@misc{PfetschBorndoerfer2005, author = {Pfetsch, Marc and Bornd{\"o}rfer, Ralf}, title = {Routing in Line Planning for Public Transportation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8706}, number = {05-36}, year = {2005}, abstract = {The line planning problem is one of the fundamental problems in strategic planning of public and rail transport. It consists in finding lines and corresponding frequencies in a network such that a giv en demand can be satisfied. There are two objectives. Passengers want to minimize travel times, the transport company wishes to minimize operating costs. We investigate three variants of a multi-commo dity flow model for line planning that differ with respect to passenger routings. The first model allows arbitrary routings, the second only unsplittable routings, and the third only shortest path rou tings with respect to the network. We compare these models theoretically and computationally on data for the city of Potsdam.}, language = {en} } @misc{BorndoerferGroetschelPfetsch2005, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and Pfetsch, Marc}, title = {A Column-Generation Approach to Line Planning in Public Transport}, doi = {/10.1287/trsc.1060.0161}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8522}, number = {05-18}, year = {2005}, abstract = {The line planning problem is one of the fundamental problems in strategic planning of public and rail transport. It consists in finding lines and corresponding frequencies in a transport network such that a given travel demand can be satisfied. There are (at least) two objectives. The transport company wishes to minimize operating costs, the passengers want to minimize travel times. We propose a n ew multi-commodity flow model for line planning. Its main features, in comparison to existing models, are that the passenger paths can be freely routed and that the lines are generated dynamically. We discuss properties of this model and investigate its complexity. Results with data for the city of Potsdam, Germany, are reported.}, language = {en} } @misc{BorndoerferGroetschelPfetsch2005, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and Pfetsch, Marc}, title = {Public Transport to the fORe!}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8562}, number = {05-22}, year = {2005}, abstract = {Can OR methods help the public transport industry to break even? The article gives evidence that there exist significant potentials in this direction, which can be harnessed by a combination of modern mathematical methods and local planning knowledge. Many of the planning steps in public transport are classical combinatorial problems, which can be solved in unprecedented size and quality due the rapid progress in large-scale optimization. Three examples on vehicle scheduling, duty scheduling, and integrated vehicle and duty scheduling illustrate the level that has been reached and the improvements that can be achieved today. Extensions of such methods to further questions of strategic, online, and market-oriented planning are currently investigated. In this way, OR can make a significant contribution to answer the basic but extremely difficult question ``What is a good public transport network?.}, language = {en} } @misc{BorndoerferGroetschelLoebel2000, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and L{\"o}bel, Andreas}, title = {Der schnellste Weg zum Ziel}, journal = {Alles Mathematik}, editor = {Aigner, Martin and Behrends, Ehrhard}, publisher = {Vieweg Verlag}, address = {Braunschweig/Wiesbaden}, doi = {10.1007/978-3-322-96366-6_5}, pages = {45 -- 76}, year = {2000}, language = {en} } @incollection{BorndoerferGroetschelJaeger2008, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and Jaeger, Ulrich}, title = {Planungsprobleme im {\"o}ffentlichen Verkehr}, booktitle = {PRODUKTIONSFAKTOR MATHEMATIK - Wie Mathematik Technik und Wirtschaft bewegt}, editor = {Gr{\"o}tschel, Martin and Lucas, Klaus and Mehrmann, Volker}, publisher = {acatech - Deutsche Akademie der Technikwissenschaften und Springer}, pages = {127 -- 153}, year = {2008}, language = {en} } @inproceedings{BorndoerferGroetschelPfetsch2008, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and Pfetsch, Marc}, title = {Models for Line Planning in Public Transport}, volume = {600}, booktitle = {Computer-aided Systems in Public Transport (CASPT 2004)}, editor = {Hickman, Mark and Mirchandani, Pitu and Voß, Stefan}, publisher = {Springer-Verlag}, doi = {10.1007/978-3-540-73312-6_18}, pages = {363 -- 378}, year = {2008}, language = {en} } @article{BorndoerferGroetschelPfetsch2007, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and Pfetsch, Marc}, title = {A Column-Generation Approach to Line Planning in Public Transport}, volume = {41}, journal = {Transportation Science (INFORMS)}, number = {1}, doi = {10.1287/trsc.1060.0161}, pages = {123 -- 132}, year = {2007}, language = {en} } @misc{BorndoerferFerreiraMartin1997, author = {Bornd{\"o}rfer, Ralf and Ferreira, Carlos E. and Martin, Alexander}, title = {Matrix Decomposition by Branch-and-Cut}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2839}, number = {SC-97-14}, year = {1997}, abstract = {In this paper we investigate whether matrices arising from linear or integer programming problems can be decomposed into so-called {\em bordered block diagonal form}. More precisely, given some matrix \$A\$, we try to assign as many rows as possible to some number of blocks of limited size such that no two rows assigned to different blocks intersect in a common column. Bordered block diagonal form is desirable because it can guide and speed up the solution process for linear and integer programming problems. We show that various matrices from the \%LP- and MIP-libraries \Netlib{} and MIPLIB can indeed be decomposed into this form by computing optimal decompositions or decompositions with proven quality. These computations are done with a branch-and-cut algorithm based on polyhedral investigations of the matrix decomposition problem.}, language = {en} } @misc{BorndoerferGroetschelHerzogetal.1996, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and Herzog, Werner and Klostermeier, Fridolin and Konsek, Wilhelm and K{\"u}ttner, Christian}, title = {K{\"u}rzen muß nicht Kahlschlag heißen - das Beispiel Telebus-Behindertenfahrdienst Berlin}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2510}, number = {SC-96-41}, year = {1996}, abstract = {M{\"u}ssen Etatk{\"u}rzungen bei staatlichen Dienstleistungseinrichtungen notwendig zu Leistungseinschr{\"a}nkungen oder Geb{\"u}hrenerh{\"o}hungen f{\"u}hren? Wir zeigen am Beispiel des Berliner Behindertenfahrdienstes {\em Telebus}, da\ss{} Sparzwang auch als Chance zur Verbesserung der eigenen Verwaltungs- und Arbeitsabl{\"a}ufe genutzt werden kann. Durch st{\"a}rkere Dienstleistungsorientierung, Vereinfachung der Arbeitsabl{\"a}ufe und durch den Einsatz von moderner EDV und von mathematischen Optimierungsmethoden zur Fahrzeugeinsatzplanung werden bei Telebus heute staatliche Leistungen trotz geringeren Etats besser erbracht als vorher.}, language = {de} } @misc{BorndoerferGroetschelKlostermeieretal.1996, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and Klostermeier, Fridolin and K{\"u}ttner, Christian}, title = {Telebus Berlin - Mobilit{\"a}t f{\"u}r Behinderte}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2500}, number = {SC-96-40}, year = {1996}, abstract = {Steigendes Mobilit{\"a}tsbed{\"u}rfnis der Behinderten bei angespannter Haushaltslage --- diese Situation ergab vor drei Jahren beim Berliner Behindertenfahrdienst {\em Telebus\/} Handlungsbedarf. Gleichzeitig stie\ss{} die verwendete manuelle (Fahrzeug-)Tourenplanung mit damals etwa 1.000 Fahrtw{\"u}nschen pro Tag an ihre Grenzen. Zur L{\"o}sung dieser Probleme war der effiziente Einsatz von Computern und von {\em mathematischen Optimierungsverfahren\/} erforderlich. Ergebnis des daraufhin gestarteten {\em Telebus-Projektes\/} ist die Entwicklung eines neuen, alle Arbeitsabl{\"a}ufe unterst{\"u}tzenden Computersystems, das seit {\"u}ber einem Jahr im Einsatz ist. Herzst{\"u}ck dieses Systems ist ein auf mathematischen Methoden der ganzzahligen Optimierung basierendes Verfahren zur Tourenplanung. Ziel dieses Artikels ist die Beschreibung dieses Verfahrens und seiner Verwendung bei der Behindertenbef{\"o}rderung. Das Beispiel Telebus zeigt, da\ss{} der Einsatz mathematischer Optimierungstechniken neue M{\"o}glichkeiten f{\"u}r Kosteneinsparungen bei gleichzeitiger Serviceverbesserung auch in anderen Bereichen des {\"O}PNV er{\"o}ffnet.}, language = {de} } @misc{AbdelHamidBorndoerfer1994, author = {Abdel-Hamid, Atef Abdel-Aziz and Bornd{\"o}rfer, Ralf}, title = {On the Complexity of Storage Assignment Problems.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1430}, number = {SC-94-14}, year = {1994}, abstract = {{\def\NP{\hbox{\$\cal N\kern-.1667em\cal P\$}} The {\sl storage assignment problem} asks for the cost minimal assignment of containers with different sizes to storage locations with different capacities. Such problems arise, for instance, in the optimal control of automatic storage devices in flexible manufacturing systems. This problem is known to be \$\NP\$-hard in the strong sense. We show that the storage assignment problem is \$\NP\$-hard for {\sl bounded sizes and capacities}, even if the sizes have values \$1\$ and~\$2\$ and the capacities value~\$2\$ only, a case we encountered in practice. Moreover, we prove that no polynomial time \$\epsilon\$-approximation algorithm exists. This means that almost all storage assignment problems arising in practice are indeed hard.}}, language = {en} } @misc{BorndoerferLoebelStrubbeetal.1998, author = {Bornd{\"o}rfer, Ralf and L{\"o}bel, Andreas and Strubbe, Uwe and V{\"o}lker, Manfred}, title = {Zielorientierte Dienstplanoptimierung}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3847}, number = {SC-98-41}, year = {1998}, abstract = {Dieser Artikel behandelt einen Ansatz zur zielorientierten Optimierung der Dienstplanung im {\"O}PNV. Der Ansatz zielt auf die vollst{\"a}ndige Ausnutzung aller planerischen Freiheitsgrade unter korrekter Ber{\"u}cksichtigung von gesetzlichen, tariflichen, technischen und betrieblichen Rahmenbedingungen. Er basiert auf mathematischen Optimierungstechniken, die wir gegenw{\"a}rtig in einem vom Bundesministerium f{\"u}r Bildung und Forschung ({\tt bmb+f}) gef{\"o}rderten Verbundprojekt in einer Kooperation zwischen der HanseCom GmbH, der IVU GmbH und dem Konrad-Zuse-Zentrum f{\"u}r Informationstechnik Berlin entwickeln. Es ist geplant, das Verfahren in die Softwareprodukte HOT II, MICROBUS II und OPUS zu integrieren. Verhandlungen mit den Berliner Verkehrsbetrieben {\"u}ber eine Projektbeteiligung und Integration unserer Software in BERTA sind zur Zeit im Gang. Wir beschreiben die Methodik des Ansatzes, diskutieren Aspekte seiner praktischen Verwendung, und wir berichten {\"u}ber den Stand der Entwicklung.}, language = {de} } @misc{BorndoerferEisenblaetterGroetscheletal.1997, author = {Bornd{\"o}rfer, Ralf and Eisenbl{\"a}tter, Andreas and Gr{\"o}tschel, Martin and Martin, Alexander}, title = {Frequency Assignment in Cellular Phone Networks}, doi = {10.1023/A:1018908907763}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3044}, number = {SC-97-35}, year = {1997}, abstract = {We present a graph-theoretic model for the \emph{frequency assignment problem} in Cellular Phone Networks: Obeying several technical and legal restrictions, frequencies have to be assigned to transceivers so that interference is as small as possible. This optimization problem is NP-hard. Good approximation cannot be guaranteed, unless P = NP. We describe several assignment heuristics. These heuristics are simple and not too hard to implement. We give an assessment of the heuristics' efficiency and practical usefulness. For this purpose, typical instances of frequency assignment problems with up to 4240 transceivers and 75 frequencies of a German cellular phone network operator are used. The results are satisfying from a practitioner's point of view. The best performing heuristics were integrated into a network planning system used in practice.}, language = {en} } @misc{BorndoerferGroetschelLoebel1998, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and L{\"o}bel, Andreas}, title = {Optimization of Transportation Systems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3529}, number = {SC-98-09}, year = {1998}, abstract = {The world has experienced two hundred years of unprecedented advances in vehicle technology, transport system development, and traffic network extension. Technical progress continues but seems to have reached some limits. Congestion, pollution, and increasing costs have created, in some parts of the world, a climate of hostility against transportation technology. Mobility, however, is still increasing. What can be done? There is no panacea. Interdisciplinary cooperation is necessary, and we are going to argue in this paper that {\em Mathematics\/} can contribute significantly to the solution of some of the problems. We propose to employ methods developed in the {\em Theory of Optimization\/} to make better use of resources and existing technology. One way of optimization is better planning. We will point out that {\em Discrete Mathematics\/} provides a suitable framework for planning decisions within transportation systems. The mathematical approach leads to a better understanding of problems. Precise and quantitative models, and advanced mathematical tools allow for provable and reproducible conclusions. Modern computing equipment is suited to put such methods into practice. At present, mathematical methods contribute, in particular, to the solution of various problems of {\em operational planning}. We report about encouraging {\em results\/} achieved so far.}, language = {en} } @misc{BorndoerferGrimmReutheretal.2016, author = {Bornd{\"o}rfer, Ralf and Grimm, Boris and Reuther, Markus and Schlechte, Thomas}, title = {Optimization of Handouts for Rolling Stock Rotations Visualization}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61430}, year = {2016}, abstract = {A railway operator creates (rolling stock) rotations in order to have a precise master plan for the operation of a timetable by railway vehicles. A rotation is considered as a cycle that multiply traverses a set of operational days while covering trips of the timetable. As it is well known, the proper creation of rolling stock rotations by, e.g., optimization algorithms is challenging and still a topical research subject. Nevertheless, we study a completely different but strongly related question in this paper, i.e.: How to visualize a rotation? For this purpose, we introduce a basic handout concept, which directly leads to the visualization, i.e., handout of a rotation. In our industrial application at DB Fernverkehr AG, the handout is exactly as important as the rotation itself. Moreover, it turns out that also other European railway operators use exactly the same methodology (but not terminology). Since a rotation can have many handouts of different quality, we show how to compute optimal ones through an integer program (IP) by standard software. In addition, a construction as well as an improvement heuristic are presented. Our computational results show that the heuristics are a very reliable standalone approach to quickly find near-optimal and even optimal handouts. The efficiency of the heuristics is shown via a computational comparison to the IP approach.}, language = {en} } @article{BorndoerferKarbsteinPfetsch2012, author = {Bornd{\"o}rfer, Ralf and Karbstein, Marika and Pfetsch, Marc}, title = {Models for Fare Planning in Public Transport}, volume = {160}, journal = {Discrete Applied Mathematics}, number = {18}, doi = {10.1016/j.dam.2012.02.027}, pages = {2591 -- 2605}, year = {2012}, language = {en} } @inproceedings{EulerBorndoerfer2019, author = {Euler, Ricardo and Bornd{\"o}rfer, Ralf}, title = {A Graph- and Monoid-based Framework for Price-Sensitive Routing in Local Public Transportation Networks}, volume = {75}, booktitle = {19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)}, doi = {10.4230/OASIcs.ATMOS.2019.12}, pages = {12:1 -- 12:15}, year = {2019}, abstract = {We present a novel framework to mathematically describe the fare systems of local public transit companies. The model allows the computation of a provably cheapest itinerary even if prices depend on a number of parameters and non-linear conditions. Our approach is based on a ticket graph model to represent tickets and their relation to each other. Transitions between tickets are modeled via transition functions over partially ordered monoids and a set of symbols representing special properties of fares (e.g. surcharges). Shortest path algorithms rely on the subpath optimality property. This property is usually lost when dealing with complicated fare systems. We restore it by relaxing domination rules for tickets depending on the structure of the ticket graph. An exemplary model for the fare system of Mitteldeutsche Verkehrsbetriebe (MDV) is provided. By integrating our framework in the multi-criteria RAPTOR algorithm we provide a price-sensitive algorithm for the earliest arrival problem and assess its performance on data obtained from MDV. We discuss three preprocessing techniques that improve run times enough to make the algorithm applicable for real-time queries.}, language = {en} } @article{BorndoerferHoppmannKarbsteinetal.2020, author = {Bornd{\"o}rfer, Ralf and Hoppmann, Heide and Karbstein, Marika and Lindner, Niels}, title = {Separation of cycle inequalities in periodic timetabling}, journal = {Discrete Optimization}, number = {35}, doi = {10.1016/j.disopt.2019.100552}, pages = {100552}, year = {2020}, abstract = {Cycle inequalities play an important role in the polyhedral study of the periodic timetabling problem in public transport. We give the first pseudo-polynomial time separation algorithm for cycle inequalities, and we contribute a rigorous proof for the pseudo-polynomial time separability of the change-cycle inequalities. Moreover, we provide several NP-completeness results, indicating that pseudo-polynomial time is best possible. The efficiency of these cutting planes is demonstrated on real-world instances of the periodic timetabling problem.}, language = {en} } @article{BorndoerferLindnerRoth2020, author = {Bornd{\"o}rfer, Ralf and Lindner, Niels and Roth, Sarah}, title = {A Concurrent Approach to the Periodic Event Scheduling Problem}, journal = {Journal of Rail Transport Planning \& Management}, number = {15}, issn = {2210-9706}, doi = {10.1016/j.jrtpm.2019.100175}, pages = {100175}, year = {2020}, abstract = {We introduce a concurrent solver for the periodic event scheduling problem (PESP). It combines mixed integer programming techniques, the modulo network simplex method, satisfiability approaches, and a new heuristic based on maximum cuts. Running these components in parallel speeds up the overall solution process. This enables us to significantly improve the current upper and lower bounds for all benchmark instances of the library PESPlib.}, language = {en} } @misc{BreugemBorndoerferSchlechteetal.2019, author = {Breugem, Thomas and Bornd{\"o}rfer, Ralf and Schlechte, Thomas and Schulz, Christof}, title = {A Three-Phase Heuristic for Cyclic Crew Rostering with Fairness Requirements}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-74297}, year = {2019}, abstract = {In this paper, we consider the Cyclic Crew Rostering Problem with Fairness Requirements (CCRP-FR). In this problem, attractive cyclic rosters have to be constructed for groups of employees, considering multiple, a priori determined, fairness levels. The attractiveness follows from the structure of the rosters (e.g., sufficient rest times and variation in work), whereas fairness is based on the work allocation among the different roster groups. We propose a three-phase heuristic for the CCRP-FR, which combines the strength of column generation techniques with a large-scale neighborhood search algorithm. The design of the heuristic assures that good solutions for all fairness levels are obtained quickly, and can still be further improved if additional running time is available. We evaluate the performance of the algorithm using real-world data from Netherlands Railways, and show that the heuristic finds close to optimal solutions for many of the considered instances. In particular, we show that the heuristic is able to quickly find major improvements upon the current sequential practice: For most instances, the heuristic is able to increase the attractiveness by at least 20\% in just a few minutes.}, language = {en} }