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 - Menne, Ulrich A1 - Raack, Christian A1 - Wessäly, Roland A1 - Kharitonov, Daniel T1 - Optimal Degree of Optical Circuit Switching in IP-over-WDM Networks N2 - In this paper, we study the influence of technology, traffic properties and price trends on optimized design of a reference IP-over-WDM network with rich underlying fiber topology. In each network node, we investigate the optimal degree of traffic switching in an optical (lambda) domain versus an electrical (packet) domain, also known as measure of \emph{node transparency}. This measure is studied in connection to changes in traffic volume, demand affinity, optical circuit speeds and equipment cost. By applying variable design constraints, we assess the relative roles of the two distinct equipment groups, IP routers and optical cross-connects, with respect to resulting changes in cost-sensitive network architectures. T3 - ZIB-Report - 11-50 KW - IP-over-WDM KW - Circuit Switching KW - Opacity Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14843 SN - 1438-0064 ER - TY - THES A1 - Karbstein, Marika T1 - Line Planning and Connectivity N2 - This thesis introduces the Steiner connectivity problem. It is a generalization of the well known Steiner tree problem. Given a graph G = (V, E) and a subset T ⊆ V of the nodes, the Steiner tree problem consists in finding a cost minimal set of edges connecting all nodes in T . The Steiner connectivity problem chooses, instead of edges, from a given set of paths a subset to connect all nodes in T . We show in the first part of this thesis that main results about complexity, approximation, integer programming formulations, and polyhedra can be generalized from the Steiner tree problem to the Steiner connectivity problem. An example for a straightforward generalization are the Steiner partition inequalities, a fundamental class of facet defining inequalities for the Steiner tree problem. They can be defined for the Steiner connectivity problem in an analogous way as for the Steiner tree problem. An example for a generalization that needs more effort is the definition of a directed cut formulation and the proof that this dominates the canonical undirected cut formulation enriched by all Steiner partition inequalities. For the Steiner connectivity problem this directed cut formulation leads to extended formulations, a concept that is not necessary for the Steiner tree problem. There are also major differences between both problems. For instance, the case T = V for the Steiner connectivity problem is equivalent to a set covering problem and, hence, not a polynomial solvable case as in the Steiner tree problem. The Steiner connectivity problem is not only an interesting generalization of the Steiner tree problem but also the underlying connectivity problem in line planning with inte- grated passenger routing. The integrated line planning and passenger routing problem is an important planning problem in service design of public transport and the topic of the second part. Given is the infrastructure network of a public transport system where the edges correspond to streets and tracks and the nodes correspond to stations/stops of lines. The task is to find paths in the infrastructure network for lines and passengers such that the capacities of the lines suffice to transport all passengers. Existing models in the literature that integrate a passenger routing in line planning either treat transfers in a rudimentary way and, hence, neglect an important aspect for the choice of the pas- senger routes, or they treat transfers in a too comprehensive way and cannot be solved for large scale real world problems. We propose a new model that focuses on direct connections. The attractiveness of transfer free connections is increased by introducing a transfer penalty for each non-direct connection. In this way, a passenger routing is computed that favors direct connections. For the computation of this model we also implemented algorithms influenced by the results for the Steiner connectivity problem. We can compute with our model good solutions that minimize a weighted sum of line operating costs and passengers travel times. These solutions improve the solutions of an existing approach, that does not consider direct connections, by up to 17%. In contrast to a comprehensive approach, that considers every transfer and for which we could not even solve the root LP within 10 hours for large instances, the solutions of the new model, computed in the same time, are close to optimality (<1%) or even optimal for real world instances. In a project with the Verkehr in Potsdam GmbH to compute the line plan for 2010 we showed that our approach is applicable in practice and can be used to solve real world problems. Y1 - 2013 UR - www.zib.de/karbstein/scplpp.pdf SN - 978-3-8439-1062-0 ER - TY - GEN A1 - Karbstein, Marika T1 - Integrated Line Planning and Passenger Routing: Connectivity and Transfers N2 - The integrated line planning and passenger routing problem is an important planning problem in service design of public transport. A major challenge is the treatment of transfers. A main property of a line system is its connectivity. In this paper we show that analysing the connecvitiy aspect of a line plan gives a new idea to handle the transfer aspect of the line planning problem. T3 - ZIB-Report - 14-42 KW - line planning, transfers,Steiner connectivity problem Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-52986 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Sagnol, Guillaume A1 - Schlechte, Thomas A1 - Swarat, Elmar T1 - Optimal Toll Enforcement - an Integration of Vehicle Routing and Duty Rostering N2 - We present the problem of planning mobile tours of inspectors on German motorways to enforce the payment of the toll for heavy good trucks. This is a special type of vehicle routing problem with the objective to conduct as good inspections as possible on the complete network. In addition, the crews of the tours have to be scheduled. Thus, we developed a personalized crew rostering model. The planning of daily tours and the rostering are combined in a novel integrated approach and formulated as a complex and large scale Integer Program. The paper focuses first on different requirements for the rostering and how they can be modeled in detail. The second focus is on a bicriterion analysis of the planning problem to find the balance between the control quality and the roster acceptance. On the one hand the tour planning is a profit maximization problem and on the other hand the rostering should be made in a employee friendly way. Finally, computational results on real-world instances show the practicability of our method. T3 - ZIB-Report - 13-79 KW - vehicle routing KW - crew rostering KW - integer programming KW - bicriteria optimization Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-45107 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Neumann, Marika A1 - Pfetsch, Marc T1 - Fare Planning for Public Transport N2 - In this paper we introduce the fare planning problem for public transport which consists in designing a system of fares maximizing revenue. We propose a new simple general model for this problem. It i s based on a demand function and constraints for the different fares. The constraints define the structure of the fare system, e.g., distance dependent fares or zone fares. We discuss a simple example with a quadratic demand function and distance dependent fares. Then we introduce a more realistic discrete choice model in which passengers choose between different alternatives depending on the numb er of trips per month. We demonstrate the examples by computational experiments. T3 - ZIB-Report - 05-20 KW - fare planning KW - demand function KW - discrete choice model Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8541 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Neumann, Marika A1 - Pfetsch, Marc T1 - Angebotsplanung im öffentlichen Nahverkehr T1 - Service Design in Public Transport N2 - Die Angebotsplanung im öffentlichen Nahverkehr umfasst die Aufgaben der Netz-, Linien-,Fahr- und Preisplanung. Wir stellen zwei mathematische Optimierungsmodelle zur Linien- und Preisplanung vor. Wir zeigen anhand von Berechnungen für die Verkehrsbetriebe in Potsdam(ViP), dass sich damit komplexe Zusammenhänge quantitativ analysieren lassen. Auf diese Weise untersuchen wir die Auswirkungen von Freiheitsgraden auf die Konstruktion von Linien und die Wahl von Reisewegen der Passagiere, Abhängigkeiten zwischen Kosten und Reisezeiten sowie den Einfluss verschiedener Preissysteme auf Nachfrage und Kostendeckung. T3 - ZIB-Report - 08-04 KW - Preisplanung KW - Linienplanung KW - Optimierung Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10555 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Neumann, Marika A1 - Pfetsch, Marc T1 - Models for Fare Planning in Public Transport N2 - The optimization of fare systems in public transit allows to pursue objectives such as the maximization of demand, revenue, profit, or social welfare. We propose a non-linear optimization approach to fare planning that is based on a detailed discrete choice model of user behavior. The approach allows to analyze different fare structures, optimization objectives, and operational scenarios involving, e.g., subsidies. We use the resulting models to compute optimized fare systems for the city of Potsdam, Germany. T3 - ZIB-Report - 08-16 KW - Preisplanung KW - Nachfragefunktion KW - Optimierung KW - Nahverkehr Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10708 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Neumann, Marika A1 - Pfetsch, Marc T1 - Optimal Fares for Public Transport N2 - The \emph{fare planning problem} for public transport is to design a system of fares that maximize the revenue. We introduce a nonlinear optimization model to approach this problem. It is based on a d iscrete choice logit model that expresses demand as a function of the fares. We illustrate our approach by computing and comparing two different fare systems for the intercity network of the Netherlands. T3 - ZIB-Report - 05-35 KW - fare planning KW - demand function KW - discrete choice model Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8698 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Neumann, Marika T1 - Models for Line Planning with Transfers N2 - We propose a novel integer programming approach to transfer minimization for line planning problems in public transit. The idea is to incorporate penalties for transfers that are induced by “connection capacities” into the construction of the passenger paths. We show that such penalties can be dealt with by a combination of shortest and constrained shortest path algorithms such that the pricing problem for passenger paths can be solved efficiently. Connection capacity penalties (under)estimate the true transfer times. This error is, however, not a problem in practice. We show in a computational comparison with two standard models on a real-world scenario that our approach can be used to minimize passenger travel and transfer times for large-scale line planning problems with accurate results. T3 - ZIB-Report - 10-11 KW - Linienplanung KW - Umsteigen KW - Ganzzahlige Programmierung KW - Kombinatorische Optimierung KW - line planning KW - transfers KW - integer programming KW - combinatorial optimization Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11742 SN - 1438-0064 ER -