@misc{BorndoerferHeismann2012, author = {Bornd{\"o}rfer, Ralf and Heismann, Olga}, title = {Minimum Cost Hyperassignments with Applications to ICE/IC Rotation Planning}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14564}, number = {11-46}, year = {2012}, abstract = {Vehicle rotation planning is a fundamental problem in rail transport. It decides how the railcars, locomotives, and carriages are operated in order to implement the trips of the timetable. One important planning requirement is operational regularity, i.e., using the rolling stock in the same way on every day of operation. We propose to take regularity into account by modeling the vehicle rotation planning problem as a minimum cost hyperassignment problem (HAP). Hyperassignments are generalizations of assignments from directed graphs to directed hypergraphs. Finding a minimum cost hyperassignment is NP-hard. Most instances arising from regular vehicle rotation planning, however, can be solved well in practice. We show that, in particular, clique inequalities strengthen the canonical LP relaxation substantially.}, language = {en} } @misc{BorndoerferKarbstein2012, author = {Bornd{\"o}rfer, Ralf and Karbstein, Marika}, title = {A Note on Menger's Theorem for Hypergraphs}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14471}, number = {12-03}, year = {2012}, abstract = {We prove the companion Theorem to Menger's Theorem for hypergraphs. This result gives rise to a new class of blocking pairs of ideal matrices, that generalize the incidence matrices of cuts and paths.}, language = {en} } @inproceedings{BorndoerferMuraSchlechte2009, author = {Bornd{\"o}rfer, Ralf and Mura, Annette and Schlechte, Thomas}, title = {Vickrey Auctions for Railway Tracks}, booktitle = {Operations Research Proceedings 2008}, editor = {Fleischmann, Bernhard and Borgwardt, Karl and Klein, Robert and Tuma, Axel}, publisher = {Springer-Verlag}, pages = {551 -- 556}, year = {2009}, language = {en} } @inproceedings{BorndoerferNeumannPfetsch2009, author = {Bornd{\"o}rfer, Ralf and Neumann, Marika and Pfetsch, Marc}, title = {The Line Connectivity Problem}, booktitle = {Operations Research Proceedings 2008}, editor = {Fleischmann, Bernhard and Borgwardt, Karl and Klein, Robert and Tuma, Axel}, publisher = {Springer-Verlag}, pages = {557 -- 562}, year = {2009}, language = {en} } @inproceedings{BorndoerferGroetschelKlostermeieretal.1999, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and Klostermeier, Fridolin and K{\"u}ttner, Christian}, title = {Telebus Berlin: Vehicle Scheduling in a Dial-a-Ride System}, booktitle = {Proceedings of the 7th International Workshop on Computer-Aided Transit Scheduling}, editor = {Wilson, Nigel}, publisher = {Springer Verlag}, address = {Berlin}, doi = {10.1007/978-3-642-85970-0_19}, pages = {391 -- 422}, year = {1999}, language = {en} } @inproceedings{BorndoerferSchlechteWeider2010, author = {Bornd{\"o}rfer, Ralf and Schlechte, Thomas and Weider, Steffen}, title = {Railway Track Allocation by Rapid Branching}, volume = {14}, booktitle = {Proceedings of the 10th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems}, editor = {Erlebach, Thomas and L{\"u}bbecke, Marco}, publisher = {Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik}, address = {Dagstuhl, Germany}, doi = {http://dx.doi.org/10.4230/OASIcs.ATMOS.2010.13}, pages = {13 -- 23}, year = {2010}, language = {en} } @inproceedings{BorndoerferNeumannPfetsch2008, author = {Bornd{\"o}rfer, Ralf and Neumann, Marika and Pfetsch, Marc}, title = {Angebotsplanung im {\"o}ffentlichen Nahverkehr}, booktitle = {HEUREKA'08}, publisher = {FGSV Verlag}, year = {2008}, language = {en} } @misc{Borndoerfer2004, author = {Bornd{\"o}rfer, Ralf}, title = {Combinatorial Packing Problems}, journal = {The Sharpest Cut - The Impact of Manfred Padberg and His Work}, editor = {Gr{\"o}tschel, Martin}, publisher = {SIAM}, address = {Philadelphia}, pages = {19 -- 32}, year = {2004}, language = {en} } @misc{BorndoerferKarbstein2012, author = {Bornd{\"o}rfer, Ralf and Karbstein, Marika}, title = {A Direct Connection Approach to Integrated Line Planning and Passenger Routing}, volume = {25}, journal = {ATMOS 2012 - 12th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems}, editor = {Delling, Daniel and Liberti, Leo}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum f{\"u}r Informatik}, issn = {1438-0064}, doi = {http://dx.doi.org/10.4230/OASIcs.ATMOS.2012.47}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-15812}, pages = {47 -- 57}, year = {2012}, abstract = {The treatment of transfers is a major challenge in line planning. Existing models either route passengers and lines sequentially, and hence disregard essential degrees of freedom, or they are of extremely large scale, and seem to be computationally intractable. We propose a novel direct connection approach that allows an integrated optimization of line and passenger routing, including accurate estimates of the number of direct travelers, for large-scale real-world instances.}, language = {en} } @misc{BorndoerferNeumann2010, author = {Bornd{\"o}rfer, Ralf and Neumann, Marika}, title = {Models for Line Planning with Transfers}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11742}, number = {10-11}, year = {2010}, abstract = {We propose a novel integer programming approach to transfer minimization for line planning problems in public transit. The idea is to incorporate penalties for transfers that are induced by "connection capacities" into the construction of the passenger paths. We show that such penalties can be dealt with by a combination of shortest and constrained shortest path algorithms such that the pricing problem for passenger paths can be solved efficiently. Connection capacity penalties (under)estimate the true transfer times. This error is, however, not a problem in practice. We show in a computational comparison with two standard models on a real-world scenario that our approach can be used to minimize passenger travel and transfer times for large-scale line planning problems with accurate results.}, language = {en} } @misc{BorndoerferNeumann2010, author = {Bornd{\"o}rfer, Ralf and Neumann, Marika}, title = {Linienoptimierung - reif f{\"u}r die Praxis?}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11832}, number = {10-20}, year = {2010}, abstract = {Wir stellen in dieser Arbeit ein mathematisches Optimierungsmodell zur Bestimmung eines optimalen Linienplans vor, das sowohl die Fahrzeiten und die Anzahl der Umstiege ber{\"u}cksichtigt als auch die Kosten des Liniennetzes. Dieses Modell deckt wichtige praktische Anforderungen ab, die in einem gemeinsamen Projekt mit den Verkehrsbetrieben in Potsdam (ViP) formuliert wurden. In diesem Projekt wurde der Linienplan 2010 f{\"u}r Potsdam entwickelt. Unsere Berechnungen zeigen, dass die mathematische Optimierung in nichts einer "Handplanung" des Liniennetzes nachsteht. Im Gegenteil, mit Hilfe des Optimierungsprogramms ist es m{\"o}glich, durch Ver{\"a}nderung der Parameter mehrere verschiedene Szenarien zu berechnen, miteinander zu vergleichen und Aussagen {\"u}ber minimale Kosten und Fahrzeiten zu machen.}, language = {de} } @misc{Beckenbach2017, author = {Beckenbach, Isabel}, title = {A Hypergraph Network Simplex Algorithm}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64539}, year = {2017}, abstract = {We describe a network simplex algorithm for the minimum cost flow problem on graph-based hypergraphs which are directed hypergraphs of a particular form occurring in railway rotation planning. The algorithm is based on work of Cambini, Gallo, and Scutell{\`a} who developed a hypergraphic generalization of the network simplex algorithm. Their main theoretical result is the characterization of basis matrices. We give a similar characterization for graph-based hypergraphs and show that some operations of the simplex algorithm can be done combinatorially by exploiting the underlying digraph structure.}, language = {en} } @inproceedings{GrimmBorndoerferReutheretal.2017, author = {Grimm, Boris and Bornd{\"o}rfer, Ralf and Reuther, Markus and Schade, Stanley and Schlechte, Thomas}, title = {A Propagation Approach to Acyclic Rolling Stock Rotation Optimization}, booktitle = {Proceedings of the IAROR conference RailLille}, year = {2017}, abstract = {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.}, language = {en} } @inproceedings{BorndoerferSagnolSwarat2012, author = {Bornd{\"o}rfer, Ralf and Sagnol, Guillaume and Swarat, Elmar}, title = {A Case Study on Optimizing Toll Enforcements on Motorways}, volume = {22}, booktitle = {3rd Student Conference on Operational Research}, doi = {10.4230/OASIcs.SCOR.2012.1}, pages = {1 -- 10}, year = {2012}, abstract = {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.}, language = {en} } @article{BorndoerferSagnolSchlechteetal.2016, author = {Bornd{\"o}rfer, Ralf and Sagnol, Guillaume and Schlechte, Thomas and Swarat, Elmar}, title = {Optimal duty rostering for toll enforcement inspectors}, volume = {252(2)}, journal = {Annals of Operations Research}, edition = {252}, publisher = {Springer US}, doi = {10.1007/s10479-016-2152-1}, pages = {383 -- 406}, year = {2016}, abstract = {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.}, language = {en} } @article{BeckenbachScheidweiler2017, author = {Beckenbach, Isabel and Scheidweiler, Robert}, title = {Perfect f-Matchings and f-Factors in Hypergraphs - A Combinatorial Approach}, volume = {340}, journal = {Discrete Mathematics}, number = {10}, doi = {10.1016/j.disc.2017.05.005}, pages = {2499 -- 2506}, year = {2017}, abstract = {We prove characterizations of the existence of perfect f-matchings in uniform mengerian and perfect hypergraphs. Moreover, we investigate the f-factor problem in balanced hypergraphs. For uniform balanced hypergraphs we prove two existence theorems with purely combinatorial arguments, whereas for non-uniform balanced hypergraphs we show that the f-factor problem is NP-hard.}, language = {de} } @inproceedings{BorndoerferSchenkerSkutellaetal.2016, author = {Bornd{\"o}rfer, Ralf and Schenker, Sebastian and Skutella, Martin and Strunk, Timo}, title = {PolySCIP}, volume = {9725}, booktitle = {Mathematical Software - ICMS 2016, 5th International Conference, Berlin, Germany, July 11-14, 2016, Proceedings}, editor = {Greuel, G.-M. and Koch, Thorsten and Paule, Peter and Sommese, Andrew}, edition = {Mathematical Software - ICMS 2016}, publisher = {Springer International Publishing}, isbn = {978-3-319-42431-6}, doi = {10.1007/978-3-319-42432-3_32}, pages = {259 -- 264}, year = {2016}, abstract = {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.}, language = {en} } @article{BorndoerferHoppmannKarbstein2016, author = {Bornd{\"o}rfer, Ralf and Hoppmann, Heide and Karbstein, Marika}, title = {Passenger routing for periodic timetable optimization}, journal = {Public Transport}, publisher = {Springer-Verlag Berlin Heidelberg}, doi = {10.1007/s12469-016-0132-0}, year = {2016}, abstract = {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.}, language = {en} } @inproceedings{Hoppmann2016, author = {Hoppmann, Heide}, title = {An Extended Formulation for the Line Planning Problem}, booktitle = {Operations Research Proceedings 2015}, doi = {10.1007/978-3-319-42902-1_2}, pages = {11 -- 17}, year = {2016}, abstract = {In this paper we present a novel extended formulation for the line planning problem that is based on what we call "configurations" of lines and frequencies. Configurations account for all possible options to provide a required transportation capacity on an infrastructure edge. The proposed configuration model is strong in the sense that it implies several facet-defining inequalities for the standard model: set cover, symmetric band, MIR, and multicover inequalities. These theoretical findings can be confirmed in computational results. Further, we show how this concept can be generalized to define configurations for subsets of edges; the generalized model implies additional inequalities from the line planning literature.}, language = {en} } @inproceedings{BorndoerferHoppmannKarbstein2016, author = {Bornd{\"o}rfer, Ralf and Hoppmann, Heide and Karbstein, Marika}, title = {Separation of Cycle Inequalities for the Periodic Timetabling Problem}, volume = {57}, booktitle = {24th Annual European Symposium on Algorithms (ESA 2016)}, doi = {10.4230/LIPIcs.ESA.2016.21}, year = {2016}, abstract = {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.}, language = {en} } @article{BorndoerferKarbstein2015, author = {Bornd{\"o}rfer, Ralf and Karbstein, Marika}, title = {Metric inequalities for routings on direct connections with application to line planning}, volume = {18}, journal = {Discrete Optimization}, pages = {56 -- 73}, year = {2015}, abstract = {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.}, language = {en} } @misc{BorndoerferBreuerGrimmetal.2017, author = {Bornd{\"o}rfer, Ralf and Breuer, Matthias and Grimm, Boris and Reuther, Markus and Schade, Stanley and Schlechte, Thomas}, title = {Timetable Sparsification by Rolling Stock Rotation Optimization}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-65948}, year = {2017}, abstract = {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.}, language = {en} } @inproceedings{BorndoerferSagnolSwarat2012, author = {Bornd{\"o}rfer, Ralf and Sagnol, Guillaume and Swarat, Elmar}, title = {An IP Approach to Toll Enforcement Optimization on German Motorways}, booktitle = {Operations Research Proceedings 2011}, doi = {10.1007/978-3-642-29210-1_51}, pages = {317 -- 322}, year = {2012}, abstract = {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.}, language = {en} } @inproceedings{BorndoerferBuwayaSagnoletal.2013, author = {Bornd{\"o}rfer, Ralf and Buwaya, Julia and Sagnol, Guillaume and Swarat, Elmar}, title = {Optimizing Toll Enforcement in Transportation Networks: a Game-Theoretic Approach}, volume = {41}, booktitle = {Proceedings of INOC'2013}, doi = {http://dx.doi.org//10.1016/j.endm.2013.05.100}, pages = {253 -- 260}, year = {2013}, abstract = {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.}, language = {en} } @inproceedings{BorndoerferOmontSagnoletal.2012, author = {Bornd{\"o}rfer, Ralf and Omont, Bertrand and Sagnol, Guillaume and Swarat, Elmar}, title = {A Stackelberg game to optimize the distribution of controls in transportation networks}, volume = {105}, booktitle = {Proceedings of the 3rd International Conference on Game Theory for Networks (GAMENETS 2012)}, doi = {http://dx.doi.org/10.1007/978-3-642-35582-0_17}, pages = {224 -- 235}, year = {2012}, abstract = {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.}, language = {en} }