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 - 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 - Krumke, Sven A1 - Rambau, Jörg A1 - Weider, Steffen T1 - An Approximation Algorithm for the Non-Preemptive Capacitated Dial-a-Ride Problem N2 - In the Capacitated Dial-a-Ride Problem (CDARP) we are given a transportation network and a finite set of transportation jobs. Each job specifies the source and target location which are both part of the network. A server which can carry at most $C$~objects at a time can move on the transportation network in order to process the transportation requests. The problem CDARP consists of finding a shortest transportation for the jobs starting and ending at a designated start location. In this paper we are concerned with the restriction of CDARP to graphs which are simple paths. This setting arises for instance when modelling applications in elevator transportation systems. It is known that even for this restricted class of graphs CDARP is NP-hard to solve. We provide a polynomial time approximation algorithm that finds a transportion of length at most thrice the length of the optimal transportation. T3 - ZIB-Report - 00-53 KW - NP-completeness KW - polynomial-time approximation algorithms KW - stacker-crane problem KW - vehicle Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6217 ER - TY - THES A1 - Weider, Steffen T1 - Integration of Vehicle and Duty Scheduling in Public Transport N2 - This thesis describes the algorithm IS-OPT that integrates scheduling of vehicles and duties in public bus transit. IS-OPT is the first algorithm which solves integrated vehicle and duty scheduling problems arising in medium sized carriers such that its solutions can be used in daily operations without further adaptions. This thesis is structured as follows: The first chapter highlights mathematical models of the planning process of public transit companies and examines their potential for integrating them with other planning steps. It also introduces descriptions of the vehicle and the duty scheduling problem. Chapter 2 motivates why it can be useful to integrate vehicle and duty scheduling, explains approaches of the literature, and gives an outline of our algorithm IS-OPT. The following chapters go into the details of the most important techniques and methods of IS-OPT: In Chapter 3 we describe how we use Lagrangean relaxation in a column generation framework. Next, in Chapter 4, we describe a variant of the proximal bundle method (PBM) that is used to approximate linear programs occurring in the solution process. We introduce here a new variant of the PBM which is able to utilize inexact function evaluation and the use of epsilon-subgradients. We also show the convergence of this method under certain assumptions. Chapter 5 treats the generation of duties for the duty scheduling problem. This problem is modeled as a resourceconstraint- shortest-path-problem with non-linear side constraints and nearly linear objective function. It is solved in a two-stage approach. At first we calculate lower bounds on the reduced costs of duties using certain nodes by a new inexact label-setting algorithm. Then we use these bounds to speed up a depth-first-search algorithm that finds feasible duties. In Chapter 6 we present the primal heuristic of IS-OPT that solves the integrated problem to integrality. We introduce a new branch-and-bound based heuristic which we call rapid branching. Rapid branching uses the proximal bundle method to compute lower bounds, it introduces a heuristic node selection scheme, and it utilizes a new branching rule that fixes sets of many variables at once. The common approach to solve the problems occurring in IS-OPT is to trade inexactness of the solutions for speed of the algorithms. This enables, as we show in Chapter 7, to solve large real world integrated problems by IS-OPT. The scheduled produced by IS-OPT save up to 5% of the vehicle and duty cost of existing schedules of regional and urban public transport companies. N2 - Diese Arbeit beschreibt den Algorithmus IS-OPT, welcher der erste Algorithmus ist, der integrierte Umlauf- und Dienstplanungsprobleme für mittelgroße Verkehrsunternehmen löst und dabei alle betrieblichen Einzelheiten berücksichtigt. Seine Lösungen können daher direkt in den täglichen Betrieb übernommen werden. Im ersten Kapitel werden mathematische Modelle für verschiedenen Probleme aus dem Planungsprozess von Nahverkehrsunternehmen beschrieben. Es werden Ansätze zur Integration der einzelnen Probleme untersucht. In diesem Kapitel werden außerdem das Umlauf- und das Dienstplanungsproblem eingeführt. Kapitel 2 motiviert, warum Integration von Umlauf- und Dienstplanung hilfreich ist oder in welchen Fällen sie sogar unabdingbar ist; es gibt einen Überblick über die vorhanden Literatur zur integrierten Umlauf- und Dienstplanung und umreißt unseren Algorithmus IS-OPT. Die weiteren Kapitel behandeln die in IS-OPT verwendeten Methoden: In Kapitel 3 beschreiben wir, wie Spaltenerzeugung für lineare Programme mit Lagrange-Relaxierung und Subgradienten-Verfahren kombiniert werden kann. In Kapitel 4 wird unsere Variante der proximalen Bündelmethode beschrieben. Diese wird benutzt um näherungsweise primale und duale Lösungen von lineare Programmen zu berechnen. Unsere Variante ist angepasst, um auch mit ungenauer Funktionsauswertung und Epsilon-Subgradienten arbeiten zu können. Wir zeigen die Konvergenz dieser Variante unter bestimmten Annahmen. Kapitel 5 behandelt das Erzeugen von Diensten für das Dienstplanungsproblem. Dieses Problem ist als ein Kürzeste-Wege-Problem mit nichtlinearen Nebenbedingungen und fast linearer Zielfunktion modelliert. Wir lösen es, indem zuerst Schranken für die reduzierten Kosten von Diensten, die bestimmte Knoten benutzen, berechnet werden. Diese Schranken werden benutzt, um in einem Tiefensuchalgorithmus den Suchbaum klein zu halten. Im Kapitel 6 präsentieren wir die neu entwickelte Heuristik "Rapid Branching", die eine ganzzahlige Lösung des integrierten Problems berechnet. Rapid Branching kann als eine spezielle Branch-and-Bound-Heuristik gesehen werden, welche die Bündelmethode benutzt. In den Knoten des Suchbaums können mehrere Variablen auf einmal fixiert werden, die mit Hilfe einer Perturbationsheuristik ausgewählt werden. In Kapitel 7 schließlich zeigen wir, daß wir mit IS-OPT auch große Probleminstanzen aus der Praxis lösen können und dabei bis zu 5% der Fahrzeug- und Dienstkosten sparen können. KW - Öffentlicher Personennahverkehr KW - lineare Optimierung KW - Umlaufplanung KW - Dienstplanung KW - Integration KW - Public Transport KW - linear Optimization KW - vehicle scheduling KW - duty scheduling KW - integration Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:83-opus-16240 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Langenhan, Andreas A1 - Löbel, Andreas A1 - Schulz, Christof A1 - Weider, Steffen T1 - Duty Scheduling Templates N2 - We propose duty templates as a novel concept to produce similar duty schedules for similar days of operation in public transit. Duty templates can conveniently handle various types of similarity requirements, and they can be implemented with ease using standard algorithmic techniques. They have produced good results in practice. T3 - ZIB-Report - 12-09 KW - duty scheduling KW - duty templates Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14699 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 - Reuther, Markus A1 - Schlechte, Thomas A1 - Weider, Steffen T1 - Vehicle Rotation Planning for Intercity Railways N2 - This paper provides a generic formulation for rolling stock planning problems in the context of intercity passenger traffic. The main contributions are a graph theoretical model and a Mixed-Integer-Programming formulation that integrate all main requirements of the considered Vehicle-Rotation-Planning problem (VRPP). We show that it is possible to solve this model for real-world instances provided by our industrial partner DB Fernverkehr AG using modern algorithms and computers. T3 - ZIB-Report - 12-11 KW - rolling-stock-planning KW - mixed-integer-programming KW - hypergraphs KW - column generation KW - rapid branching Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14731 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Schlechte, Thomas A1 - Weider, Steffen T1 - Railway Track Allocation by Rapid Branching N2 - The track allocation problem, also known as train routing problem or train timetabling problem, is to find a conflict-free set of train routes of maximum value in a railway network. Although it can be modeled as a standard path packing problem, instances of sizes relevant for real-world railway applications could not be solved up to now. We propose a rapid branching column generation approach that integrates the solution of the LP relaxation of a path coupling formulation of the problem with a special rounding heuristic. The approach is based on and exploits special properties of the bundle method for the approximate solution of convex piecewise linear functions. Computational results for difficult instances of the benchmark library TTPLIB are reported. T3 - ZIB-Report - 10-22 KW - Trassenallokationsproblem KW - Ganzzahlige Programmierung KW - Rapid-Branching-Heuristik KW - Proximale Bündelmethode KW - Optimization KW - Railway Track Allocation KW - Bundle Method KW - Rapid Branching Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11864 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Weider, Steffen T1 - A Hypergraph Model for Railway Vehicle Rotation Planning N2 - We propose a model for the integrated optimization of vehicle rotations and vehicle compositions in long distance railway passenger transport. The main contribution of the paper is a hypergraph model that is able to handle the challenging technical requirements as well as very general stipulations with respect to the ``regularity'' of a schedule. The hypergraph model directly generalizes network flow models, replacing arcs with hyperarcs. Although NP-hard in general, the model is computationally well-behaved in practice. High quality solutions can be produced in reasonable time using high performance Integer Programming techniques, in particular, column generation and rapid branching. We show that, in this way, large-scale real world instances of our cooperation partner DB Fernverkehr can be solved. T3 - ZIB-Report - 11-36 KW - Rolling Stock Planning, Hypergraph Modeling, Integer Programming, Column Generation, Rapid Branching Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0030-drops-32746 SN - 1438-0064 ER -