@misc{PfetschBorndoerfer2005, author = {Pfetsch, Marc and Bornd{\"o}rfer, Ralf}, title = {Routing in Line Planning for Public Transportation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8706}, number = {05-36}, year = {2005}, abstract = {The line planning problem is one of the fundamental problems in strategic planning of public and rail transport. It consists in finding lines and corresponding frequencies in a network such that a giv en demand can be satisfied. There are two objectives. Passengers want to minimize travel times, the transport company wishes to minimize operating costs. We investigate three variants of a multi-commo dity flow model for line planning that differ with respect to passenger routings. The first model allows arbitrary routings, the second only unsplittable routings, and the third only shortest path rou tings with respect to the network. We compare these models theoretically and computationally on data for the city of Potsdam.}, language = {en} } @misc{BorndoerferGroetschelPfetsch2005, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and Pfetsch, Marc}, title = {A Column-Generation Approach to Line Planning in Public Transport}, doi = {/10.1287/trsc.1060.0161}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8522}, number = {05-18}, year = {2005}, abstract = {The line planning problem is one of the fundamental problems in strategic planning of public and rail transport. It consists in finding lines and corresponding frequencies in a transport network such that a given travel demand can be satisfied. There are (at least) two objectives. The transport company wishes to minimize operating costs, the passengers want to minimize travel times. We propose a n ew multi-commodity flow model for line planning. Its main features, in comparison to existing models, are that the passenger paths can be freely routed and that the lines are generated dynamically. We discuss properties of this model and investigate its complexity. Results with data for the city of Potsdam, Germany, are reported.}, language = {en} } @misc{BorndoerferGroetschelPfetsch2005, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and Pfetsch, Marc}, title = {Public Transport to the fORe!}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8562}, number = {05-22}, year = {2005}, abstract = {Can OR methods help the public transport industry to break even? The article gives evidence that there exist significant potentials in this direction, which can be harnessed by a combination of modern mathematical methods and local planning knowledge. Many of the planning steps in public transport are classical combinatorial problems, which can be solved in unprecedented size and quality due the rapid progress in large-scale optimization. Three examples on vehicle scheduling, duty scheduling, and integrated vehicle and duty scheduling illustrate the level that has been reached and the improvements that can be achieved today. Extensions of such methods to further questions of strategic, online, and market-oriented planning are currently investigated. In this way, OR can make a significant contribution to answer the basic but extremely difficult question ``What is a good public transport network?.}, language = {en} } @misc{BorndoerferGroetschelLoebel2000, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and L{\"o}bel, Andreas}, title = {Der schnellste Weg zum Ziel}, journal = {Alles Mathematik}, editor = {Aigner, Martin and Behrends, Ehrhard}, publisher = {Vieweg Verlag}, address = {Braunschweig/Wiesbaden}, doi = {10.1007/978-3-322-96366-6_5}, pages = {45 -- 76}, year = {2000}, language = {en} } @inproceedings{BorndoerferGroetschelPfetsch2008, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and Pfetsch, Marc}, title = {Models for Line Planning in Public Transport}, volume = {600}, booktitle = {Computer-aided Systems in Public Transport (CASPT 2004)}, editor = {Hickman, Mark and Mirchandani, Pitu and Voß, Stefan}, publisher = {Springer-Verlag}, doi = {10.1007/978-3-540-73312-6_18}, pages = {363 -- 378}, year = {2008}, language = {en} } @article{BorndoerferGroetschelPfetsch2007, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and Pfetsch, Marc}, title = {A Column-Generation Approach to Line Planning in Public Transport}, volume = {41}, journal = {Transportation Science (INFORMS)}, number = {1}, doi = {10.1287/trsc.1060.0161}, pages = {123 -- 132}, year = {2007}, language = {en} } @misc{BorndoerferGroetschelPfetsch2004, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and Pfetsch, Marc}, title = {Models for Line Planning in Public Transport}, doi = {10.1007/978-3-540-73312-6_18}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7854}, number = {04-10}, year = {2004}, abstract = {The \emph{line planning problem} is one of the fundamental problems in strategic planning of public and rail transport. It consists of finding lines and corresponding frequencies in a public transport network such that a given travel demand can be satisfied. There are (at least) two objectives. The transport company wishes to minimize its operating cost; the passengers request short travel times. We propose two new multi-commodity flow models for line planning. Their main features, in comparison to existing models, are that the passenger paths can be freely routed and that the lines are generated dynamically.}, language = {en} } @misc{Neumann2005, type = {Master Thesis}, author = {Neumann, Marika}, title = {Mathematische Preisplanung im {\"O}PNV}, year = {2005}, language = {en} } @incollection{BorndoerferNeumannPfetsch2006, author = {Bornd{\"o}rfer, Ralf and Neumann, Marika and Pfetsch, Marc}, title = {Optimal Fares for Public Transport}, booktitle = {Operations Research Proceedings 2005}, editor = {Haasis, Hans-Dietrich and Kopfer, Herbert and Sch{\"o}nberger, J{\"o}rn}, publisher = {Springer-Verlag}, pages = {29 -- 36}, year = {2006}, language = {en} } @incollection{Neumann2007, author = {Neumann, Marika}, title = {Fare Planning for Public Transport}, booktitle = {Operations Research Proceedings 2006}, editor = {Waldmann, Karl-Heinz and Stocker, Ulrike}, publisher = {Springer-Verlag}, pages = {61 -- 66}, year = {2007}, language = {en} } @article{Neumann2007, author = {Neumann, Marika}, title = {Mathematische Preisplanung im {\"O}PNV}, journal = {OR News}, number = {30}, pages = {29 -- 31}, year = {2007}, language = {en} } @article{BorndoerferGroetschelPfetsch2006, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and Pfetsch, Marc}, title = {Public transport to the fORe}, journal = {OR/MS Today}, pages = {30 -- 40}, year = {2006}, language = {en} } @misc{BorndoerferGroetschelLoebel1999, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and L{\"o}bel, Andreas}, title = {Der Schnellste Weg zum Ziel}, doi = {10.1007/978-3-322-96366-6_5}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4209}, number = {SC-99-32}, year = {1999}, abstract = {Wir geben eine Einf{\"u}hrung in die Mathematik von und mit Wegen. Nicht auf dem k{\"u}rzesten, aber auf einem hoffentlich kurzweiligen Weg!}, language = {de} } @misc{BorndoerferNeumannPfetsch2005, author = {Bornd{\"o}rfer, Ralf and Neumann, Marika and Pfetsch, Marc}, title = {Fare Planning for Public Transport}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8541}, number = {05-20}, year = {2005}, abstract = {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.}, language = {en} } @phdthesis{Borndoerfer2010, author = {Bornd{\"o}rfer, Ralf}, title = {Mathematical Optimization and Public Transportation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-13613}, school = {Zuse Institute Berlin (ZIB)}, year = {2010}, abstract = {This cumulative thesis collects the following six papers for obtaining the habilitation at the Technische Universit{\"a}t Berlin, Fakult{\"a}t II - Mathematik und Naturwissenschaften: (1) Set packing relaxations of some integer programs. (2) Combinatorial packing problems. (3) Decomposing matrices into blocks. (4) A bundle method for integrated multi-depot vehicle and duty scheduling in public transit. (5) Models for railway track allocation. (6) A column-generation approach to line planning in public transport. Some changes were made to the papers compared to the published versions. These pertain to layout unifications, i.e., common numbering, figure, table, and chapter head layout. There were no changes with respect to notation or symbols, but some typos have been eliminated, references updated, and some links and an index was added. The mathematical content is identical. The papers are about the optimization of public transportation systems, i.e., bus networks, railways, and airlines, and its mathematical foundations, i.e., the theory of packing problems. The papers discuss mathematical models, theoretical analyses, algorithmic approaches, and computational aspects of and to problems in this area. Papers 1, 2, and 3 are theoretical. They aim at establishing a theory of packing problems as a general framework that can be used to study traffic optimization problems. Indeed, traffic optimization problems can often be modelled as path packing, partitioning, or covering problems, which lead directly to set packing, partitioning, and covering models. Such models are used in papers 4, 5, and 6 to study a variety of problems concerning the planning of line systems, buses, trains, and crews. The common aim is always to exploit as many degrees of freedom as possible, both at the level of the individual problems by using large-scale integer programming techniques, as well as on a higher level by integrating hitherto separate steps in the planning process.}, language = {en} } @book{Borndoerfer2010, author = {Bornd{\"o}rfer, Ralf}, title = {Mathematical Optimization and Public Transportation}, publisher = {TU Berlin}, year = {2010}, language = {en} } @inproceedings{PfetschBorndoerfer2006, author = {Pfetsch, Marc and Bornd{\"o}rfer, Ralf}, title = {Routing in Line Planning for Public Transportation}, booktitle = {Operations Research Proceedings 2005}, editor = {Haasis, Hans-Dietrich}, publisher = {Springer-Verlag}, pages = {405 -- 410}, year = {2006}, language = {en} } @misc{TorresTorresBorndoerferetal.2008, author = {Torres, Luis Miguel and Torres, Ramiro and Bornd{\"o}rfer, Ralf and Pfetsch, Marc}, title = {On the Line Planning Problem in Tree Networks}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11069}, number = {08-52}, year = {2008}, abstract = {We introduce an optimization model for the line planning problem in a public transportation system that aims at minimizing operational costs while ensuring a given level of quality of service in terms of available transport capacity. We discuss the computational complexity of the model for tree network topologies and line structures that arise in a real-world application at the Trolebus Integrated System in Quito. Computational results for this system are reported.}, language = {en} } @misc{Neumann2009, author = {Neumann, Marika}, title = {Fare Planning for Public Transport}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11144}, number = {09-04}, year = {2009}, abstract = {In this paper we investigate the fare planning model for public transport, which consists in designing a system of fares maximizing the revenue. We discuss a discrete choice model in which passengers choose between different travel alternatives to express the demand as a function of fares. Furthermore, we give a computational example for the city of Potsdam and discuss some theoretical aspects.}, language = {en} } @misc{BorndoerferNeumannPfetsch2005, author = {Bornd{\"o}rfer, Ralf and Neumann, Marika and Pfetsch, Marc}, title = {Optimal Fares for Public Transport}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8698}, number = {05-35}, year = {2005}, abstract = {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.}, language = {en} }