphs and hypergraphs}, volume = {341}, journal = {Discrete Mathematics}, number = {10}, doi = {10.1016/j.disc.2018.06.013}, pages = {2753 -- 2761}, year = {2018}, abstract = {We investigate the relation between Hall's theorem and Kőnig's theorem in graphs and hypergraphs. In particular, we characterize the graphs satisfying a deficiency version of Hall's theorem, thereby showing that this class strictly contains all Kőnig-Egerv{\´a}ry graphs. Furthermore, we give a generalization of Hall's theorem to normal hypergraphs.}, language = {en} }