@misc{BorndoerferHeismann2012, author = {Bornd{\"o}rfer, Ralf and Heismann, Olga}, title = {Minimum Cost Hyperassignments with Applications to ICE/IC Rotation Planning}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14564}, number = {11-46}, year = {2012}, abstract = {Vehicle rotation planning is a fundamental problem in rail transport. It decides how the railcars, locomotives, and carriages are operated in order to implement the trips of the timetable. One important planning requirement is operational regularity, i.e., using the rolling stock in the same way on every day of operation. We propose to take regularity into account by modeling the vehicle rotation planning problem as a minimum cost hyperassignment problem (HAP). Hyperassignments are generalizations of assignments from directed graphs to directed hypergraphs. Finding a minimum cost hyperassignment is NP-hard. Most instances arising from regular vehicle rotation planning, however, can be solved well in practice. We show that, in particular, clique inequalities strengthen the canonical LP relaxation substantially.}, language = {en} } @misc{BorndoerferKarbstein2012, author = {Bornd{\"o}rfer, Ralf and Karbstein, Marika}, title = {A Note on Menger's Theorem for Hypergraphs}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14471}, number = {12-03}, year = {2012}, abstract = {We prove the companion Theorem to Menger's Theorem for hypergraphs. This result gives rise to a new class of blocking pairs of ideal matrices, that generalize the incidence matrices of cuts and paths.}, 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{BorndoerferGroetschelLoebel2010, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and L{\"o}bel, Andreas}, title = {The Quickest Path to the Goal}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11840}, number = {10-21}, year = {2010}, abstract = {We provide an introduction into the mathematics of and with paths. Not on the shortest, but hopefully on an entertaining path!}, language = {en} } @misc{BorndoerferDovicaNowaketal.2010, author = {Bornd{\"o}rfer, Ralf and Dovica, Ivan and Nowak, Ivo and Schickinger, Thomas}, title = {Robust Tail Assignment}, organization = {Zuse-Institut Berlin}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11707}, number = {10-08}, year = {2010}, abstract = {We propose an efficient column generation method to minimize the probability of delay propagations along aircraft rotations. In this way, delay resistant schedules can be constructed. Computational results for large-scale real-world problems demonstrate substantial punctuality improvements. The method can be generalized to crew and integrated scheduling problems.}, 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{BorndoerferSagnolSwarat2012, author = {Bornd{\"o}rfer, Ralf and Sagnol, Guillaume and Swarat, Elmar}, title = {A Case Study on Optimizing Toll Enforcements on Motorways}, issn = {1438-0064}, doi = {10.4230/OASIcs.SCOR.2012.1}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-15498}, year = {2012}, abstract = {In this paper we present the problem of computing optimal tours of toll inspectors on German motorways. This problem is a special type of vehicle routing problem and builds up an integrated model, consisting of a tour planning and a duty rostering part. The tours should guarantee a network-wide control whose intensity is proportional to given spatial and time dependent traffic distributions. We model this using a space-time network and formulate the associated optimization problem by an integer program (IP). Since sequential approaches fail, we integrated the assignment of crews to the tours in our model. In this process all duties of a crew member must fit in a feasible roster. It is modeled as a Multi-Commodity Flow Problem in a directed acyclic graph, where specific paths correspond to feasible rosters for one month. We present computational results in a case-study on a German subnetwork which documents the practicability of our approach.}, language = {en} } @misc{BorndoerferCardonha2009, author = {Bornd{\"o}rfer, Ralf and Cardonha, Carlos}, title = {A Set Partitioning Approach to Shunting}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11326}, number = {09-18}, year = {2009}, abstract = {The Vehicle Positioning Problem (VPP) is a classical combinatorial optimization problem in public transport planning. A number of models and approaches have been suggested in the literature, which work for small problems, but not for large ones. We propose in this article a novel set partitioning model and an associated column generation solution approach for the VPP. The model provides a tight linear description of the problem. The pricing problem, and hence the LP relaxation itself, can be solved in polynomial resp. pseudo-polynomial time for some versions of the problems.}, language = {en} } @misc{Borndoerfer2009, author = {Bornd{\"o}rfer, Ralf}, title = {Discrete Optimization in Public Transportation}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11207}, number = {08-56}, year = {2009}, abstract = {The mathematical treatment of planning problems in public transit has made significant advances in the last decade. Among others, the classical problems of vehicle and crew scheduling can nowadays be solved on a routine basis using combinatorial optimization methods. This is not yet the case for problems that pertain to the design of public transit networks, and for the problems of operations control that address the implementation of a schedule in the presence of disturbances. The article gives a sketch of the state and important developments in these areas, and it addresses important challenges. The vision is that mathematical tools of computer aided scheduling (CAS) will soon play a similar role in the design and operation of public transport systems as CAD systems in manufacturing.}, language = {en} } @misc{BorndoerferHoang2008, author = {Bornd{\"o}rfer, Ralf and Hoang, Nam-Dung}, title = {Fair Ticket Prices in Public Transport}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10999}, number = {08-46}, year = {2008}, abstract = {Ticket pricing in public transport usually takes a welfare or mnemonics maximization point of view. These approaches do not consider fairness in the sense that users of a shared infrastructure should pay for the costs that they generate. We propose an ansatz to determine fair ticket prices that combines concepts from cooperative game theory and integer programming. An application to pricing railway tickets for the intercity network of the Netherlands demonstrates that, in this sense, prices that are much fairer than standard ones can be computed in this way.}, language = {en} }