@inproceedings{BorndoerferGroetschelLoebeletal.2001, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and L{\"o}bel, Andreas and Weider, Steffen}, title = {Integrierte Umlauf- und Dienstplanung im {\"o}ffentlichen Nahverkehr}, booktitle = {Neue Mathematische Verfahren in Industrie und Dienstleistungen}, year = {2001}, language = {en} } @inproceedings{BorndoerferGroetschelLoebel1997, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and L{\"o}bel, Andreas}, title = {Dienstplanung im {\"o}ffentlichen Nahverkehr}, booktitle = {Mathematische Verfahren zur L{\"o}sung von Problemstellungen in Industrie und Wirtschaft}, year = {1997}, language = {en} } @inproceedings{BorndoerferGroetschelLoebel1994, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and L{\"o}bel, Andreas}, title = {Umlaufplanung im {\"o}ffentlichen Nahverkehr}, booktitle = {Anwendungsorientierte Verbundprojekte auf dem Gebiet der Mathematik}, year = {1994}, 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} } @misc{BorndoerferGroetschelLoebel2010, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and L{\"o}bel, Andreas}, title = {The Quickest Path to the Goal}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11840}, number = {10-21}, year = {2010}, abstract = {We provide an introduction into the mathematics of and with paths. Not on the shortest, but hopefully on an entertaining path!}, language = {en} } @misc{BorndoerferGroetschelJaeger2009, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and Jaeger, Ulrich}, title = {Planning Problems in Public Transit}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11252}, number = {09-13}, year = {2009}, abstract = {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).}, language = {en} } @misc{LuceDuintjerTebbensLiesenetal.2009, author = {Luce, Robert and Duintjer Tebbens, Jurjen and Liesen, J{\"o}rg and Nabben, Robert and Gr{\"o}tschel, Martin and Koch, Thorsten and Schenk, Olaf}, title = {On the Factorization of Simplex Basis Matrices}, organization = {TU Berlin, Zuse Institute Berlin, University of Basel}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11392}, number = {09-24}, year = {2009}, abstract = {In the simplex algorithm, solving linear systems with the basis matrix and its transpose accounts for a large part of the total computation time. We investigate various methods from modern numerical linear algebra to improve the computation speed of the basis updates arising in LPs. The experiments are executed on a large real-world test set. The most widely used solution technique is sparse LU factorization, paired with an updating scheme that allows to use the factors over several iterations. Clearly, small number of fill-in elements in the LU factors is critical for the overall performance. Using a wide range of LPs we show numerically that after a simple permutation the non-triangular part of the basis matrix is so small, that the whole matrix can be factorized with (relative) fill-in close to the optimum. This permutation has been exploited by simplex practitioners for many years. But to our knowledge no systematic numerical study has been published that demonstrates the effective reduction to a surprisingly small non-triangular problem, even for large scale LPs. For the factorization of the non-triangular part most existing simplex codes use some variant of dynamic Markowitz pivoting, which originated in the late 1950s. We also show numerically that, in terms of fill-in and in the simplex context, dynamic Markowitz is quite consistently superior to other, more recently developed techniques.}, 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{ArnoldBertholdHeinzetal.2014, author = {Arnold, Thomas and Berthold, Timo and Heinz, Stefan and Vigerske, Stefan and Henrion, Ren{\´e} and Gr{\"o}tschel, Martin and Koch, Thorsten and Tischendorf, Caren and R{\"o}misch, Werner}, title = {A Jack of all Trades? Solving stochastic mixed-integer nonlinear constraint programs}, issn = {1438-0064}, doi = {10.4171/137}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-49947}, year = {2014}, abstract = {Natural gas is one of the most important energy sources in Germany and Europe. In recent years, political regulations have led to a strict separation of gas trading and gas transport, thereby assigning a central role in energy politics to the transportation and distribution of gas. These newly imposed political requirements influenced the technical processes of gas transport in such a way that the complex task of planning and operating gas networks has become even more intricate. Mathematically, the combination of discrete decisions on the configuration of a gas transport network, the nonlinear equations describing the physics of gas, and the uncertainty in demand and supply yield large-scale and highly complex stochastic mixed-integer nonlinear optimization problems. The Matheon project "Optimization of Gas Transport" takes the key role of making available the necessary core technology to solve the mathematical optimization problems which model the topology planning and the operation of gas networks. An important aspect of the academic impact is the free availability of our framework. As a result of several years of research and development, it is now possible to download a complete state-of-the-art framework for mixed-integer linear and nonlinear programming in source code at http://scip.zib.de}, language = {en} } @misc{ArnoldBertholdHeinzetal.2014, author = {Arnold, Thomas and Berthold, Timo and Heinz, Stefan and Vigerske, Stefan and Henrion, Ren{\´e} and Gr{\"o}tschel, Martin and Koch, Thorsten and Tischendorf, Caren and R{\"o}misch, Werner}, title = {A Jack of all Trades? Solving stochastic mixed-integer nonlinear constraint programs}, volume = {1}, journal = {MATHEON - Mathematics for Key Technologies}, editor = {Deuflhard, Peter and Gr{\"o}tschel, Martin and H{\"o}mberg, Dietmar and Horst, Ulrich and Kramer, J{\"u}rg and Mehrmann, Volker and Polthier, Konrad and Schmidt, Frank and Sch{\"u}tte, Christof and Skutella, Martin and Sprekels, J{\"u}rgen}, publisher = {European Mathematical Society}, doi = {10.4171/137}, pages = {135 -- 146}, year = {2014}, abstract = {Natural gas is one of the most important energy sources in Germany and Europe. In recent years, political regulations have led to a strict separation of gas trading and gas transport, thereby assigning a central role in energy politics to the transportation and distribution of gas. These newly imposed political requirements influenced the technical processes of gas transport in such a way that the complex task of planning and operating gas networks has become even more intricate. Mathematically, the combination of discrete decisions on the configuration of a gas transport network, the nonlinear equations describing the physics of gas, and the uncertainty in demand and supply yield large-scale and highly complex stochastic mixed-integer nonlinear optimization problems. The Matheon project "Optimization of Gas Transport" takes the key role of making available the necessary core technology to solve the mathematical optimization problems which model the topology planning and the operation of gas networks. An important aspect of the academic impact is the free availability of our framework. As a result of several years of research and development, it is now possible to download a complete state-of-the-art framework for mixed-integer linear and nonlinear programming in source code at http://scip.zib.de}, language = {en} } @article{Groetschel2015, author = {Gr{\"o}tschel, Martin}, title = {Die IMU und ihr Sekretariat}, volume = {23}, journal = {Mitteilungen der DMV}, number = {1}, doi = {10.1515/dmvm-2015-0012}, pages = {24 -- 29}, year = {2015}, abstract = {Was macht die International Mathematical Union (IMU) eigentlich, und wozu ist das IMU-Sekretariat da? ...}, language = {de} }