TY - GEN A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Löbel, Andreas ED - Aigner, Martin ED - Behrends, Ehrhard T1 - Der schnellste Weg zum Ziel T2 - Alles Mathematik Y1 - 2000 U6 - https://doi.org/10.1007/978-3-322-96366-6_5 SP - 45 EP - 76 PB - Vieweg Verlag CY - Braunschweig/Wiesbaden ER - TY - GEN A1 - Grötschel, Martin A1 - Löbel, Andreas A1 - Völker, Manfred T1 - Optimierung des Fahrzeugumlaufs im Öffentlichen Nahverkehr N2 - This paper addresses the problem of scheduling vehicles in a public mass transportation system. We show how this problem can be modelled as a special multicommodity flow problem and outline the solution methodology we have developed. Based on polyhedral investigations, we have designed and implemented a branch&cut algorithm and various heuristics with which real vehicle scheduling problems of truely large scale can be solved to optimality. We describe some implementation issues and report computational results. T3 - ZIB-Report - SC-96-08 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2195 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Löbel, Andreas T1 - Optimization of Transportation Systems N2 - 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. T3 - ZIB-Report - SC-98-09 KW - Transportation Systems KW - Optimization KW - Discrete Mathematics Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3529 ER - TY - CHAP A1 - Grötschel, Martin A1 - Löbel, Andreas A1 - Völker, Manfred ED - Hoffmann, Karl-Heinz ED - Jäger, Willi ED - Lohmann, Thomas ED - Schunck (Hrsg.), Hermann T1 - Optimierung des Fahrzeugumlaufs im Öffentlichen Nahverkehr T2 - Mathematik Y1 - 1997 SP - 609 EP - 624 PB - Springer ER - TY - GEN A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Löbel, Andreas T1 - Duty Scheduling in Public Transit N2 - This article is about \emph{adaptive column generation techniques} for the solution of duty scheduling problems in public transit. The current optimization status is exploited in an adaptive approach to guide the subroutines for duty generation, LP resolution, and schedule construction toward relevant parts of a large problem. Computational results for three European scenarios are reported. T3 - ZIB-Report - 01-02 KW - Duty Scheduling KW - Constraint Shortest Paths Problem KW - Column Generation Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6286 ER - TY - GEN A1 - Grötschel, Martin A1 - Borndörfer, Ralf A1 - Löbel, Andreas ED - Jäger, Willi ED - Krebs, Hans-Joachim T1 - Duty Scheduling in Public Transit T2 - MATHEMATICS – Key Technology for the Future Y1 - 2003 U6 - https://doi.org/10.1007/978-3-642-55753-8_50 SP - 653 EP - 674 PB - Springer ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Löbel, Andreas ED - Butzer, Paul Leo ED - Jongen, Hubertus ED - Oberschelp, Walter T1 - Alcuin’s Transportation Problems and Integer Programming T2 - Charlemagne and his Heritage. 1200 Years of Civilization and Science in Europe. Karl der Grosse und sein Nachwirken . 1200 Jahre Kultur und Wissenschaft in Europa Y1 - 1998 VL - 2 SP - 379 EP - 409 PB - Brepols Publisher CY - Turnhout ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Löbel, Andreas ED - Aigner, Martin ED - Behrends, Ehrhard T1 - The Quickest Path to the Goal JF - Mathematics Everywhere Y1 - 2010 UR - http://www.ams.org/bookstore-getitem/item=MBK-72 SP - 27 EP - 51 PB - American Mathematical Society CY - Providence, Rhode Iland, USA ER - TY - GEN A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Löbel, Andreas T1 - Der Schnellste Weg zum Ziel N2 - Wir geben eine Einführung in die Mathematik von und mit Wegen. Nicht auf dem kürzesten, aber auf einem hoffentlich kurzweiligen Weg! T3 - ZIB-Report - SC-99-32 KW - Kürzeste Wege KW - Kombinatorische Optimierung KW - Operations Research Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4209 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Löbel, Andreas A1 - Weider, Steffen T1 - Integrierte Umlauf- und Dienstplanung im öffentlichen Nahverkehr T2 - Neue Mathematische Verfahren in Industrie und Dienstleistungen Y1 - 2001 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Löbel, Andreas T1 - Dienstplanung im öffentlichen Nahverkehr T2 - Mathematische Verfahren zur Lösung von Problemstellungen in Industrie und Wirtschaft Y1 - 1997 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Löbel, Andreas T1 - Umlaufplanung im öffentlichen Nahverkehr T2 - Anwendungsorientierte Verbundprojekte auf dem Gebiet der Mathematik Y1 - 1994 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Löbel, Andreas T1 - The Quickest Path to the Goal N2 - We provide an introduction into the mathematics of and with paths. Not on the shortest, but hopefully on an entertaining path! T3 - ZIB-Report - 10-21 KW - shortest paths KW - combinatorial optimization KW - operations research Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11840 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 -