TY - GEN A1 - Borndörfer, Ralf A1 - Löbel, Andreas A1 - Weider, Steffen T1 - A Bundle Method for Integrated Multi-Depot Vehicle and Duty Scheduling in Public Transit N2 - This article proposes a Lagrangean relaxation approach to solve integrated duty and vehicle scheduling problems arising in public transport. The approach is based on the proximal bundle method for the solution of concave decomposable functions, which is adapted for the approximate evaluation of the vehicle and duty scheduling components. The primal and dual information generated by the bundle method is used to guide a branch-and-bound type algorithm. Computational results for large-scale real-world integrated vehicle and duty scheduling problems with up to 1,500 timetabled trips are reported. Compared with the results of a classical sequential approach and with reference solutions, integrated scheduling offers remarkable potentials in savings and drivers' satisfaction. T3 - ZIB-Report - 04-14 KW - vehicle scheduling KW - crew scheduling KW - integrated scheduling KW - public transit KW - bundle method Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7898 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 - Borndörfer, Ralf A1 - Löbel, Andreas A1 - Weider, Steffen T1 - Integrierte Umlauf- und Dienstplanung im Öffentlichen Nahverkehr N2 - Wir beschreiben einen Ansatz zur integrierten Umlauf- und Dienstplanung im öffentlichen Nahverkehr. Der Ansatz zielt auf die Verbesserung des Gesamtwirkungsgrades dieser beiden Planungsschritte und auf die besondere Planungsproblematik im Regionalverkehr. Wir entwickeln dazu mathematische Optimierungstechniken für den Einsatz in den Planungssystemen MICROBUS II und DIVA. T3 - ZIB-Report - 02-10 KW - Integrierte Umlauf- und Dienstplanung KW - Umlaufplanung KW - Dienstplanung KW - Optimierung KW - Regionalverkehr Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6773 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Schelten, Uwe A1 - Schlechte, Thomas A1 - Weider, Steffen T1 - A Column Generation Approach to Airline Crew Scheduling N2 - The airline crew scheduling problem deals with the construction of crew rotations in order to cover the flights of a given schedule at minimum cost. The problem involves complex rules for the legality and costs of individual pairings and base constraints for the availability of crews at home bases. A typical instance considers a planning horizon of one month and several thousand flights. We propose a column generation approach for solving airline crew scheduling problems that is based on a set partitioning model. We discuss algorithmic aspects such as the use of bundle techniques for the fast, approximate solution of linear programs, a pairing generator that combines Lagrangean shortest path and callback techniques, and a novel rapid branching'' IP heuristic. Computational results for a number of industrial instances are reported. Our approach has been implemented within the commercial crew scheduling system NetLine/Crew of Lufthansa Systems Berlin GmbH. T3 - ZIB-Report - 05-37 KW - Integer Programming KW - Airline Crew Scheduling KW - Branch and Generate Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8713 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 -