@misc{MasingLindnerBorndoerfer2022, author = {Masing, Berenike and Lindner, Niels and Bornd{\"o}rfer, Ralf}, title = {The Price of Symmetric Line Plans in the Parametric City}, issn = {1438-0064}, arxiv = {http://arxiv.org/abs/2201.09756}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-85648}, year = {2022}, abstract = {We consider the line planning problem in public transport in the Parametric City, an idealized model that captures typical scenarios by a (small) number of parameters. The Parametric City is rotation symmetric, but optimal line plans are not always symmetric. This raises the question to quantify the symmetry gap between the best symmetric and the overall best solution. For our analysis, we formulate the line planning problem as a mixed integer linear program, that can be solved in polynomial time if the solutions are forced to be symmetric. The symmetry gap is provably small when a specific Parametric City parameter is fixed, and we give an approximation algorithm for line planning in the Parametric City in this case. While the symmetry gap can be arbitrarily large in general, we show that symmetric line plans are a good choice in most practical situations.}, language = {en} } @misc{MasingLindnerBorndoerfer2021, author = {Masing, Berenike and Lindner, Niels and Bornd{\"o}rfer, Ralf}, title = {Optimal Line Plans in the Parametric City and the Impact of In-Motion Costs}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-84195}, year = {2021}, abstract = {Line planning in public transport involves determining vehicle routes and assigning frequencies of service such that travel demands are satisfied. We evaluate how line plans, which are optimal with respect to in-motion costs (IMC), the objective function depending purely on arc-lengths for both user and operator costs, performs with respect to the value of resources consumed (VRC). The latter is an elaborate, socio-economic cost function which includes discomfort caused by delay, boarding and alighting times, and transfers. Even though discomfort is a large contributing factor to VRC and is entirely disregarded in IMC, we observe that the two cost functions are qualitatively comparable.}, language = {en} } @misc{Masing2021, author = {Masing, Berenike}, title = {Optimal Line Planning in the Parametric City}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-83238}, year = {2021}, abstract = {We formulate the line planning problem in public transport as a mixed integer linear program (MILP), which selects both passenger and vehicle routes, such that travel demands are met with respect to minimized travel times for both operators and users. We apply MILP to the Parametric City, a generic city model developed by Fielbaum et al. While the infrastructure graph and demand are entirely rotation symmetric, asymmetric optimal line plans can occur. Using group theory, we analyze the properties of symmetric solutions and introduce a symmetry gap to measure their deviation of the optimum. We also develop a 1+(1+\sqrt{2})/g-approximation algorithm, depending only on the cost related parameter g. Supported by computational experiments, we conclude that in practice symmetric line plans provide good solutions for the line planning problem in the Parametric City.}, language = {en} } @misc{BorndoerferArslanElijazyferetal.2016, author = {Bornd{\"o}rfer, Ralf and Arslan, Oytun and Elijazyfer, Ziena and G{\"u}ler, Hakan and Renken, Malte and Sahin, G{\"u}venc and Schlechte, Thomas}, title = {Line Planning on Path Networks with Application to the Istanbul Metrob{\"u}s}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-60119}, year = {2016}, abstract = {Bus rapid transit systems in developing and newly industrialized countries often consist of a trunk with a path topology. On this trunk, several overlapping lines are operated which provide direct connections. The demand varies heavily over the day, with morning and afternoon peaks typically in reverse directions. We propose an integer programming model for this problem, derive a structural property of line plans in the static (or single period) ``unimodal demand'' case, and consider approaches to the solution of the multi-period version that rely on clustering the demand into peak and off-peak service periods. An application to the Metrob{\"u}s system of Istanbul is discussed.}, language = {en} } @misc{BorndoerferKarbstein2015, author = {Bornd{\"o}rfer, Ralf and Karbstein, Marika}, title = {Metric Inequalities for Routings on Direct Connections with Application in Line Planning}, issn = {1438-0064}, doi = {10.1016/j.disopt.2015.07.004}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-53507}, year = {2015}, abstract = {We consider multi-commodity flow problems in which capacities are installed on paths. In this setting, it is often important to distinguish between flows on direct connection routes, using single paths, and flows that include path switching. We derive a feasibility condition for path capacities supporting such direct connection flows similar to the feasibility condition for arc capacities in ordinary multi-commodity flows. The concept allows to solve large-scale real-world line planning problems in public transport including a novel passenger routing model that favors direct connections over connections with transfers.}, language = {en} } @misc{BorndoerferHoppmannKarbstein2013, author = {Bornd{\"o}rfer, Ralf and Hoppmann, Heide and Karbstein, Marika}, title = {A Configuration Model for the Line Planning Problem}, issn = {1438-0064}, doi = {10.4230/OASIcs.ATMOS.2013.68}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-41903}, year = {2013}, abstract = {We propose a novel extended formulation for the line planning problem in public transport. It is based on a new concept of frequency configurations that account for all possible options to provide a required transportation capacity on an infrastructure edge. We show that this model yields a strong LP relaxation. It implies, in particular, general classes of facet defining inequalities for the standard model.}, language = {en} } @misc{BorndoerferKarbstein2012, author = {Bornd{\"o}rfer, Ralf and Karbstein, Marika}, title = {A Direct Connection Approach to Integrated Line Planning and Passenger Routing}, volume = {25}, journal = {ATMOS 2012 - 12th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems}, editor = {Delling, Daniel and Liberti, Leo}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum f{\"u}r Informatik}, issn = {1438-0064}, doi = {http://dx.doi.org/10.4230/OASIcs.ATMOS.2012.47}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-15812}, pages = {47 -- 57}, year = {2012}, abstract = {The treatment of transfers is a major challenge in line planning. Existing models either route passengers and lines sequentially, and hence disregard essential degrees of freedom, or they are of extremely large scale, and seem to be computationally intractable. We propose a novel direct connection approach that allows an integrated optimization of line and passenger routing, including accurate estimates of the number of direct travelers, for large-scale real-world instances.}, language = {en} } @misc{BorndoerferNeumann2010, author = {Bornd{\"o}rfer, Ralf and Neumann, Marika}, title = {Models for Line Planning with Transfers}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11742}, number = {10-11}, year = {2010}, abstract = {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.}, language = {en} } @misc{TorresTorresBorndoerferetal.2008, author = {Torres, Luis Miguel and Torres, Ramiro and Bornd{\"o}rfer, Ralf and Pfetsch, Marc}, title = {Line Planning on Paths and Tree Networks with Applications to the Quito Trolebus System (Extended Abstract)}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11076}, number = {08-53}, year = {2008}, abstract = {Line planning is an important step in the strategic planning process of a public transportation system. In this paper, we discuss an optimization model for this problem in order to minimize operation costs while guaranteeing a certain level of quality of service, in terms of available transport capacity. We analyze the problem for path and tree network topologies as well as several categories of line operation that are important for the Quito Trolebus system. It turns out that, from a computational complexity worst case point of view, the problem is hard in all but the most simple variants. In practice, however, instances based on real data from the Trolebus System in Quito can be solved quite well, and significant optimization potentials can be demonstrated.}, 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{TorresTorresBorndoerferetal.2008, author = {Torres, Luis Miguel and Torres, Ramiro and Bornd{\"o}rfer, Ralf and Pfetsch, Marc}, title = {Line Planning on Paths and Tree Networks with Applications to the Quito Trolebus System}, organization = {ZIB}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10869}, number = {08-35}, year = {2008}, abstract = {Line planning is an important step in the strategic planning process of a public transportation system. In this paper, we discuss an optimization model for this problem in order to minimize operation costs while guaranteeing a certain level of quality of service, in terms of available transport capacity. We analyze the problem for path and tree network topologies as well as several categories of line operation that are important for the Quito Trolebus system. It turns out that, from a computational complexity worst case point of view, the problem is hard in all but the most simple variants. In practice, however, instances based on real data from the Trolebus System in Quito can be solved quite well, and significant optimization potentials can be demonstrated.}, language = {en} } @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{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} }