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 - CHAP A1 - Borndörfer, Ralf A1 - Löbel, Andreas A1 - Strubbe, Uwe A1 - Völker, Manfred T1 - Zielorientierte Dienstplanoptimierung T2 - Heureka ’99 Y1 - 1999 UR - http://opus.kobv.de/zib/volltexte/1998/385/ SP - 171 EP - 194 PB - Forschungsgesellschaft für Strassen- und Verkehrswesen CY - Köln ER - TY - GEN A1 - Borndörfer, Ralf A1 - Löbel, Andreas T1 - Dienstplanoptimierung im ÖPNV Y1 - 2000 UR - http://www.uni-duisburg.de/FB11/PUBL/PRPLIST/prp00.html ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Löbel, Andreas A1 - Weider, Steffen ED - Hickman, Mark ED - Mirchandani, Pitu ED - Voß, Stefan T1 - A Bundle Method for Integrated Multi-Depot Vehicle and Duty Scheduling in Public Transit T2 - Computer-aided Systems in Public Transport Y1 - 2008 UR - http://opus.kobv.de/zib/volltexte/2004/790/ VL - 600 SP - 3 EP - 24 PB - Springer-Verlag ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Löbel, Andreas A1 - Weider, Steffen T1 - Integrierte Umlauf- und Dienstplanung im Öffentlichen Verkehr T2 - Heureka ’02 Y1 - 2002 UR - http://opus.kobv.de/zib/volltexte/2002/678/ SP - 77 EP - 98 PB - Forschungsgesellschaft für Straßen- und Verkehrswesen CY - Köln 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 - Löbel, Andreas A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Weider, Steffen T1 - Rapid Branching N2 - We propose rapid branching (RB) as a general branch-and-bound heuristic for solving large scale optimization problems in traffic and transport. The key idea is to combine a special branching rule and a greedy node selection strategy in order to produce solutions of controlled quality rapidly and efficiently. We report on three successful applications of the method for integrated vehicle and crew scheduling, railway track allocation, and railway vehicle rotation planning. T3 - ZIB-Report - 12-10 KW - large scale optimization KW - rapid branching KW - column generation Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14728 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 - TY - GEN A1 - Löbel, Andreas T1 - Solving Large-Scale Multiple-Depot Vehicle Scheduling Problems N2 - This paper presents an integer linear programming approach with delayed column generation for the {\em NP} Multiple-Depot Vehicle Scheduling Problem (MDVSP) in public mass transit. We describe in detail all basic ingredients of our approach that are indispensable to solve truly large-scale real-world instances to optimality, and we report on computational investigations that are based on real-world instances from the city of Berlin, the city of Hamburg, and the region around Hamburg. These real-world instances have up to 25 thousand timetabled trips and 70 million dead-head trips. Computational tests using the data of the Hamburger Hochbahn AG indicate savings of several vehicles and a cost reduction of about 10\% compared with the solution provided by HOT II, the vehicle scheduling tool of the HanseCom GmbH, Hamburg. Parts of our algorithms are already integrated in the BERTA system of the Berliner Verkehrsbetriebe (BVG) and will soon be integrated in the MICROBUS system of the Gesellschaft für Informatik, Verkehrs- und Umweltplanung mbH (IVU), Berlin. T3 - ZIB-Report - SC-97-17 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2866 ER -