TY - GEN A1 - Borndörfer, Ralf A1 - Ferreira, Carlos E. A1 - Martin, Alexander T1 - Matrix Decomposition by Branch-and-Cut N2 - 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. T3 - ZIB-Report - SC-97-14 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2839 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Herzog, Werner A1 - Klostermeier, Fridolin A1 - Konsek, Wilhelm A1 - Küttner, Christian T1 - Kürzen muß nicht Kahlschlag heißen - das Beispiel Telebus-Behindertenfahrdienst Berlin N2 - Müssen Etatkürzungen bei staatlichen Dienstleistungseinrichtungen notwendig zu Leistungseinschränkungen oder Gebührenerhöhungen führen? Wir zeigen am Beispiel des Berliner Behindertenfahrdienstes {\em Telebus}, da\ss{} Sparzwang auch als Chance zur Verbesserung der eigenen Verwaltungs- und Arbeitsabläufe genutzt werden kann. Durch stärkere Dienstleistungsorientierung, Vereinfachung der Arbeitsabläufe 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. T3 - ZIB-Report - SC-96-41 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2510 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Klostermeier, Fridolin A1 - Küttner, Christian T1 - Telebus Berlin - Mobilität für Behinderte N2 - Steigendes Mobilitätsbedürfnis 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 Fahrtwünschen pro Tag an ihre Grenzen. Zur Lösung 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 Arbeitsabläufe unterstützenden Computersystems, das seit über einem Jahr im Einsatz ist. Herzstück 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 Behindertenbeförderung. Das Beispiel Telebus zeigt, da\ss{} der Einsatz mathematischer Optimierungstechniken neue Möglichkeiten für Kosteneinsparungen bei gleichzeitiger Serviceverbesserung auch in anderen Bereichen des ÖPNV eröffnet. T3 - ZIB-Report - SC-96-40 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2500 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 - JOUR A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Klostermeier, Fridolin A1 - Küttner, Christian T1 - Berliner Telebussystem bietet Mobilität für Behinderte JF - Der Nahverkehr Y1 - 1997 VL - 1/2 SP - 20 EP - 22 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Klostermeier, Fridolin A1 - Küttner, Christian T1 - Optimierung des Berliner Behindertenfahrdienstes JF - DMV-Mitteilungen Y1 - 1997 VL - 2 SP - 38 EP - 43 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 - GEN A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Klostermeier, Fridolin A1 - Küttner, Christian T1 - Telebus-Disposition: Ein Konzept zur Serviceverbesserung bei gleichzeitiger Kostensenkung.[nur hausintern] N2 - "`Telebus"' ist der soziale Behindertenfahrdienst im Land Berlin. Das Telebus-Forschungsprojekt des Konrad-Zuse-Zentrums für Informationstechnik (ZIB) hat das Ziel, den Fahrdienst (insbesondere die Disposition der Telebusse) zu verbessern, d.h. kundenfreundlicher zu gestalten und gleichzeitig billiger zu machen. In diesem Bericht werden die bisherigen Ergebnisse dargestellt und weitere Möglichkeiten zur Verbesserung des Service und zur Reduzierung der Kosten skizziert. \originalTeX T3 - ZIB-Report - TR-93-03 Y1 - 1993 N1 - Volltext nur Hausintern 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 - JOUR A1 - Borndörfer, Ralf A1 - Ferreira, Carlos A1 - Martin, Alexander T1 - Decomposing Matrices into Blocks JF - SIAM J. Optim. Y1 - 1998 UR - http://opus.kobv.de/zib/volltexte/1997/285/ VL - 9 IS - 1 SP - 236 EP - 269 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Weismantel, Robert T1 - Set Packing Relaxations of Some Integer Programs JF - Math. Programming Y1 - 2000 UR - http://opus.kobv.de/zib/volltexte/1997/300/ VL - 88 SP - 425 EP - 450 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Klostermeier, Fridolin A1 - Küttner, Christian T1 - Telebus Berlin – Mobilität für Behinderte JF - Der Nahverkehr Y1 - 1997 UR - http://opus.kobv.de/zib/volltexte/1996/251/ VL - 1–2 SP - 20 EP - 22 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Weismantel, Robert T1 - Discrete Relaxations of Combinatorial Programs JF - Discrete Appl. Math. Y1 - 2001 UR - http://opus.kobv.de/zib/volltexte/1997/324/ VL - 112 IS - 1–3 SP - 11 EP - 26 ER - TY - THES A1 - Borndörfer, Ralf T1 - Aspects of Set Packing, Partitioning, and Covering N2 - Diese Dissertation befaßt sich mit ganzzahligen Programmen mit 0/1 Systemen: SetPacking-, Partitioning- und Covering-Probleme. Die drei Teile der Dissertation behandeln polyedrische, algorithmische und angewandte Aspekte derartiger Modelle. Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10126 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 - Klostermeier, Fridolin A1 - Küttner, Christian ED - Wilson, Nigel T1 - Telebus Berlin: Vehicle Scheduling in a Dial-a-Ride System T2 - Proceedings of the 7th International Workshop on Computer-Aided Transit Scheduling Y1 - 1999 U6 - https://doi.org/10.1007/978-3-642-85970-0_19 SP - 391 EP - 422 PB - Springer Verlag CY - Berlin ER - TY - THES A1 - Borndörfer, Ralf T1 - Aspects of Set Packing, Partitioning, and Covering Y1 - 1998 UR - http://opus.kobv.de/zib/volltexte/1998/1028/ ER - TY - GEN A1 - Borndörfer, Ralf ED - Grötschel, Martin T1 - Combinatorial Packing Problems T2 - The Sharpest Cut – The Impact of Manfred Padberg and His Work Y1 - 2004 UR - http://opus.kobv.de/zib/volltexte/2003/726/ SP - 19 EP - 32 PB - SIAM CY - Philadelphia 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 T1 - Combinatorial Packing Problems N2 - This article investigates a certain class of combinatorial packing problems and some polyhedral relations between such problems and the set packing problem. T3 - ZIB-Report - 03-03 KW - Packing problems KW - polyhedral combinatorics Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7255 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 - Borndörfer, Ralf A1 - Ferreira, Carlos E. A1 - Martin, Alexander T1 - Decomposing Matrices into Blocks N2 - 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 MITLIB 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. In practice, however, one would use heuristics to find a good decomposition. We present several heuristic ideas and test their performance. Finally, we investigate the usefulness of optimal matrix decompositions into bordered block diagonal form for integer programming by using such decompositions to guide the branching process in a branch-and-cut code for general mixed integer programs. T3 - ZIB-Report - SC-97-15 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2849 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Klostermeier, Fridolin A1 - Küttner, Christian T1 - Telebus Berlin: Vehicle Scheduling in a Dial-a-Ride System N2 - {\em Telebus\/} is Berlin's dial-a-ride system for handicapped people that cannot use the public transportation system. The service is provided by a fleet of about 100 mini-busses and includes aid to get in and out of the vehicle. Telebus has between 1,000 and 1,500 transportation requests per day. The problem arises to schedule these requests into the vehicles such that punctual service is provided while operation costs should be minimum. Additional constraints include pre-rented vehicles, fixed bus driver shift lengths, obligatory breaks, and different vehicle capacities. We use a {\em set partitioning\/} approach for the solution of the bus scheduling problem that consists of two steps. The first {\em clustering\/} step identifies segments of possible bus tours (``orders'') such that more than one person is transported at a time; the aim in this step is to reduce the size of the problem and to make use of larger vehicle capacities. The problem to select a set of orders such that the traveling distance of the vehicles within the orders is minimal is a set partitioning problem that we can solve to optimality. In the second step the selected orders are {\em chained\/} to yield possible bus tours respecting all side constraints. The problem to select a set of such bus tours such that each order is serviced once and the total traveling distance of the vehicles is minimum is again a set partitioning problem that we solve approximately. We have developed a computer system for the solution of the bus scheduling problem that includes a branch-and-cut algorithm for the solution of the set partitioning problems. A version of this system is in operation at Telebus since July 1995. Its use made it possible that Telebus can service today about 30\% more requests per day for the same amount of money than before. T3 - ZIB-Report - SC-97-23 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2925 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Weismantel, Robert T1 - Set Packing Relaxations of Some Integer Programs N2 - This paper is about {\em set packing relaxations\/} of combinatorial optimization problems associated with acyclic digraphs and linear orderings, cuts and multicuts, and vertex packings themselves. Families of inequalities that are valid for such a relaxation as well as the associated separation routines carry over to the problems under investigation. T3 - ZIB-Report - SC-97-30 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2998 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Weismantel, Robert T1 - Discrete Relaxations of Combinatorial Programs N2 - This paper investigates {\em relations\/} among combinatorial optimization problems. To establish such relations we introduce a transformation technique \mbox{---{\em aggregation}---} that allows to relax an integer program by means of another integer program. We prove that various families of prominent inequalities for the acyclic subdigraph problem, the multiple knapsack problem, the max cut, graph, and the clique partitioning problem, the set covering problem, and the set packing problem can be derived and separated in polynomial time in this way. Our technique is algorithmic. It has been implemented and used in a set partitioning code. T3 - ZIB-Report - SC-97-54 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3230 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Klostermeier, Fridolin A1 - Küttner, Christian T1 - Optimierung des Berliner Behindertenfahrdienstes N2 - In diesem Artikel geben wir einen Überblick über das Telebus-Projekt am Konrad-Zuse-Zentrum, Berlin, durch das der Behindertenfahrdienst in Berlin reorganisiert und optimiert wurde. Wir berichten kurz über die mathematischen Probleme und, etwas ausführlicher, über die nicht-mathematischen Schwierigkeiten, die bei der Durchführung dieses Projektes auftraten. T3 - ZIB-Report - SC-97-10 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2799 ER -