@misc{BorndoerferReutherSchlechte2014, author = {Bornd{\"o}rfer, Ralf and Reuther, Markus and Schlechte, Thomas}, title = {A Coarse-To-Fine Approach to the Railway Rolling Stock Rotation Problem}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-51009}, year = {2014}, abstract = {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.}, language = {en} } @misc{Hoppmann2014, type = {Master Thesis}, author = {Hoppmann, Heide}, title = {A Configuration Model for the Line Planning Problem}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-51610}, pages = {108}, year = {2014}, abstract = {In this thesis we present a novel extended formulation for the line planning problem that is based on what we call "configurations" of lines and frequencies. Configurations are combinatorial building blocks of primal solutions; they rule out the "capacity numerics" and make the problem purely combinatorial. The concept of configurations can also be adapted to other capacitated network design problems. The configuration model is strong in the sense that it implies several facet-defining inequalities for the standard model: set cover, symmetric band, multicover, and MIR inequalities. These theoretical findings can be confirmed in computations, however, the enormous number of configurations can blow up the formulation for large instances. We propose a mixed model that enriches the standard model by a judiciously chosen subset of configurations that provide a good compromise between model strength and size. Computational results for large-scale line planning problems are presented.}, language = {en} } @inproceedings{BlancoSchlechte2014, author = {Blanco, Marco and Schlechte, Thomas}, title = {Analysis of Micro-Macro Transformations of Railway Networks}, booktitle = {Operations Research Proceedings 2013}, doi = {10.1007/978-3-319-07001-8_6}, pages = {37 -- 42}, year = {2014}, abstract = {A common technique in the solution of large or complex optimization problems is the use of micro-macro transformations. In this paper, we carry out a theoretical analysis of such transformations for the track allocation problem in railway networks. We prove that the cumulative rounding technique of Schlechte et al. satisfies two of three natural optimality criteria and that this performance cannot be improved. We also show that under extreme circumstances, this technique can perform inconveniently by underestimating the global optimal value.}, language = {en} } @inproceedings{HeismannBorndoerfer2014, author = {Heismann, Olga and Bornd{\"o}rfer, Ralf}, title = {A Generalization of Odd Set Inequalities for the Set Packing Problem}, booktitle = {Operations Research Proceedings 2013}, doi = {10.1007/978-3-319-07001-8_26}, pages = {193 -- 199}, year = {2014}, abstract = {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.}, language = {en} } @misc{GroetschelBorndoerfer2014, author = {Gr{\"o}tschel, Martin and Bornd{\"o}rfer, Ralf}, title = {Mathematik im Verkehr}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-50287}, year = {2014}, abstract = {Nach einem kurzen Abriss {\"u}ber die Bedeutung des Verkehrssektors als eine wichtige Schl{\"u}sseltechnologie im gesamten Verlauf der Menschheitsgeschichte skizzieren wir die Rolle der Mathematik f{\"u}r Verkehr und Transport. Wir spekulieren dann {\"u}ber zuk{\"u}nftige Entwicklungen, insbesondere im Bereich des {\"o}ffentlichen Personenverkehrs, und begr{\"u}nden, dass die in diesem Bereich anstehenden Herausforderungen nur mit dem Einsatz mathematischer Methoden angemessen bew{\"a}ltigt werden k{\"o}nnen. Die demographischen Prozesse, die in verschiedenen Teilen der Welt unterschiedlich verlaufen, wie z.B. {\"U}beralterung in Europa oder dynamische Trends zu Megast{\"a}dten in Entwicklungsl{\"a}ndern, sich {\"a}ndernde Lebens- und Produktionsverh{\"a}ltnisse, stark wachsender Bedarf nach Mobilit{\"a}t und enormes Anwachsen der Komplexit{\"a}t der Verkehrsplanung und -durchf{\"u}hrung, machen einen verst{\"a}rkten 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 m{\"u}ssen. Hier wird intensive Kooperation zwischen vielen beteiligten Akteuren gefragt sein.}, language = {de} } @misc{BorndoerferDittbrennerLangenhanetal.2014, author = {Bornd{\"o}rfer, Ralf and Dittbrenner, Bastian and Langenhan, Andreas and Seidl, Stephan and Weider, Steffen}, title = {Integrierte Dienst- und Dienstreihenfolgeplanung zur Erh{\"o}hung der Fahrerzufriedenheit}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-50270}, year = {2014}, abstract = {Wir stellen einen mathematischen Optimierungsansatz zur integrierten Dienst- und Dienstreihenfolgeplanung im {\"o}ffentlichen Nahverkehr vor, mit dem sich bei konstanten Personalkosten die Fahrerzufriedenheit deutlich steigern l{\"a}sst.}, language = {de} } @misc{HeismannBorndoerfer2014, author = {Heismann, Olga and Bornd{\"o}rfer, Ralf}, title = {A Generalization of Odd Set Inequalities for the Set Packing Problem}, issn = {1438-0064}, doi = {10.1007/978-3-319-07001-8_26}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-51010}, year = {2014}, abstract = {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.}, language = {en} } @phdthesis{Heismann2014, author = {Heismann, Olga}, title = {The Hypergraph Assignment Problem}, year = {2014}, abstract = {This thesis deals with the hypergraph assignment problem (HAP), a set partitioning problem in a special type of hypergraph. The HAP generalizes the assignment problem from bipartite graphs to what we call bipartite hypergraphs, and is motivated by applications in railway vehicle rotation planning. The main contributions of this thesis concern complexity, polyhedral results, analyses of random instances, and primal methods for the HAP. We prove that the HAP is NP-hard and APX-hard even for small hyperedge sizes and hypergraphs with a special partitioned structure. We also study the complexity of the set packing and covering relaxations of the HAP, and present for certain cases polynomial exact or approximation algorithms. A complete linear description is known for the assignment problem. We therefore also study the HAP polytope. There, we have a huge number of facet-defining inequalities already for a very small problem size. We describe a method for dividing the inequalities into equivalence classes without resorting to a normal form. Within each class, facets are related by certain symmetries and it is sufficient to list one representative of each class to give a complete picture of the structural properties of the polytope. We propose the algorithm "HUHFA" for the classification that is applicable not only to the HAP but combinatorial optimization problems involving symmetries in general. In the largest possible HAP instance for which we could calculate the complete linear description, we have 14049 facets, which can be divided into 30 symmetry classes. We can combinatorially interpret 16 of these classes. This is possible by employing cliques to generalize the odd set inequalities for the matching problem. The resulting inequalities are valid for the polytope associated with the set packing problem in arbitrary hypergraphs and have a clear combinatorial meaning. An analysis of random instances provides a better insight into the structure of hyperassignments. Previous work has extensively analyzed random instances for the assignment problem theoretically and practically. As a generalization of these results for the HAP, we prove bounds on the expected value of a minimum cost hyperassignment that uses half of the maximum possible number of hyperedges that are not edges. In a certain complete partitioned hypergraph G2,2n with i. i. d. exponential random variables with mean 1 as hyperedge costs it lies between 0.3718 and 1.8310 if the vertex number tends to infinity. Finally, we develop an exact combinatorial solution algorithm for the HAP that combines three methods: A very large-scale neighborhood search, the composite columns method for the set partitioning problem, and the network simplex algorithm.}, language = {en} } @article{BorndoerferBuwayaSagnoletal.2015, author = {Bornd{\"o}rfer, Ralf and Buwaya, Julia and Sagnol, Guillaume and Swarat, Elmar}, title = {Network spot-checking games: Theory and application to toll enforcing in transportation networks}, volume = {65}, journal = {Networks}, publisher = {Wiley Periodicals, Inc.}, doi = {10.1002/net.21596}, pages = {312 -- 328}, year = {2015}, abstract = {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.}, language = {en} } @inproceedings{BorndoerferHoppmannKarbstein2017, author = {Bornd{\"o}rfer, Ralf and Hoppmann, Heide and Karbstein, Marika}, title = {Umsteigen ohne Warten}, booktitle = {HEUREKA 2017}, year = {2017}, abstract = {Wir stellen einen mathematischen Optimierungsansatz zur Berechnung von periodischen Taktfahrpl{\"a}nen vor, bei dem die Umsteigezeiten unter Ber{\"u}cksichtigung des Passagierverhaltens minimiert werden. Wir untersuchen damit den Einfluss wichtiger Systemparameter und Verhaltensmuster auf die Bef{\"o}rderungsqualit{\"a}t.}, language = {de} } @misc{BorndoerferHoppmannKarbstein2015, author = {Bornd{\"o}rfer, Ralf and Hoppmann, Heide and Karbstein, Marika}, title = {Passenger Routing for Periodic Timetable Optimization}, issn = {1438-0064}, doi = {10.1007/s12469-016-0132-0}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-56739}, year = {2015}, abstract = {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.}, language = {en} } @article{BorndoerferReutherSchlechteetal.2016, author = {Bornd{\"o}rfer, Ralf and Reuther, Markus and Schlechte, Thomas and Waas, Kerstin and Weider, Steffen}, title = {Integrated Optimization of Rolling Stock Rotations for Intercity Railways}, volume = {50}, journal = {Transportation Science}, number = {3}, doi = {10.1287/trsc.2015.0633}, pages = {863 -- 877}, year = {2016}, abstract = {This paper proposes a highly integrated solution approach for rolling stock planning problems in the context of long distance passenger traffic between cities. The main contributions are a generic hypergraph-based mixed-integer programming model for the considered rolling stock rotation problem and an integrated algorithm for its solution. The newly developed algorithm is able to handle a large spectrum of industrial railway requirements, such as vehicle composition, maintenance constraints, infrastructure capacities, and regularity aspects. We show that our approach has the power to produce rolling stock rotations that can be implemented in practice. In this way, the rolling stock rotations at the largest German long distance operator Deutsche Bahn Fernverkehr AG could be optimized by an automated system utilizing advanced mathematical programming techniques.}, language = {en} } @misc{BorndoerferKarbstein2015, author = {Bornd{\"o}rfer, Ralf and Karbstein, Marika}, title = {Neue Planungsinstrumente nutzen: Das Verkehrsangebot verbessern und Kosten sparen}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-55439}, year = {2015}, abstract = {Wir illustrieren anhand des Liniennetzes der Stadt Potsdam das Potenzial mathematischer Methoden der Angebotsplanung. Wir zeigen, dass das "bestm{\"o}gliche" Verkehrsangebot stark von planerischen Vorgaben beeinflusst wird, mit denen man die Erreichung unterschiedlicher und teilweise gegenl{\"a}ufiger Ziele steuern kann. Die Komplexit{\"a}t des Systems f{\"u}hrt zum Auftreten von R{\"u}ckkoppelungseffekten, die man nicht mit Hilfe von Daumenregeln beherrschen kann. Vielmehr ist der Einsatz moderner Planungsverfahren in einer interdisziplin{\"a}ren Zusammenarbeit von politischen Entscheidungstr{\"a}gern, Verkehrsingenieuren und Mathematikern notwendig, um die aktuellen Herausforderungen in der Verkehrsplanung zu meistern. Der Artikel dokumentiert einen Beitrag zum 7. {\"O}PNV Innovationskongress des Ministeriums f{\"u}r Verkehr und Infrastruktur des Landes Baden-W{\"u}rttemberg, der vom 9.-11. M{\"a}rz 2015 in Freiburg stattfand.}, language = {de} }