TY - GEN A1 - Borndörfer, Ralf A1 - Sagnol, Guillaume A1 - Swarat, Elmar T1 - A Case Study on Optimizing Toll Enforcements on Motorways N2 - In this paper we present the problem of computing optimal tours of toll inspectors on German motorways. This problem is a special type of vehicle routing problem and builds up an integrated model, consisting of a tour planning and a duty rostering part. The tours should guarantee a network-wide control whose intensity is proportional to given spatial and time dependent traffic distributions. We model this using a space-time network and formulate the associated optimization problem by an integer program (IP). Since sequential approaches fail, we integrated the assignment of crews to the tours in our model. In this process all duties of a crew member must fit in a feasible roster. It is modeled as a Multi-Commodity Flow Problem in a directed acyclic graph, where specific paths correspond to feasible rosters for one month. We present computational results in a case-study on a German subnetwork which documents the practicability of our approach. T3 - ZIB-Report - 12-21 KW - Vehicle Routing Problem KW - Duty Rostering KW - Integer Programming KW - Operations Research Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-15498 SN - 1438-0064 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 - CHAP A1 - Borndörfer, Ralf A1 - Sagnol, Guillaume A1 - Swarat, Elmar T1 - A Case Study on Optimizing Toll Enforcements on Motorways T2 - 3rd Student Conference on Operational Research N2 - In this paper we present the problem of computing optimal tours of toll inspectors on German motorways. This problem is a special type of vehicle routing problem and builds up an integrated model, consisting of a tour planning and a duty rostering part. The tours should guarantee a network-wide control whose intensity is proportional to given spatial and time dependent traffic distributions. We model this using a space-time network and formulate the associated optimization problem by an integer program (IP). Since sequential approaches fail, we integrated the assignment of crews to the tours in our model. In this process all duties of a crew member must fit in a feasible roster. It is modeled as a Multi-Commodity Flow Problem in a directed acyclic graph, where specific paths correspond to feasible rosters for one month. We present computational results in a case-study on a German subnetwork which documents the practicability of our approach. Y1 - 2012 U6 - https://doi.org/10.4230/OASIcs.SCOR.2012.1 VL - 22 SP - 1 EP - 10 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Sagnol, Guillaume A1 - Schlechte, Thomas A1 - Swarat, Elmar T1 - Optimal duty rostering for toll enforcement inspectors JF - Annals of Operations Research N2 - We present the problem of planning mobile tours of inspectors on German motorways to enforce the payment of the toll for heavy good trucks. This is a special type of vehicle routing problem with the objective to conduct as good inspections as possible on the complete network. In addition, we developed a personalized crew rostering model, to schedule the crews of the tours. The planning of daily tours and the rostering are combined in a novel integrated approach and formulated as a complex and large scale Integer Program. The main focus of this paper extends our previous publications on how different requirements for the rostering can be modeled in detail. The second focus is on a bi-criteria analysis of the planning problem to find the balance between the control quality and the roster acceptance. Finally, computational results on real-world instances show the practicability of our method and how different input parameters influence the problem complexity. Y1 - 2016 U6 - https://doi.org/10.1007/s10479-016-2152-1 VL - 252(2) SP - 383 EP - 406 PB - Springer US ET - 252 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Arslan, Oytun A1 - Elijazyfer, Ziena A1 - Güler, Hakan A1 - Renken, Malte A1 - Sahin, Güvenc A1 - Schlechte, Thomas T1 - Line Planning on Path Networks with Application to the Istanbul Metrobüs N2 - Bus rapid transit systems in developing and newly industrialized countries often consist of a trunk with a path topology. On this trunk, several overlapping lines are operated which provide direct connections. The demand varies heavily over the day, with morning and afternoon peaks typically in reverse directions. We propose an integer programming model for this problem, derive a structural property of line plans in the static (or single period) ``unimodal demand'' case, and consider approaches to the solution of the multi-period version that rely on clustering the demand into peak and off-peak service periods. An application to the Metrobüs system of Istanbul is discussed. T3 - ZIB-Report - 16-38 KW - line planning KW - unimodal demand Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-60119 SN - 1438-0064 ER - TY - CHAP A1 - Blanco, Marco A1 - Borndörfer, Ralf A1 - Hoang, Nam-Dung A1 - Kaier, Anton A1 - Schienle, Adam A1 - Schlechte, Thomas A1 - Schlobach, Swen ED - Marc, Goerigk T1 - Solving Time Dependent Shortest Path Problems on Airway Networks Using Super-Optimal Wind T2 - 16th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2016) N2 - We study the Flight Planning Problem for a single aircraft, which deals with finding a path of minimal travel time in an airway network. Flight time along arcs is affected by wind speed and direction, which are functions of time. We consider three variants of the problem, which can be modeled as, respectively, a classical shortest path problem in a metric space, a time-dependent shortest path problem with piecewise linear travel time functions, and a time-dependent shortest path problem with piecewise differentiable travel time functions. The shortest path problem and its time-dependent variant have been extensively studied, in particular, for road networks. Airway networks, however, have different characteristics: the average node degree is higher and shortest paths usually have only few arcs. We propose A* algorithms for each of the problem variants. In particular, for the third problem, we introduce an application-specific "super-optimal wind" potential function that overestimates optimal wind conditions on each arc, and establish a linear error bound. We compare the performance of our methods with the standard Dijkstra algorithm and the Contraction Hierarchies (CHs) algorithm. Our computational results on real world instances show that CHs do not perform as well as on road networks. On the other hand, A* guided by our potentials yields very good results. In particular, for the case of piecewise linear travel time functions, we achieve query times about 15 times shorter than CHs. Y1 - 2016 U6 - https://doi.org/10.4230/OASIcs.ATMOS.2016.12 VL - 54 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Schenker, Sebastian A1 - Skutella, Martin A1 - Strunk, Timo ED - Greuel, G.-M. ED - Koch, Thorsten ED - Paule, Peter ED - Sommese, Andrew T1 - PolySCIP T2 - Mathematical Software – ICMS 2016, 5th International Conference, Berlin, Germany, July 11-14, 2016, Proceedings N2 - PolySCIP is a new solver for multi-criteria integer and multi-criteria linear programs handling an arbitrary number of objectives. It is available as an official part of the non-commercial constraint integer programming framework SCIP. It utilizes a lifted weight space approach to compute the set of supported extreme non-dominated points and unbounded non-dominated rays, respectively. The algorithmic approach can be summarized as follows: At the beginning an arbitrary non-dominated point is computed (or it is determined that there is none) and a weight space polyhedron created. In every next iteration a vertex of the weight space polyhedron is selected whose entries give rise to a single-objective optimization problem via a combination of the original objectives. If the ptimization of this single-objective problem yields a new non-dominated point, the weight space polyhedron is updated. Otherwise another vertex of the weight space polyhedron is investigated. The algorithm finishes when all vertices of the weight space polyhedron have been investigated. The file format of PolySCIP is based on the widely used MPS format and allows a simple generation of multi-criteria models via an algebraic modelling language. Y1 - 2016 SN - 978-3-319-42431-6 U6 - https://doi.org/10.1007/978-3-319-42432-3_32 VL - 9725 SP - 259 EP - 264 PB - Springer International Publishing ET - Mathematical Software – ICMS 2016 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Hoppmann, Heide A1 - Karbstein, Marika T1 - Passenger routing for periodic timetable optimization BT - Planning and Operations JF - Public Transport N2 - The task of periodic timetabling is to determine trip arrival and departure times in a public transport system such that travel and transfer times are minimized. This paper investigates periodic timetabling models with integrated passenger routing. We show that different routing models can have a huge influence on the quality of the entire system: Whatever metric is applied, the performance ratios of timetables w.r.t. different routing models can be arbitrarily large. Computations on a real-world instance for the city of Wuppertal substantiate the theoretical findings. These results indicate the existence of untapped optimization potentials that can be used to improve the efficiency of public transport systems by integrating passenger routing. Y1 - 2016 U6 - https://doi.org/10.1007/s12469-016-0132-0 PB - Springer-Verlag Berlin Heidelberg ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Hoppmann, Heide A1 - Karbstein, Marika T1 - Separation of Cycle Inequalities for the Periodic Timetabling Problem T2 - 24th Annual European Symposium on Algorithms (ESA 2016) N2 - Cycle inequalities play an important role in the polyhedral study of the periodic timetabling problem. We give the first pseudo-polynomial time separation algorithm for cycle inequalities, and we give a rigorous proof for the pseudo-polynomial time separability of the change-cycle inequalities. The efficiency of these cutting planes is demonstrated on real-world instances of the periodic timetabling problem. Y1 - 2016 U6 - https://doi.org/10.4230/LIPIcs.ESA.2016.21 VL - 57 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Karbstein, Marika T1 - Metric inequalities for routings on direct connections with application to line planning JF - Discrete Optimization N2 - We consider multi-commodity flow problems in which capacities are installed on paths. In this setting, it is often important to distinguish between flows on direct connection routes, using single paths, and flows that include path switching. We derive a feasibility condition for path capacities supporting such direct connection flows similar to the well-known feasibility condition for arc capacities in ordinary multi-commodity flows. The condition can be expressed in terms of a class of metric inequalities for routings on direct connections. We illustrate the concept on the example of the line planning problem in public transport and present an application to large-scale real-world problems. Y1 - 2015 VL - 18 SP - 56 EP - 73 ER - TY - CHAP A1 - Sprösser, Gunther A1 - Schenker, Sebastian A1 - Pittner, Andreas A1 - Borndörfer, Ralf A1 - Rethmeier, Michael A1 - Chang, Ya-Ju A1 - Finkbeiner, Matthias T1 - Sustainable Welding Process Selection based on Weight Space Partitions T2 - Procedia CIRP Y1 - 2016 U6 - https://doi.org/10.1016/j.procir.2016.01.077 VL - 40 SP - 127 EP - 132 ER - TY - CHAP A1 - Schenker, Sebastian A1 - Steingrímsson, Jón Garðar A1 - Borndörfer, Ralf A1 - Seliger, Günther T1 - Modelling of Bicycle Manufacturing via Multi-criteria Mixed Integer Programming T2 - Procedia CIRP Y1 - 2015 U6 - https://doi.org/10.1016/j.procir.2014.07.068 VL - 26 SP - 276 EP - 280 ER - TY - CHAP A1 - Gausemeier, Pia A1 - Seliger, Günther A1 - Schenker, Sebastian A1 - Borndörfer, Ralf T1 - Nachhaltige Technologiepfade für unterschiedliche Entwicklungsniveaus mithilfe mehrkriterieller Entscheidungsfindung T2 - Vorausschau und Technologieplanung Y1 - 2014 SN - 978-3-942647-53-3 VL - 334 SP - 65 EP - 94 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 - 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 - CHAP A1 - Borndörfer, Ralf A1 - Sagnol, Guillaume A1 - Swarat, Elmar T1 - An IP Approach to Toll Enforcement Optimization on German Motorways T2 - Operations Research Proceedings 2011 N2 - This paper proposes the first model for toll enforcement optimization on German motorways. The enforcement is done by mobile control teams and our goal is to produce a schedule achieving network-wide control, proportional to spatial and time-dependent traffic distributions. Our model consists of two parts. The first plans control tours using a vehicle routing approach with profits and some side constraints. The second plans feasible rosters for the control teams. Both problems can be modeled as Multi-Commodity Flow Problems. Adding additional coupling constraints produces a large-scale integrated integer programming formulation. We show that this model can be solved to optimality for real world instances associated with a control area in East Germany. Y1 - 2012 U6 - https://doi.org/10.1007/978-3-642-29210-1_51 SP - 317 EP - 322 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Buwaya, Julia A1 - Sagnol, Guillaume A1 - Swarat, Elmar T1 - Optimizing Toll Enforcement in Transportation Networks: a Game-Theoretic Approach T2 - Proceedings of INOC'2013 N2 - We present a game-theoretic approach to optimize the strategies of toll enforcement on a motorway network. In contrast to previous approaches, we consider a network with an arbitrary topology, and we handle the fact that users may choose their Origin-Destination path; in particular they may take a detour to avoid sections with a high control rate. We show that a Nash equilibrium can be computed with an LP (although the game is not zero-sum), and we give a MIP for the computation of a Stackelberg equilibrium. Experimental results based on an application to the enforcement of a truck toll on German motorways are presented. Y1 - 2013 U6 - https://doi.org/http://dx.doi.org//10.1016/j.endm.2013.05.100 VL - 41 SP - 253 EP - 260 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Omont, Bertrand A1 - Sagnol, Guillaume A1 - Swarat, Elmar T1 - A Stackelberg game to optimize the distribution of controls in transportation networks T2 - Proceedings of the 3rd International Conference on Game Theory for Networks (GAMENETS 2012) N2 - We propose a game theoretic model for the spatial distribution of inspectors on a transportation network. The problem is to spread out the controls so as to enforce the payment of a transit toll. We formulate a linear program to find the control distribution which maximizes the expected toll revenue, and a mixed integer program for the problem of minimizing the number of evaders. Furthermore, we show that the problem of finding an optimal mixed strategy for a coalition of $N$ inspectors can be solved efficiently by a column generation procedure. Finally, we give experimental results from an application to the truck toll on German motorways. Y1 - 2012 U6 - https://doi.org/http://dx.doi.org/10.1007/978-3-642-35582-0_17 VL - 105 SP - 224 EP - 235 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 - JOUR A1 - Borndörfer, Ralf A1 - Heismann, Olga T1 - The hypergraph assignment problem JF - Discrete Optimization Y1 - 2015 U6 - https://doi.org/10.1016/j.disopt.2014.11.002 VL - 15 SP - 15 EP - 25 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Jaeger, Ulrich T1 - Planning Problems in Public Transit N2 - Every day, millions of people are transported by buses, trains, and airplanes in Germany. Public transit (PT) is of major importance for the quality of life of individuals as well as the productivity of entire regions. Quality and efficiency of PT systems depend on the political framework (state-run, market oriented) and the suitability of the infrastructure (railway tracks, airport locations), the existing level of service (timetable, flight schedule), the use of adequate technologies (information, control, and booking systems), and the best possible deployment of equipment and resources (energy, vehicles, crews). The decision, planning, and optimization problems arising in this context are often gigantic and “scream” for mathematical support because of their complexity. This article sketches the state and the relevance of mathematics in planning and operating public transit, describes today’s challenges, and suggests a number of innovative actions. The current contribution of mathematics to public transit is — depending on the transportation mode — of varying depth. Air traffic is already well supported by mathematics. Bus traffic made significant advances in recent years, while rail traffic still bears significant opportunities for improvements. In all areas of public transit, the existing potentials are far from being exhausted. For some PT problems, such as vehicle and crew scheduling in bus and air traffic, excellent mathematical tools are not only available, but used in many places. In other areas, such as rolling stock rostering in rail traffic, the performance of the existing mathematical algorithms is not yet sufficient. Some topics are essentially untouched from a mathematical point of view; e.g., there are (except for air traffic) no network design or fare planning models of practical relevance. PT infrastructure construction is essentially devoid of mathematics, even though enormous capital investments are made in this area. These problems lead to questions that can only be tackled by engineers, economists, politicians, and mathematicians in a joint effort. Among other things, the authors propose to investigate two specific topics, which can be addressed at short notice, are of fundamental importance not only for the area of traffic planning, should lead to a significant improvement in the collaboration of all involved parties, and, if successful, will be of real value for companies and customers: • discrete optimal control: real-time re-planning of traffic systems in case of disruptions, • model integration: service design in bus and rail traffic. Work on these topics in interdisciplinary research projects could be funded by the German ministry of research and education (BMBF), the German ministry of economics (BMWi), or the German science foundation (DFG). T3 - ZIB-Report - 09-13 KW - öffentlicher Verkehr KW - diskrete Optimierung KW - ganzzahlige Programmierung KW - public transit KW - discrete optimization KW - integer programming Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11252 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Cardonha, Carlos T1 - A Set Partitioning Approach to Shunting N2 - The Vehicle Positioning Problem (VPP) is a classical combinatorial optimization problem in public transport planning. A number of models and approaches have been suggested in the literature, which work for small problems, but not for large ones. We propose in this article a novel set partitioning model and an associated column generation solution approach for the VPP. The model provides a tight linear description of the problem. The pricing problem, and hence the LP relaxation itself, can be solved in polynomial resp. pseudo-polynomial time for some versions of the problems. T3 - ZIB-Report - 09-18 KW - integer programming KW - set partitioning KW - combinatorial packing KW - vehicle positioning Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11326 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Neumann, Marika A1 - Pfetsch, Marc T1 - The Steiner Connectivity Problem N2 - The Steiner connectivity problem is a generalization of the Steiner tree problem. It consists in finding a minimum cost set of simple paths to connect a subset of nodes in an undirected graph. We show that polyhedral and algorithmic results on the Steiner tree problem carry over to the Steiner connectivity problem, namely, the Steiner cut and the Steiner partition inequalities, as well as the associated polynomial time separation algorithms, can be generalized. Similar to the Steiner tree case, a directed formulation, which is stronger than the natural undirected one, plays a central role. T3 - ZIB-Report - 09-07 KW - Steiner Tree KW - Partition Inequalities KW - Paths KW - Connectivity KW - Generalization Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11171 SN - 1438-0064 ER - TY - GEN A1 - Torres, Luis Miguel A1 - Torres, Ramiro A1 - Borndörfer, Ralf A1 - Pfetsch, Marc T1 - Line Planning on Paths and Tree Networks with Applications to the Quito Trolebus System (Extended Abstract) N2 - Line planning is an important step in the strategic planning process of a public transportation system. In this paper, we discuss an optimization model for this problem in order to minimize operation costs while guaranteeing a certain level of quality of service, in terms of available transport capacity. We analyze the problem for path and tree network topologies as well as several categories of line operation that are important for the Quito Trolebus system. It turns out that, from a computational complexity worst case point of view, the problem is hard in all but the most simple variants. In practice, however, instances based on real data from the Trolebus System in Quito can be solved quite well, and significant optimization potentials can be demonstrated. T3 - ZIB-Report - 08-53 KW - line planning KW - computational complexity KW - public transport KW - integer programming Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11076 SN - 1438-0064 ER - TY - GEN A1 - Torres, Luis Miguel A1 - Torres, Ramiro A1 - Borndörfer, Ralf A1 - Pfetsch, Marc T1 - On the Line Planning Problem in Tree Networks N2 - We introduce an optimization model for the line planning problem in a public transportation system that aims at minimizing operational costs while ensuring a given level of quality of service in terms of available transport capacity. We discuss the computational complexity of the model for tree network topologies and line structures that arise in a real-world application at the Trolebus Integrated System in Quito. Computational results for this system are reported. T3 - ZIB-Report - 08-52 KW - line planning KW - computational complexity KW - public transport optimization Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11069 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf T1 - Discrete Optimization in Public Transportation N2 - The mathematical treatment of planning problems in public transit has made significant advances in the last decade. Among others, the classical problems of vehicle and crew scheduling can nowadays be solved on a routine basis using combinatorial optimization methods. This is not yet the case for problems that pertain to the design of public transit networks, and for the problems of operations control that address the implementation of a schedule in the presence of disturbances. The article gives a sketch of the state and important developments in these areas, and it addresses important challenges. The vision is that mathematical tools of computer aided scheduling (CAS) will soon play a similar role in the design and operation of public transport systems as CAD systems in manufacturing. N2 - Die mathematische Behandlung von Planungsproblemen im öffentlichen Verkehr hat im letzten Jahrzehnt große Fortschritte gemacht. Klassische Probleme wie die Umlauf- und die Dienstplanung können heutzutage routinemäßig mit kombinatorischen Optimierungsmethoden gelöst werden. Die Behandlung von Problemen der Angebotsplanung und der Betriebssteuerung sind dagegen noch nicht ganz auf diesem Stand. Dieser Artikel gibt einen Überblick über den Stand der Forschung, über wichtige Entwicklungen und einige Herausforderungen in diesem Gebiet. Die Vision ist, dass mathematische Planungswerkzeuge im öffentlichen Verkehr (Computer Aided Scheduling, CAS) in Zukunft eine ähnliche Rolle spielen werden wie CAD-Systeme in der industriellen Fertigung. T3 - ZIB-Report - 08-56 KW - Öffentlicher Verkehr KW - Nahverkehr KW - Optimierung KW - Public Transit KW - Optimization Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11207 SN - 1438-0064 ER - TY - GEN A1 - Torres, Luis Miguel A1 - Torres, Ramiro A1 - Borndörfer, Ralf A1 - Pfetsch, Marc T1 - Line Planning on Paths and Tree Networks with Applications to the Quito Trolebus System N2 - Line planning is an important step in the strategic planning process of a public transportation system. In this paper, we discuss an optimization model for this problem in order to minimize operation costs while guaranteeing a certain level of quality of service, in terms of available transport capacity. We analyze the problem for path and tree network topologies as well as several categories of line operation that are important for the Quito Trolebus system. It turns out that, from a computational complexity worst case point of view, the problem is hard in all but the most simple variants. In practice, however, instances based on real data from the Trolebus System in Quito can be solved quite well, and significant optimization potentials can be demonstrated. T3 - ZIB-Report - 08-35 KW - line planning KW - computational complexity KW - public transport KW - integer programming Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10869 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Hoang, Nam-Dung T1 - Fair Ticket Prices in Public Transport N2 - Ticket pricing in public transport usually takes a welfare or mnemonics maximization point of view. These approaches do not consider fairness in the sense that users of a shared infrastructure should pay for the costs that they generate. We propose an ansatz to determine fair ticket prices that combines concepts from cooperative game theory and integer programming. An application to pricing railway tickets for the intercity network of the Netherlands demonstrates that, in this sense, prices that are much fairer than standard ones can be computed in this way. T3 - ZIB-Report - 08-46 KW - Ticket prices KW - cost allocation game Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10999 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Mura, Annette A1 - Schlechte, Thomas T1 - Vickrey Auctions for Railway Tracks N2 - We consider an auction of slots to run trains through a railway network. In contrast to the classical setting for combinatorial auctions, there is not only competition for slots, but slots can mutually exclude each other, such that general conflict constraints on bids arise. This turns the winner determination problem associated with such an auction into a complex combinatorial optimization problem. It also raises a number of auction design questions, in particular, on incentive compatibilty. We propose a single-shot second price auction for railway slots, the Vickrey Track Auction (VTA). We show that this auction is incentive compatible, i.e., rational bidders are always motivated to bid their true valuation, and that it produces efficient allocations, even in the presence of constraints on allocations. These properties are, however, lost when rules on the submission of bids such as, e.g., lowest bids, are imposed. Our results carry over to generalized" Vickrey auctions with combinatorial constraints. T3 - ZIB-Report - 08-34 KW - Vickrey Auktion KW - Fahrplanung KW - Vickrey Auction KW - Track Allocation Problem Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10855 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf T1 - Combinatorial Packing Problems N2 - This article investigates a certain class of combinatorial packing problems and some polyhedral relations between such problems and the set packing problem. T3 - ZIB-Report - 03-03 KW - Packing problems KW - polyhedral combinatorics Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7255 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Neumann, Marika A1 - Pfetsch, Marc T1 - Optimal Fares for Public Transport N2 - The \emph{fare planning problem} for public transport is to design a system of fares that maximize the revenue. We introduce a nonlinear optimization model to approach this problem. It is based on a d iscrete choice logit model that expresses demand as a function of the fares. We illustrate our approach by computing and comparing two different fare systems for the intercity network of the Netherlands. T3 - ZIB-Report - 05-35 KW - fare planning KW - demand function KW - discrete choice model Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8698 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 - 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 - JOUR A1 - Borndörfer, Ralf A1 - Hoang, Nam-Dung T1 - Fair ticket pricing in public transport as a constrained cost allocation game JF - Annals of Operations Research N2 - Ticket pricing in public transport usually takes a welfare maximization point of view. Such an approach, however, does not consider fairness in the sense that users of a shared infrastructure should pay for the costs that they generate. We propose an ansatz to determine fair ticket prices that combines concepts from cooperative game theory and linear and integer programming. The ticket pricing problem is considered to be a constrained cost allocation game, which is a generalization of cost allocation games that allows to deal with constraints on output prices and on the formation of coalitions. An application to pricing railway tickets for the intercity network of the Netherlands is presented. The results demonstrate that the fairness of prices can be improved substantially in this way. A preliminary version of this paper appeared in the Proceedings of HPSC 2009 (Borndörfer and Hoang 2012). This journal article introduces better model and algorithms. Y1 - 2014 U6 - https://doi.org/10.1007/s10479-014-1698-z VL - 226 SP - 51 EP - 68 ER - TY - GEN A1 - Beckenbach, Isabel A1 - Borndörfer, Ralf T1 - An Approximation Result for Matchings in Partitioned Hypergraphs N2 - We investigate the matching and perfect matching polytopes of hypergraphs having a special structure, which we call partitioned hypergraphs. We show that the integrality gap of the standard LP-relaxation is at most $2\sqrt{d}$ for partitioned hypergraphs with parts of size $\leq d$. Furthermore, we show that this bound cannot be improved to $\mathcal{O}(d^{0.5-\epsilon})$. T3 - ZIB-Report - 14-30 Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-51083 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 - Heismann, Olga A1 - Borndörfer, Ralf T1 - A Generalization of Odd Set Inequalities for the Set Packing Problem T2 - Operations Research Proceedings 2013 N2 - The set packing problem, sometimes also called the stable set problem, is a well-known NP-hard problem in combinatorial optimization with a wide range of applications and an interesting polyhedral structure, that has been the subject of intensive study. We contribute to this field by showing how, employing cliques, odd set inequalities for the matching problem can be generalized to valid inequalities for the set packing polytope with a clear combinatorial meaning. Y1 - 2014 U6 - https://doi.org/10.1007/978-3-319-07001-8_26 SP - 193 EP - 199 ER - TY - GEN A1 - Grötschel, Martin A1 - Borndörfer, Ralf T1 - Mathematik im Verkehr N2 - Nach einem kurzen Abriss über die Bedeutung des Verkehrssektors als eine wichtige Schlüsseltechnologie im gesamten Verlauf der Menschheitsgeschichte skizzieren wir die Rolle der Mathematik für Verkehr und Transport. Wir spekulieren dann über zukünftige Entwicklungen, insbesondere im Bereich des öffentlichen Personenverkehrs, und begründen, dass die in diesem Bereich anstehenden Herausforderungen nur mit dem Einsatz mathematischer Methoden angemessen bewältigt werden können. Die demographischen Prozesse, die in verschiedenen Teilen der Welt unterschiedlich verlaufen, wie z.B. Überalterung in Europa oder dynamische Trends zu Megastädten in Entwicklungsländern, sich ändernde Lebens- und Produktionsverhältnisse, stark wachsender Bedarf nach Mobilität und enormes Anwachsen der Komplexität der Verkehrsplanung und -durchführung, machen einen verstärkten Zugriff auf mathematische Modellierung, Simulation und Optimierung notwendig. Diese Entwicklung stellt sowohl große Herausforderungen an die Mathematik, wo vielfach noch keine geeigneten Methoden vorhanden sind, als auch an die Praktiker im Bereich von Verkehr und Transport, die sich mit neuen Planungs- und Steuerungstechnologien befassen und diese effizient einsetzen müssen. Hier wird intensive Kooperation zwischen vielen beteiligten Akteuren gefragt sein. T3 - ZIB-Report - 14-03 KW - Optimierung KW - öffentlicher Verkehr Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-50287 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Dittbrenner, Bastian A1 - Langenhan, Andreas A1 - Seidl, Stephan A1 - Weider, Steffen T1 - Integrierte Dienst- und Dienstreihenfolgeplanung zur Erhöhung der Fahrerzufriedenheit N2 - Wir stellen einen mathematischen Optimierungsansatz zur integrierten Dienst- und Dienstreihenfolgeplanung im öffentlichen Nahverkehr vor, mit dem sich bei konstanten Personalkosten die Fahrerzufriedenheit deutlich steigern lässt. T3 - ZIB-Report - 14-02 KW - duty scheduling KW - duty rostering KW - integrated scheduling KW - Benders' decomposition Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-50270 SN - 1438-0064 ER - TY - GEN A1 - Heismann, Olga A1 - Borndörfer, Ralf T1 - A Generalization of Odd Set Inequalities for the Set Packing Problem N2 - The set packing problem, sometimes also called the stable set problem, is a well-known NP-hard problem in combinatorial optimization with a wide range of applications and an interesting polyhedral structure, that has been the subject of intensive study. We contribute to this field by showing how, employing cliques, odd set inequalities for the matching problem can be generalized to valid inequalities for the set packing polytope with a clear combinatorial meaning. T3 - ZIB-Report - 14-28 KW - set packing KW - matching KW - hypergraph KW - inequality KW - facet Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-51010 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Omont, Bertrand A1 - Sagnol, Guillaume A1 - Swarat, Elmar T1 - A Stackelberg game to optimize the distribution of controls in transportation networks N2 - We propose a game theoretic model for the spatial distribution of inspectors on a transportation network. The problem is to spread out the controls so as to enforce the payment of a transit toll. We formulate a linear program to find the control distribution which maximizes the expected toll revenue, and a mixed integer program for the problem of minimizing the number of evaders. Furthermore, we show that the problem of finding an optimal mixed strategy for a coalition of $N$ inspectors can be solved efficiently by a column generation procedure. Finally, we give experimental results from an application to the truck toll on German motorways. T3 - ZIB-Report - 12-15 KW - Stackelberg game KW - Polymatrix game KW - Controls in transportation networks Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14995 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Sagnol, Guillaume A1 - Schwartz, Stephan T1 - An Extended Network Interdiction Problem for Optimal Toll Control N2 - We study an extension of the shortest path network interdiction problem and present a novel real-world application in this area. We consider the problem of determining optimal locations for toll control stations on the arcs of a transportation network. We handle the fact that drivers can avoid control stations on parallel secondary roads. The problem is formulated as a mixed integer program and solved using Benders decomposition. We present experimental results for the application of our models to German motorways. T3 - ZIB-Report - 15-32 KW - network interdiction Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-55405 SN - 1438-0064 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Buwaya, Julia A1 - Sagnol, Guillaume A1 - Swarat, Elmar T1 - Network spot-checking games: Theory and application to toll enforcing in transportation networks JF - Networks N2 - We introduce the class of spot-checking games (SC games). These games model problems where the goal is to distribute fare inspectors over a toll network. In an SC game, the pure strategies of network users correspond to paths in a graph, and the pure strategies of the inspectors are subset of arcs to be controlled. Although SC games are not zero-sum, we show that a Nash equilibrium can be computed by linear programming. The computation of a strong Stackelberg equilibrium (SSE) is more relevant for this problem and we give a mixed integer programming (MIP) formulation for this problem. We show that the computation of such an equilibrium is NP-hard. More generally, we prove that it is NP-hard to compute a SSE in a polymatrix game, even if the game is pairwise zero-sum. Then, we give some bounds on the price of spite, which measures how the payoff of the inspector degrades when committing to a Nash equilibrium. Finally, we report computational experiments on instances constructed from real data, for an application to the enforcement of a truck toll in Germany. These numerical results show the efficiency of the proposed methods, as well as the quality of the bounds derived in this article. Y1 - 2015 U6 - https://doi.org/10.1002/net.21596 VL - 65 SP - 312 EP - 328 PB - Wiley Periodicals, Inc. ER - TY - CHAP A1 - Sagnol, Guillaume A1 - Borndörfer, Ralf A1 - Schlechte, Thomas A1 - Swarat, Elmar ED - Lavi, Ron T1 - The Price of Spite in Spot-checking games T2 - 7th International Symposium on Algorithmic Game Theory (SAGT'2014) N2 - We introduce the class of spot-checking games (SC games). These games model problems where the goal is to distribute fare inspectors over a toll network. Although SC games are not zero-sum, we show that a Nash equilibrium can be computed by linear programming. The computation of a strong Stackelberg equilibrium is more relevant for this problem, but we show that this is NP-hard. However, we give some bounds on the \emph{price of spite}, which measures how the payoff of the inspector degrades when committing to a Nash equilibrium. Finally, we demonstrate the quality of these bounds for a real-world application, namely the enforcement of a truck toll on German motorways. Y1 - 2014 SN - 978-3-662-44802-1 U6 - https://doi.org/10.1007/978-3-662-44803-8 N1 - Brief Announcement included in Back Matter p. 293 following VL - 8768 SP - 293 PB - Springer 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 - 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 - CHAP A1 - Borndörfer, Ralf A1 - Hoppmann, Heide A1 - Karbstein, Marika T1 - Umsteigen ohne Warten T2 - HEUREKA 2017 N2 - Wir stellen einen mathematischen Optimierungsansatz zur Berechnung von periodischen Taktfahrplänen vor, bei dem die Umsteigezeiten unter Berücksichtigung des Passagierverhaltens minimiert werden. Wir untersuchen damit den Einfluss wichtiger Systemparameter und Verhaltensmuster auf die Beförderungsqualität. Y1 - 2017 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Hoppmann, Heide A1 - Karbstein, Marika T1 - Passenger Routing for Periodic Timetable Optimization N2 - The task of periodic timetabling is to schedule the trips in a public transport system by determining arrival and departure times at every station such that travel and transfer times are minimized. To date, the optimization literature generally assumes that passengers do not respond to changes in the timetable, i.e., the passenger routes are fixed. This is unrealistic and ignores potentially valuable degrees of freedom. We investigate in this paper periodic timetabling models with integrated passenger routing. We show that different routing models have a huge influence on the quality of the entire system: Whatever metric is applied, the performance ratios of timetables w.r.t. to different routing models can be arbitrarily large. Computations on a real-world instance for the city of Wuppertal substantiate the theoretical findings. These results indicate the existence of untapped optimization potentials that can be used to improve the efficiency of public transport systems. T3 - ZIB-Report - 15-55 KW - Passenger routing KW - Periodic timetabling KW - Public transport Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-56739 SN - 1438-0064 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 - JOUR A1 - Blanco, Marco A1 - Borndörfer, Ralf A1 - Brückner, Michael A1 - Hoang, Nam-Dung A1 - Schlechte, Thomas T1 - On the Path Avoiding Forbidden Pairs Polytope JF - Electronic Notes in Discrete Mathematics N2 - Given a directed, acyclic graph, a source and a sink node, and a set of forbidden pairs of arcs, the path avoiding forbidden pairs (PAFP) problem is to find a path that connects the source and sink nodes and contains at most one arc from each forbidden pair. The general version of the problem is NP-hard, but it becomes polynomially solvable for certain topological configurations of the pairs. We present the first polyhedral study of the PAFP problem. We introduce a new family of valid inequalities for the PAFP polytope and show that they are sufficient to provide a complete linear description in the special case where the forbidden pairs satisfy a disjointness property. Furthermore, we show that the number of facets of the PAFP polytope is exponential in the size of the graph, even for the case of a single forbidden pair. Y1 - 2015 U6 - https://doi.org/10.1016/j.endm.2015.07.057 VL - 50 SP - 343 EP - 348 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Karbstein, Marika T1 - Neue Planungsinstrumente nutzen: Das Verkehrsangebot verbessern und Kosten sparen N2 - Wir illustrieren anhand des Liniennetzes der Stadt Potsdam das Potenzial mathematischer Methoden der Angebotsplanung. Wir zeigen, dass das "bestmögliche" Verkehrsangebot stark von planerischen Vorgaben beeinflusst wird, mit denen man die Erreichung unterschiedlicher und teilweise gegenläufiger Ziele steuern kann. Die Komplexität des Systems führt zum Auftreten von Rückkoppelungseffekten, die man nicht mit Hilfe von Daumenregeln beherrschen kann. Vielmehr ist der Einsatz moderner Planungsverfahren in einer interdisziplinären Zusammenarbeit von politischen Entscheidungsträgern, Verkehrsingenieuren und Mathematikern notwendig, um die aktuellen Herausforderungen in der Verkehrsplanung zu meistern. Der Artikel dokumentiert einen Beitrag zum 7. ÖPNV Innovationskongress des Ministeriums für Verkehr und Infrastruktur des Landes Baden-Württemberg, der vom 9.-11. März 2015 in Freiburg stattfand. T3 - ZIB-Report - 15-33 KW - Linienplan KW - Optimierung Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-55439 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Hoppmann, Heide A1 - Karbstein, Marika T1 - Timetabling and Passenger Routing in Public Transport T2 - Appeard in: Proceedings of Conference on Advanced Systems in Public Transport 2015 (CASPT2015) N2 - The task of timetabling is to schedule the trips in a public transport system by determining periodic arrival and departure times at every station. The goal is to provide a service that is both attractive for passengers and can be operated economically. To date, timetable optimization is generally done with respect to fixed passenger routes, i.e., it is assumed that passengers do not respond to changes in the timetable. This is unrealistic and ignores potentially valuable degrees of freedom. We investigate in this paper periodic timetabling models with integrated passenger routing. We propose several models that differ in the allowed passenger paths and the objectives. We compare these models theoretically and report on computations on real-world instances for the city of Wuppertal. T3 - ZIB-Report - 15-31 KW - Passenger routing KW - Periodic timetabling KW - Public transport Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-55305 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Hoppmann, Heide A1 - Karbstein, Marika T1 - Umsteigen ohne Warten N2 - Wir stellen einen mathematischen Optimierungsansatz zur Berechnung von periodischen Taktfahrplänen vor, bei dem die Umsteigezeiten unter Berücksichtigung des Passagierverhaltens minimiert werden. Wir untersuchen damit den Einfluss wichtiger Systemparameter und Verhaltensmuster auf die Beförderungsqualität. T3 - ZIB-Report - 17-05 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-62006 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 - CHAP A1 - Schenker, Sebastian A1 - Vierhaus, Ingmar A1 - Borndörfer, Ralf A1 - Fügenschuh, Armin A1 - Skutella, Martin ED - Stark, Rainer ED - Seliger, Günther ED - Bonvoisin, Jérémy T1 - Optimisation Methods in Sustainable Manufacturing BT - Challenges, Solutions and Implementation Perspectives T2 - Sustainable Manufacturing N2 - Sustainable manufacturing is driven by the insight that the focus on the economic dimension in current businesses and lifestyles has to be broadened to cover all three pillars of sustainability: economic development, social development, and environmental protection. Y1 - 2017 SN - 978-3-319-48514-0 U6 - https://doi.org/10.1007/978-3-319-48514-0_15 SP - 239 EP - 253 PB - Springer International Publishing ER - TY - GEN A1 - Borndörfer, Ralf A1 - Schulz, Christof A1 - Seidl, Stephan A1 - Weider, Steffen T1 - Integration of Duty Scheduling and Rostering to Increase Driver Satisfaction N2 - 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. T3 - ZIB-Report - 15-50 KW - Benders decomposition KW - driver satisfaction KW - duty templates KW - duty scheduling KW - rostering Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-56299 SN - 1438-0064 ER - TY - GEN A1 - Beckenbach, Isabel A1 - Borndörfer, Ralf T1 - A Hall Condition for Normal Hypergraphs N2 - Conforti, Cornuéjols, Kapoor, and Vusković gave a Hall-type condition for the non-existence of a perfect matching in a balanced hypergraph. We generalize this result to the class of normal hypergraphs. T3 - ZIB-Report - 15-45 KW - Matchings in hypergraphs KW - Normal hypergraphs KW - Hall condition Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-56175 SN - 1438-0064 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Karbstein, Marika T1 - Neue Planungsinstrumente nutzen: Das Verkehrsangebot verbessern und Kosten sparen JF - Verkehr und Technik N2 - Wir illustrieren anhand des Liniennetzes der Stadt Potsdam das Potenzial mathematischer Methoden der Angebotsplanung. Wir zeigen, dass das "bestmögliche" Verkehrsangebot stark von planerischen Vorgaben beeinflusst wird, mit denen man die Erreichung unterschiedlicher und teilweise gegenläufiger Ziele steuern kann. Die Komplexität des Systems führt zum Auftreten von Rückkoppelungseffekten, die man nicht mit Hilfe von Daumenregeln beherrschen kann. Vielmehr ist der Einsatz moderner Planungsverfahren in einer interdisziplinären Zusammenarbeit von politischen Entscheidungsträgern, Verkehrsingenieuren und Mathematikern notwendig, um die aktuellen Herausforderungen in der Verkehrsplanung zu meistern. Der Artikel dokumentiert einen Beitrag zum 7. ÖPNV Innovationskongress des Ministeriums für Verkehr und Infrastruktur des Landes Baden-Württemberg, der vom 9.-11. März 2015 in Freiburg stattfand. Y1 - 2015 VL - 68 IS - 7 SP - 239 EP - 243 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Hoppmann, Heide A1 - Karbstein, Marika T1 - Timetabling and Passenger Routing in Public Transport T2 - Proceedings of Conference on Advanced Systems in Public Transport 2015 (CASPT2015) N2 - The task of timetabling is to schedule the trips in a public transport system by determining periodic arrival and departure times at every station. The goal is to provide a service that is both attractive for passengers and can be operated economically. To date, timetable optimization is generally done with respect to fixed passenger routes, i.e., it is assumed that passengers do not respond to changes in the timetable. This is unrealistic and ignores potentially valuable degrees of freedom. We investigate in this paper periodic timetabling models with integrated passenger routing. We propose several models that differ in the allowed passenger paths and the objectives. We compare these models theoretically and report on computations on real-world instances for the city of Wuppertal. KW - Passenger routing KW - Periodic timetabling KW - Public transport Y1 - 2015 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Sagnol, Guillaume A1 - Schlechte, Thomas A1 - Swarat, Elmar T1 - Optimal Toll Enforcement - an Integration of Vehicle Routing and Duty Rostering N2 - We present the problem of planning mobile tours of inspectors on German motorways to enforce the payment of the toll for heavy good trucks. This is a special type of vehicle routing problem with the objective to conduct as good inspections as possible on the complete network. In addition, the crews of the tours have to be scheduled. Thus, we developed a personalized crew rostering model. The planning of daily tours and the rostering are combined in a novel integrated approach and formulated as a complex and large scale Integer Program. The paper focuses first on different requirements for the rostering and how they can be modeled in detail. The second focus is on a bicriterion analysis of the planning problem to find the balance between the control quality and the roster acceptance. On the one hand the tour planning is a profit maximization problem and on the other hand the rostering should be made in a employee friendly way. Finally, computational results on real-world instances show the practicability of our method. T3 - ZIB-Report - 13-79 KW - vehicle routing KW - crew rostering KW - integer programming KW - bicriteria optimization Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-45107 SN - 1438-0064 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 - 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 - Heismann, Olga T1 - The Hypergraph Assignment Problem N2 - The hypergraph assignment problem (HAP) is the generalization of assignments from directed graphs to directed hypergraphs. It serves, in particular, as a universal tool to model several train composition rules in vehicle rotation planning for long distance passenger railways. We prove that even for problems with a small hyperarc size and hypergraphs with a special partitioned structure the HAP is NP-hard and APX-hard. Further, we present an extended integer linear programming formulation which implies, e. g., all clique inequalities. T3 - ZIB-Report - 12-14 KW - directed hypergraphs KW - hyperassignment KW - assignment Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14822 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 - Langenhan, Andreas A1 - Löbel, Andreas A1 - Schulz, Christof A1 - Weider, Steffen T1 - Duty Scheduling Templates N2 - 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. T3 - ZIB-Report - 12-09 KW - duty scheduling KW - duty templates Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14699 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Löbel, Andreas T1 - Alcuin's Transportation Problems and Integer Programming N2 - The need to solve {\it transportation problems\/} was and still is one of the driving forces behind the development of the mathematical disciplines of graph theory, optimization, and operations research. Transportation problems seem to occur for the first time in the literature in the form of the four ''River Crossing Problems'' in the book Propositiones ad acuendos iuvenes. The {\it Propositiones\/} ---the oldest collection of mathematical problems written in Latin--- date back to the $8$th century A.D. and are attributed to Alcuin of York, one of the leading scholars of his time, a royal advisor to Charlemagne at his Frankish court. Alcuin's river crossing problems had no impact on the development of mathematics. However, they already display all the characteristics of today's large-scale real transportation problems. From our point of view, they could have been the starting point of combinatorics, optimization, and operations research. We show the potential of Alcuin's problems in this respect by investigating his problem~18 about a wolf, a goat and a bunch of cabbages with current mathematical methods. This way, we also provide the reader with a leisurely introduction into the modern theory of integer programming. T3 - ZIB-Report - SC-95-27 Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-1932 ER - TY - CHAP A1 - Euler, Ricardo A1 - Borndörfer, Ralf A1 - Puchert, Christian A1 - Takkula, Tuomo T1 - ULD Build-Up Scheduling with Logic-Based Benders Decomposition T2 - Integration of Constraint Programming, Artificial Intelligence, and Operations Research N2 - We study a complex planning and scheduling problem arising from the build-up process of air cargo pallets and containers, collectively referred to as unit load devices (ULD), in which ULDs must be assigned to workstations for loading. Since air freight usually becomes available gradually along the planning horizon, ULD build-ups must be scheduled neither too early to avoid underutilizing ULD capacity, nor too late to avoid resource conflicts with other flights. Whenever possible, ULDs should be built up in batches, thereby giving ground handlers more freedom to rearrange cargo and utilize the ULD's capacity efficiently. The resulting scheduling problem has an intricate cost function and produces large time-expanded models, especially for longer planning horizons. We propose a logic-based Benders decomposition approach that assigns batches to time intervals and workstations in the master problem, while the actual schedule is decided in a subproblem. By choosing appropriate intervals, the subproblem becomes a feasibility problem that decomposes over the workstations. Additionally, the similarity of many batches is exploited by a strengthening procedure for no-good cuts. We benchmark our approach against a time-expanded MIP formulation from the literature on a publicly available data set. It solves 15% more instances to optimality and decreases run times by more than 50% in the geometric mean. This improvement is especially pronounced for longer planning horizons of up to one week, where the Benders approach solves over 50% instances more than the baseline Y1 - 2024 U6 - https://doi.org/10.1007/978-3-031-60597-0_17 VL - 14742 SP - 259 EP - 276 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Euler, Ricardo A1 - Karbstein, Marika T1 - Ein Graphen-basiertes Modell zur Beschreibung von Preissystemen im öffentlichen Nahverkehr JF - HEUREKA 21 N2 - In dieser Arbeit wird ein graphenbasiertes Modell zur Einbindung von Preissystemen des öffentlichen Nahverkehrs in Routing-Algorithmen vorgestellt. Jeder Knoten des Graphen repräsentiert einen abstrakten Preiszustand einer Route und ist an einen tatsächlichen Preis gekoppelt. Damit sind sehr einfache und konzise Beschreibungen von Tarifstrukturen möglich, diesich algorithmisch behandeln lassen. Durch das zeitgleiche Tracken eines Pfades im Routinggraphen im Ticketgraphen kann schon während einer Routenberechnung der Preis bestimmt werden. Dies ermöglicht die Berechnung von preisoptimalen Routen. An den Tarifsystemen der Verkehrsverbünde MDV (Mitteldeutscher Verkehrsverbund) und VBB (Verkehrsverbund Berlin-Brandenburg) wird die Konstruktion des Modells detailliert erläutert. Y1 - 2021 UR - https://verlag.fgsv-datenbanken.de/tagungsbaende?kat=HEUREKA&subkat=FGSV+002%2F127+%282021%29&fanr=&va=&titel=&text=&autor=&tagungsband=1256&_titel=Ein+Graphen-basiertes+Modell+zur+Beschreibung+von+Preissystemen+im+%C3%B6ffentlichen+Nahverkehr VL - 002/127 SP - 1 EP - 15 PB - FGSV CY - Stuttgart ER - TY - GEN A1 - Maristany de las Casas, Pedro A1 - Sedeno-Noda, Antonio A1 - Borndörfer, Ralf T1 - An Improved Multiobjective Shortest Path Algorithm N2 - We present a new label-setting algorithm for the Multiobjective Shortest Path (MOSP) problem that computes the minimal complete set of efficient paths for a given instance. The size of the priority queue used in the algorithm is bounded by the number of nodes in the input graph and extracted labels are guaranteed to be efficient. These properties allow us to give a tight output-sensitive running time bound for the new algorithm that can almost be expressed in terms of the running time of Dijkstra's algorithm for the Shortest Path problem. Hence, we suggest to call the algorithm \emph{Multiobjective Dijkstra Algorithm} (MDA). The simplified label management in the MDA allows us to parallelize some subroutines. In our computational experiments, we compare the MDA and the classical label-setting MOSP algorithm by Martins', which we improved using new data structures and pruning techniques. On average, the MDA is $\times2$ to $\times9$ times faster on all used graph types. On some instances the speedup reaches an order of magnitude. T3 - ZIB-Report - 20-26 KW - Multiobjective Shortest Path Problem KW - Output-Sensitive Multiobjective Combinatorial Problems KW - Network Optimization Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-79712 SN - 1438-0064 ER - TY - GEN A1 - Prause, Felix A1 - Borndörfer, Ralf A1 - Grimm, Boris A1 - Tesch, Alexander T1 - Approximating the RSRP with Predictive Maintenance N2 - We study the solution of the rolling stock rotation problem with predictive maintenance (RSRP-PM) by an iterative refinement approach that is based on a state-expanded event-graph. In this graph, the states are parameters of a failure distribution, and paths correspond to vehicle rotations with associated health state approximations. An optimal set of paths including maintenance can be computed by solving an integer linear program. Afterwards, the graph is refined and the procedure repeated. An associated linear program gives rise to a lower bound that can be used to determine the solution quality. Computational results for two instances derived from real world timetables of a German railway company are presented. The results show the effectiveness of the approach and the quality of the solutions. T3 - ZIB-Report - 23-04 KW - Rolling Stock Rotation Planning KW - Predictive Maintenance KW - Integer Linear Programming KW - Heuristic KW - Lower Bound Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-89531 SN - 1438-0064 ER - TY - GEN A1 - Löbel, Fabian A1 - Borndörfer, Ralf A1 - Weider, Steffen T1 - Electric Bus Scheduling with Non-Linear Charging, Power Grid Bottlenecks, and Dynamic Recharge Rates N2 - 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. Y1 - 2024 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Löbel, Andreas A1 - Löbel, Fabian A1 - Weider, Steffen T1 - Solving the Electric Bus Scheduling Problem by an Integrated Flow and Set Partitioning Approach T2 - 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024) N2 - 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. Y1 - 2024 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0030-drops-211992 VL - 123 SP - 11:1 EP - 11:16 PB - Schloss Dagstuhl -- Leibniz-Zentrum für Informatik CY - Dagstuhl, Germany ER - TY - JOUR A1 - Prause, Felix A1 - Borndörfer, Ralf T1 - An Iterative Refinement Approach for the Rolling Stock Rotation Problem with Predictive Maintenance N2 - The rolling stock rotation problem with predictive maintenance (RSRP-PdM) involves the assignment of trips to a fleet of vehicles with integrated maintenance scheduling based on the predicted failure probability of the vehicles. These probabilities are determined by the health states of the vehicles, which are considered to be random variables distributed by a parameterized family of probability distribution functions. During the operation of the trips, the corresponding parameters get updated. In this article, we present a dual solution approach for RSRP-PdM and generalize a linear programming based lower bound for this problem to families of probability distribution functions with more than one parameter. For this purpose, we define a rounding function that allows for a consistent underestimation of the parameters and model the problem by a state-expanded event-graph in which the possible states are restricted to a discrete set. This induces a flow problem that is solved by an integer linear program. We show that the iterative refinement of the underlying discretization leads to solutions that converge from below to an optimal solution of the original instance. Thus, the linear relaxation of the considered integer linear program results in a lower bound for RSRP-PdM. Finally, we report on the results of computational experiments conducted on a library of test instances. Y1 - 2024 ER - TY - JOUR A1 - Prause, Felix A1 - Borndörfer, Ralf A1 - Grimm, Boris A1 - Tesch, Alexander T1 - Approximating rolling stock rotations with integrated predictive maintenance JF - Journal of Rail Transport Planning & Management N2 - We study the solution of the rolling stock rotation problem with predictive maintenance (RSRP-PdM) by an iterative refinement approach that is based on a state-expanded event-graph. In this graph, the states are parameters of a failure distribution, and paths correspond to vehicle rotations with associated health state approximations. An optimal set of paths including maintenance can be computed by solving an integer linear program. Afterwards, the graph is refined and the procedure repeated. An associated linear program gives rise to a lower bound that can be used to determine the solution quality. Computational results for six instances derived from real-world timetables of a German railway company are presented. The results show the effectiveness of the approach and the quality of the solutions. Y1 - 2024 U6 - https://doi.org/10.1016/j.jrtpm.2024.100434 VL - 30 SP - 100434 ER - TY - JOUR A1 - Sahin, Guvenc A1 - Digehsara, Amin Ahmadi A1 - Borndörfer, Ralf T1 - Efficient Algorithms for the Multi-Period Line Planning Problem in Public Transportation JF - Open Access Series in Informatics (OASIcs), 21st Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2021) N2 - In order to plan and schedule a demand-responsive public transportation system, both temporal and spatial changes in demand should be taken into account even at the line planning stage. We study the multi-period line planning problem with integrated decisions regarding dynamic allocation of vehicles among the lines. Given the NP-hard nature of the line planning problem, the multi-period version is clearly difficult to solve for large public transit networks even with advanced solvers. It becomes necessary to develop algorithms that are capable of solving even the very-large instances in reasonable time. For instances which belong to real public transit networks, we present results of a heuristic local branching algorithm and an exact approach based on constraint propagation. Y1 - 2021 U6 - https://doi.org/10.4230/OASIcs.ATMOS.2021.17 VL - 96 SP - 17:1 EP - 17:6 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Danecker, Fabian A1 - Weiser, Martin T1 - A Discrete-Continuous Algorithm for Free Flight Planning JF - Algorithms N2 - We propose a hybrid discrete-continuous algorithm for flight planning in free flight airspaces. In a first step, our DisCOptER method discrete-continuous optimization for enhanced resolution) computes a globally optimal approximate flight path on a discretization of the problem using the A* method. This route initializes a Newton method that converges rapidly to the smooth optimum in a second step. The correctness, accuracy, and complexity of the method are goverened by the choice of the crossover point that determines the coarseness of the discretization. We analyze the optimal choice of the crossover point and demonstrate the asymtotic superority of DisCOptER over a purely discrete approach. KW - shortest path KW - flight planning KW - free flight KW - discrete-continuous algorithm KW - optimal control KW - discrete optimization Y1 - 2020 U6 - https://doi.org/10.3390/a14010004 SN - 1438-0064 VL - 14 IS - 1 SP - 4 PB - MDPI ER - TY - GEN A1 - Prause, Felix A1 - Borndörfer, Ralf T1 - Construction of a Test Library for the Rolling Stock Rotation Problem with Predictive Maintenance N2 - We describe the development of a test library for the rolling stock rotation problem with predictive maintenance (RSRP-PdM). Our approach involves the utilization of genuine timetables from a private German railroad company. The generated instances incorporate probability distribution functions for modeling the health states of the vehicles and the considered trips possess varying degradation functions. RSRP-PdM involves assigning trips to a fleet of vehicles and scheduling their maintenance based on their individual health states. The goal is to minimize the total costs consisting of operational costs and the expected costs associated with vehicle failures. The failure probability is dependent on the health states of the vehicles, which are assumed to be random variables distributed by a family of probability distributions. Each distribution is represented by the parameters characterizing it and during the operation of the trips, these parameters get altered. Our approach incorporates non-linear degradation functions to describe the inference of the parameters but also linear ones could be applied. The resulting instances consist of the timetables of the individual lines that use the same vehicle type. Overall, we employ these assumptions and utilize open-source data to create a library of instances with varying difficulty. Our approach is vital for evaluating and comparing algorithms designed to solve the RSRP-PdM. T3 - ZIB-Report - 23-20 KW - Rolling Stock Rotation Planning KW - Predictive Maintenance KW - Test Library Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-91734 SN - 1438-0064 ER - TY - GEN A1 - Löbel, Fabian A1 - Borndörfer, Ralf A1 - Weider, Steffen T1 - Non-Linear Battery Behavior in Electric Vehicle Scheduling Problems N2 - 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. T3 - ZIB-Report - 23-24 KW - Electric Vehicle Scheduling KW - Non-Linear Charging Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-92441 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 - JOUR A1 - Sahin, Guvenc A1 - Ahmadi, Amin A1 - Borndörfer, Ralf A1 - Schlechte, Thomas T1 - Multi-period line planning with resource transfers JF - Transportation Research Part C: Emerging Technologies N2 - Urban transportation systems are subject to a high level of variation and fluctuation in demand over the day. When this variation and fluctuation are observed in both time and space, it is crucial to develop line plans that are responsive to demand. A multi-period line planning approach that considers a changing demand during the planning horizon is proposed. If such systems are also subject to limitations of resources, a dynamic transfer of resources from one line to another throughout the planning horizon should also be considered. A mathematical modelling framework is developed to solve the line planning problem with a cost-oriented approach considering transfer of resources during a finite length planning horizon of multiple periods. We use real-life public transportation network data for our computational results. We analyze whether or not multi-period solutions outperform single period solutions in terms of feasibility and relevant costs. The importance of demand variation on multi-period solutions is investigated. We evaluate the impact of resource transfer constraints on the effectiveness of solutions. We also study the effect of period lengths along with the problem parameters that are significant for and sensitive to the optimality of solutions. Y1 - 2020 U6 - https://doi.org/10.1016/j.trc.2020.102726 VL - 119 SP - 102726 ER - TY - CHAP A1 - Löbel, Fabian A1 - Borndörfer, Ralf A1 - Weider, Steffen T1 - Non-Linear Charge Functions for Electric Vehicle Scheduling with Dynamic Recharge Rates T2 - 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023) N2 - 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. Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0030-drops-187765 VL - 115 SP - 15:1 EP - 15:6 ER - TY - JOUR A1 - Euler, Ricardo A1 - Lindner, Niels A1 - Borndörfer, Ralf T1 - Price optimal routing in public transportation JF - EURO Journal on Transportation and Logistics KW - Management Science and Operations Research KW - Transportation KW - Modeling and Simulation Y1 - 2024 U6 - https://doi.org/10.1016/j.ejtl.2024.100128 SN - 2192-4376 VL - 13 SP - 1 EP - 15 PB - Elsevier BV ER - TY - JOUR A1 - Euler, Ricardo A1 - Maristany de las Casas, Pedro A1 - Borndörfer, Ralf T1 - Logic-Constrained Shortest Paths for Flight Planning N2 - The Logic-Constrained Shortest Path Problem (LCSP) combines a one-to-one shortest path problem with satisfiability constraints imposed on the routing graph. This setting arises in flight planning, where air traffic control (ATC) authorities are enforcing a set of traffic flow restrictions (TFRs) on aircraft routes in order to increase safety and throughput. We propose a new branch and bound-based algorithm for the LCSP. The resulting algorithm has three main degrees of freedom: the node selection rule, the branching rule and the conflict. While node selection and branching rules have been long studied in the MIP and SAT communities, most of them cannot be applied out of the box for the LCSP. We review the existing literature and develop tailored variants of the most prominent rules. The conflict, the set of variables to which the branching rule is applied, is unique to the LCSP. We analyze its theoretical impact on the B&B algorithm. In the second part of the paper, we show how to model the Flight Planning Problem with TFRs as an LCSP and solve it using the branch and bound algorithm. We demonstrate the algorithm’s efficiency on a dataset consisting of a global flight graph and a set of around 20000 real TFRs obtained from our industry partner Lufthansa Systems GmbH. We make this dataset publicly available. Finally, we conduct an empirical in-depth analysis of node selection rules, branching rules and conflicts. Carefully choosing an appropriate combination yields an improvement of an order of magnitude compared to an uninformed choice. Y1 - 2024 ER - TY - JOUR A1 - Maristany de las Casas, Pedro A1 - Sedeno-Noda, Antonio A1 - Borndörfer, Ralf T1 - An Improved Multiobjective Shortest Path Algorithm JF - Computers & Operations Research N2 - We present a new label-setting algorithm for the Multiobjective Shortest Path (MOSP) problem that computes a minimum complete set of efficient paths for a given instance. The size of the priority queue used in the algorithm is bounded by the number of nodes in the input graph and extracted labels are guaranteed to be efficient. These properties allow us to give a tight output-sensitive running time bound for the new algorithm that can almost be expressed in terms of the running time of Dijkstra’s algorithm for the Shortest Path problem. Hence, we suggest to call the algorithm Multiobjective Dijkstra Algorithm (MDA). The simplified label management in the MDA allows us to parallelize some subroutines. In our computational experiments, we compare the MDA and the classical label-setting MOSP algorithm by Martins, which we improved using new data structures and pruning techniques. On average, the MDA is 2 to 9 times faster on all used graph types. On some instances the speedup reaches an order of magnitude. Y1 - 2021 U6 - https://doi.org/10.1016/j.cor.2021.105424 VL - 135 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 - JOUR A1 - Maristany de las Casas, Pedro A1 - Borndörfer, Ralf A1 - Kraus, Luitgard A1 - Sedeño-Noda, Antonio T1 - An FPTAS for Dynamic Multiobjective Shortest Path Problems JF - Algorithms N2 - The Dynamic Multiobjective Shortest Path problem features multidimensional costs that can depend on several variables and not only on time; this setting is motivated by flight planning applications and the routing of electric vehicles. We give an exact algorithm for the FIFO case and derive from it an FPTAS for both, the static Multiobjective Shortest Path (MOSP) problems and, under mild assumptions, for the dynamic problem variant. The resulting FPTAS is computationally efficient and beats the known complexity bounds of other FPTAS for MOSP problems. Y1 - 2021 U6 - https://doi.org/https://doi.org/10.3390/a14020043 VL - 14 IS - 2 SP - 1 EP - 22 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Danecker, Fabian A1 - Weiser, Martin T1 - Newton's Method for Global Free Flight Trajectory Optimization N2 - Globally optimal free flight trajectory optimization can be achieved with a combination of discrete and continuous optimization. A key requirement is that Newton's method for continuous optimization converges in a sufficiently large neighborhood around a minimizer. We show in this paper that, under certain assumptions, this is the case. T3 - ZIB-Report - 23-08 Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-89876 ER - TY - JOUR A1 - Euler, Ricardo A1 - Lindner, Niels A1 - Borndörfer, Ralf T1 - Price Optimal Routing in Public Transportation N2 - We consider the price-optimal earliest arrival problem in public transit (POEAP) in which we aim to calculate the Pareto-front of journeys with respect to ticket price and arrival time in a public transportation network. Public transit fare structures are often a combination of various fare strategies such as, e.g., distance-based fares, zone-based fares or flat fares. The rules that determine the actual ticket price are often very complex. Accordingly, fare structures are notoriously difficult to model as it is in general not sufficient to simply assign costs to arcs in a routing graph. Research into POEAP is scarce and usually either relies on heuristics or only considers restrictive fare models that are too limited to cover the full scope of most real-world applications. We therefore introduce conditional fare networks (CFNs), the first framework for representing a large number of real-world fare structures. We show that by relaxing label domination criteria, CFNs can be used as a building block in label-setting multi-objective shortest path algorithms. By the nature of their extensive modeling capabilities, optimizing over CFNs is NP-hard. However, we demonstrate that adapting the multi-criteria RAPTOR (MCRAP) algorithm for CFNs yields an algorithm capable of solving POEAP to optimality in less than 400 ms on average on a real-world data set. By restricting the size of the Pareto-set, running times are further reduced to below 10 ms. Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-86414 ER - TY - CHAP A1 - Euler, Ricardo A1 - Borndörfer, Ralf A1 - Strunk, Timo A1 - Takkula, Tuomo T1 - ULD Build-Up Scheduling with Dynamic Batching in an Air Freight Hub T2 - Operations Research Proceedings 2021 N2 - Air freight is usually shipped in standardized unit load devices (ULDs). The planning process for the consolidation of transit cargo from inbound flights or locally emerging shipments into ULDs for outbound flights is called build-up scheduling. More specifically, outbound ULDs must be assigned a time and a workstation subject to both workstation capacity constraints and the availability of shipments which in turn depends on break-down decisions for incoming ULDs. ULDs scheduled for the same outbound flight should be built up in temporal and spatial proximity. This serves both to minimize overhead in transportation times and to allow workers to move freight between ULDs. We propose to address this requirement by processing ULDs for the same outbound flight in batches. For the above build-up scheduling problem, we introduce a multi-commodity network design model. Outbound flights are modeled as commodities; transit cargo is represented by cargo flow volume and unpack and batch decisions are represented as design variables. The model is solved with a standard MIP solver on a set of benchmark data. For instances with a limited number of resource conflicts, near-optimal solutions are found in under two hours for a whole week of operations. Y1 - 2022 U6 - https://doi.org/10.1007/978-3-031-08623-6_38 SP - 254 EP - 260 ER - TY - JOUR A1 - Maristany de las Casas, Pedro A1 - Kraus, Luitgard A1 - Sedeno-Noda, Antonio A1 - Borndörfer, Ralf T1 - Targeted multiobjective Dijkstra Algorithm JF - Networks N2 - We introduce the Targeted Multiobjective Dijkstra Algorithm (T-MDA), a label setting algorithm for the One-to-One Multiobjective Shortest Path (MOSP) Problem. It is based on the recently published Multiobjective Dijkstra Algorithm (MDA) and equips it with A*-like techniques. For any explored subpath, a label setting MOSP algorithm decides whether the subpath can be discarded or must be stored as part of the output. A major design choice is how to store subpaths from the moment they are first explored until the mentioned final decision can be made. The T-MDA combines the polynomially bounded size of the priority queue used in the MDA and alazy management of paths that are not in the queue. The running time bounds from the MDA remain valid. In practice, the T-MDA outperforms known algorithms from the literature and the increased memory consumption is negligible. In this paper, we benchmark the T-MDA against an improved version of the state of the art NAMOA∗drOne-to-One MOSP algorithm from the literature on a standard testbed. Y1 - 2023 U6 - https://doi.org/10.1002/net.22174 VL - 82 IS - 3 SP - 277 EP - 298 ER - TY - CHAP A1 - Masing, Berenike A1 - Lindner, Niels A1 - Borndörfer, Ralf ED - Trautmann, Norbert ED - Drägi, Mario T1 - Optimal Line Plans in the Parametric City and the Impact of In-Motion Costs T2 - Operations Research Proceedings 2021 N2 - Line planning in public transport involves determining vehicle routes and assigning frequencies of service such that travel demands are satisfied. We evaluate how line plans, which are optimal with respect to in-motion costs (IMC), the objective function depending purely on arc-lengths for both user and operator costs, performs with respect to the value of resources consumed (VRC). The latter is an elaborate, socio-economic cost function which includes discomfort caused by delay, boarding and alighting times, and transfers. Even though discomfort is a large contributing factor to VRC and is entirely disregarded in IMC,  we observe that the two cost functions are qualitatively comparable. Y1 - 2022 SN - 978-3-031-08623-6 U6 - https://doi.org/10.1007/978-3-031-08623-6_44 SP - 295 EP - 301 PB - Springer, Cham ER - TY - CHAP A1 - Blanco, Marco A1 - Borndörfer, Ralf A1 - Maristany de las Casas, Pedro T1 - An A* Algorithm for Flight Planning Based on Idealized Vertical Profiles T2 - 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022) N2 - The Flight Planning Problem is to find a minimum fuel trajectory between two airports in a 3D airway network under consideration of the wind. We show that this problem is NP-hard, even in its most basic version. We then present a novel A∗ heuristic, whose potential function is derived from an idealized vertical profile over the remaining flight distance. This potential is, under rather general assumptions, both admissible and consistent and it can be computed efficiently. The method outperforms the state-of-the-art heuristic on real-life instances. Y1 - 2022 U6 - https://doi.org/10.4230/OASIcs.ATMOS.2022.1 VL - 106 SP - 1:1 EP - 1:15 ER - TY - JOUR A1 - Masing, Berenike A1 - Lindner, Niels A1 - Borndörfer, Ralf T1 - The price of symmetric line plans in the Parametric City JF - Transportation Research Part B: Methodological N2 - We consider the line planning problem in public transport in the Parametric City, an idealized model that captures typical scenarios by a (small) number of parameters. The Parametric City is rotation symmetric, but optimal line plans are not always symmetric. This raises the question to quantify the symmetry gap between the best symmetric and the overall best solution. For our analysis, we formulate the line planning problem as a mixed integer linear program, that can be solved in polynomial time if the solutions are forced to be symmetric. We prove that the symmetry gap is small when a specific Parametric City parameter is fixed, and we give an approximation algorithm for line planning in the Parametric City in this case. While the symmetry gap can be arbitrarily large in general, we show that symmetric line plans are a good choice in most practical situations. Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-88613 VL - 166 SP - 419 EP - 443 ER - TY - CHAP A1 - Grimm, Boris A1 - Borndörfer, Ralf A1 - Bushe, Julian T1 - Assignment Based Resource Constrained Path Generation for Railway Rolling Stock Optimization T2 - 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023) N2 - The fundamental task of every passenger railway operator is to offer an attractive railway timetable to the passengers while operating it as cost efficiently as possible. The available rolling stock has to be assigned to trips so that all trips are operated, operational requirements are satisfied, and the operating costs are minimum. This so-called Rolling Stock Rotation Problem (RSRP) is well studied in the literature. In this paper we consider an acyclic version of the RSRP that includes vehicle maintenance. As the latter is an important aspect, maintenance services have to be planned simultaneously to ensure the rotation’s feasibility in practice. Indeed, regular maintenance is important for the safety and reliability of the rolling stock as well as enforced by law in many countries. We present a new integer programming formulation that links a hyperflow to model vehicle compositions and their coupling decisions to a set of path variables that take care of the resource consumption of the individual vehicles. To solve the model we developed different column generation algorithms which are compared to each other as well as to the MILP flow formulation of [Ralf Borndörfer et al., 2016] on a test set of real world instances. Y1 - 2023 U6 - https://doi.org/https://doi.org/10.4230/OASIcs.ATMOS.2023.13 VL - 115 SP - 13:1 EP - 13:15 PB - Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik CY - Dagstuhl, Germany ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Grimm, Boris A1 - Schade, Stanley T1 - A Robustness Analysis of Long Distance Train Crew Schedules in Germany T2 - Proceedings Of The Fifth Iinternational Conference On Railway Technology: Research, Development and Maintenance N2 - Nowadays railway networks are highly complex and often very fragile systems. A wide variety of individual operations that influence each other have to go hand in hand to end up with a smoothly and efficiently running system. Many of these operations suffer from uncertainty as trains could be delayed, the signaling system be disrupted or scheduled crews could be ill. Usually these opartions could be organized hierarchically from long term strategical decisions to real time decision management. Each stage in the hierarchy defines a different mathematical optimization problem, which is solved sequentially. At every stage the knowledge about preceding or succeeding planning stages may vary and also the interaction between two stages in this chain of problems may vary from almost no interaction to highly dependent situations. This paper deals with a topic that is an example for the latter case, namely the interaction between vehicle schedules, vehicle punctuality, and crew schedules. To reduce the number of potential rescheduling actions we developed a software tool in cooperation with our practical partner DB Fernverkehr AG (DBF) to predict a certain set of critical crew schedules. This tool evaluates, predicts, and determines "bottlenecks" in the crew schedule in the sense of potentially required rescheduling actions due to likely delays. The approach was tested on real life crew and train timetable data of DBF and can be regarded as the computation of key performance indicators, which is often desired. For our experiments we had access to the operated timetable and crew schedule of DBF for periods of two and six weeks in 2019. Y1 - 2023 U6 - https://doi.org/10.4203/ccc.1.23.17 SN - 2753-3239 VL - CCC 1 ER - TY - CHAP A1 - Löbel, Fabian A1 - Lindner, Niels A1 - Borndörfer, Ralf ED - Neufeld, Janis S. ED - Buscher, Udo ED - Lasch, Rainer ED - Möst, Dominik ED - Schönberger, Jörn T1 - The Restricted Modulo Network Simplex Method for Integrated Periodic Timetabling and Passenger Routing T2 - Operations Research Proceedings 2019 N2 - The Periodic Event Scheduling Problem is a well-studied NP-hard problem with applications in public transportation to find good periodic timetables. Among the most powerful heuristics to solve the periodic timetabling problem is the modulo network simplex method. In this paper, we consider the more difficult version with integrated passenger routing and propose a refined integrated variant to solve this problem on real-world-based instances. Y1 - 2020 SN - 978-3-030-48438-5 U6 - https://doi.org/https://doi.org/10.1007/978-3-030-48439-2_92 SP - 757 EP - 763 PB - Springer International Publishing CY - Cham ER - TY - JOUR A1 - Breugem, Thomas A1 - Schlechte, Thomas A1 - Schulz, Christof A1 - Borndörfer, Ralf T1 - A three-phase heuristic for the Fairness-Oriented Crew Rostering Problem JF - Computers & Operations Research N2 - The Fairness-Oriented Crew Rostering Problem (FCRP) considers the joint optimization of attractiveness and fairness in cyclic crew rostering. Like many problems in scheduling and logistics, the combinatorial complexity of cyclic rostering causes exact methods to fail for large-scale practical instances. In case of the FCRP, this is accentuated by the additionally imposed fairness requirements. Hence, heuristic methods are necessary. We present a three-phase heuristic for the FCRP combining column generation techniques with variable-depth neighborhood search. The heuristic exploits different mathematical formulations to find feasible solutions and to search for improvements. We apply our methodology to practical instances from Netherlands Railways (NS), the main passenger railway operator in the Netherlands Our results show the three-phase heuristic finds good solutions for most instances and outperforms a state-of-the-art commercial solver. Y1 - 2023 U6 - https://doi.org/10.1016/j.cor.2023.106186 VL - 154 SP - 106186 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Danecker, Fabian A1 - Weiser, Martin T1 - Convergence Properties of Newton’s Method for Globally Optimal Free Flight Trajectory Optimization T2 - 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023) N2 - The algorithmic efficiency of Newton-based methods for Free Flight Trajectory Optimization is heavily influenced by the size of the domain of convergence. We provide numerical evidence that the convergence radius is much larger in practice than what the theoretical worst case bounds suggest. The algorithm can be further improved by a convergence-enhancing domain decomposition. Y1 - 2023 U6 - https://doi.org/10.4230/OASIcs.ATMOS.2023.3 VL - 115 SP - 3:1 EP - 3:6 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Danecker, Fabian A1 - Weiser, Martin T1 - Newton's Method for Global Free Flight Trajectory Optimization JF - Operations Research Forum N2 - Globally optimal free flight trajectory optimization can be achieved with a combination of discrete and continuous optimization. A key requirement is that Newton's method for continuous optimization converges in a sufficiently large neighborhood around a minimizer. We show in this paper that, under certain assumptions, this is the case. Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-91846 VL - 4 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Danecker, Fabian A1 - Weiser, Martin T1 - Error Bounds for Discrete-Continuous Free Flight Trajectory Optimization JF - Journal of Optimization Theory and Applications N2 - Flight planning, the computation of optimal routes in view of flight time and fuel consumption under given weather conditions, is traditionally done by finding globally shortest paths in a predefined airway network. Free flight trajectories, not restricted to a network, have the potential to reduce the costs significantly, and can be computed using locally convergent continuous optimal control methods. Hybrid methods that start with a discrete global search and refine with a fast continuous local optimization combine the best properties of both approaches, but rely on a good switchover, which requires error estimates for discrete paths relative to continuous trajectories. Based on vertex density and local complete connectivity, we derive localized and a priori bounds for the flight time of discrete paths relative to the optimal continuous trajectory, and illustrate their properties on a set of benchmark problems. It turns out that localization improves the error bound by four orders of magnitude, but still leaves ample opportunities for tighter bounds using a posteriori error estimators. Y1 - 2023 U6 - https://doi.org/10.1007/s10957-023-02264-7 VL - 198 SP - 830 EP - 856 ER - TY - GEN A1 - Masing, Berenike A1 - Lindner, Niels A1 - Borndörfer, Ralf T1 - The Price of Symmetric Line Plans in the Parametric City N2 - We consider the line planning problem in public transport in the Parametric City, an idealized model that captures typical scenarios by a (small) number of parameters. The Parametric City is rotation symmetric, but optimal line plans are not always symmetric. This raises the question to quantify the symmetry gap between the best symmetric and the overall best solution. For our analysis, we formulate the line planning problem as a mixed integer linear program, that can be solved in polynomial time if the solutions are forced to be symmetric. The symmetry gap is provably small when a specific Parametric City parameter is fixed, and we give an approximation algorithm for line planning in the Parametric City in this case. While the symmetry gap can be arbitrarily large in general, we show that symmetric line plans are a good choice in most practical situations. T3 - ZIB-Report - 22-01 KW - line planning KW - mixed integer programming KW - parametric city modeling Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-85648 SN - 1438-0064 ER -