TY - GEN A1 - Borndörfer, Ralf A1 - Erol, Berkan A1 - Graffagnino, Thomas A1 - Schlechte, Thomas A1 - Swarat, Elmar T1 - Optimizing the Simplon Railway Corridor N2 - This paper presents a case study on a railway timetable optimization for the very dense Simplon corridor, a major railway connection in the Alps between Switzerland and Italy. Starting from a detailed microscopic network as it is used in railway simulation, the data is transformed by an automatic procedure to a less detailed macroscopic network, that is sufficient for the purpose of capacity planning and amenable to state-of-the-art integer programming optimization methods. In this way, the macroscopic railway network is saturated with trains. Finally, the corresponding timetable is re-transformed to the microscopic level in such a way that it can be operated without any conflicts among the slots. Using this integer programming based micro-macro aggregation-disaggregation approach, it becomes for the first time possible to generate a profit maximal and conflict free timetable for the complete Simplon corridor over an entire day by a simultaneous optimization of all trains requests. This also allows to to undertake a sensitivity analysis of various problem parameters. T3 - ZIB-Report - 10-24 KW - Trassenallokation KW - Netzwerkaggregation KW - Fallstudie KW - Simplon Korridor KW - railway track allocation KW - network aggregation KW - case study KW - Simplon corridor Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11892 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Lukac, Sascha A1 - Mitusch, Kay A1 - Schlechte, Thomas A1 - Schultz, Sören A1 - Tanner, Andreas T1 - An Auctioning Approach to Railway Slot Allocation N2 - We present an approach to implement an auction of railway slots. Railway network, train driving characteristics, and safety requirements are described by a simplified, but still complex macroscopic model. In this environment, slots are modelled as combinations of scheduled track segments. The auction design builds on the iterative combinatorial auction. However, combinatorial bids are restricted to some types of slot bundles that realize positive synergies between slots. We present a bidding language that allows bidding for these slot bundles. An integer programming approach is proposed to solve the winner determination problem of our auction. Computational results for auction simulations in the Hannover-Fulda-Kassel area of the German railway network give evidence that auction approaches can induce a more efficient use of railway capacity. T3 - ZIB-Report - 05-45 KW - Railway Slot Allocation KW - Train Dispatching KW - Combinatorial Auctions Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8786 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Schlechte, Thomas T1 - Models for Railway Track Allocation N2 - This article is about the optimal track allocation problem (OPTRA) to find, in a given railway network, a conflict free set of train routes of maximum value. We study two types of integer programming formulations: a standard formulation that models block conflicts in terms of packing constraints, and a new extended formulation that is based on additional configuration' variables. We show that the packing constraints in the standard formulation stem from an interval graph, and that they can be separated in polynomial time. It follows that the LP relaxation of a strong version of this model, including all clique inequalities from block conflicts, can be solved in polynomial time. We prove that the extended formulation produces the same LP bound, and that it can also be computed with this model in polynomial time. Albeit the two formulations are in this sense equivalent, the extended formulation has advantages from a computational point of view, because it features a constant number of rows and is therefore amenable to standard column generation techniques. Results of an empirical model comparison on mesoscopic data for the Hannover-Fulda-Kassel region of the German long distance railway network are reported. T3 - ZIB-Report - 07-02 KW - Railway Slot Allocation KW - Train Timetabling KW - Combinatorial Optimization KW - Linear and Integer Programming Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9451 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Schlechte, Thomas T1 - Solving Railway Track Allocation Problems N2 - The \emph{optimal track allocation problem} (\textsc{OPTRA}), also known as the train routing problem or the train timetabling problem, is to find, in a given railway network, a conflict-free set of train routes of maximum value. We propose a novel integer programming formulation for this problem that is based on additional configuration' variables. Its LP-relaxation can be solved in polynomial time. These results are the theoretical basis for a column generation algorithm to solve large-scale track allocation problems. Computational results for the Hanover-Kassel-Fulda area of the German long distance railway network involving up to 570 trains are reported. T3 - ZIB-Report - 07-20 KW - railway track allocation KW - timetabling KW - column generation Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9631 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 - Erol, Berkan A1 - Klemenz, Marc A1 - Schlechte, Thomas A1 - Schultz, Sören A1 - Tanner, Andreas T1 - TTPLIB 2008 - A Library for Train Timetabling Problems N2 - We introduce (TTPlib), a data library for train timetabling problems that can be accessed at http://ttplib.zib.de. In version 1.0, the library contains data related to 50 scenarios. Most instances result from the combination of macroscopic railway networks and several train request sets for the German long distance area containing Hannover, Kassel and Fulda, short denoted by Ha-Ka-Fu. In this paper, we introduce the data concepts of TTPlib, describe the scenarios included in the library and provide a free visualization tool TraVis. T3 - ZIB-Report - 08-19 KW - Fahrplanung KW - Problembibliothek KW - Optimierung KW - Train Timetabling Problem KW - Data Library KW - Optimization Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10732 SN - 1438-0064 ER - TY - GEN A1 - Schlechte, Thomas A1 - Borndörfer, Ralf T1 - Balancing Efficiency and Robustness – A Bi-criteria Optimization Approach to Railway Track Allocation N2 - Technical restrictions and challenging details let railway traffic become one of the most complex transportation systems. Routing trains in a conflict-free way through a track network is one of the basic scheduling problems for any railway company. This article focuses on a robust extension of this problem, also known as train timetabling problem (TTP), which consists in finding a schedule, a conflict free set of train routes, of maximum value for a given railway network. However, timetables are not only required to be profitable. Railway companies are also interested in reliable and robust solutions. Intuitively, we expect a more robust track allocation to be one where disruptions arising from delays are less likely to be propagated causing delays of subsequent trains. This trade-off between an efficient use of railway infrastructure and the prospects of recovery leads us to a bi-criteria optimization approach. On the one hand we want to maximize the profit of a schedule, that is more or less to maximize the number of feasible routed trains. On the other hand if two trains are scheduled as tight as possible after each other it is clear that a delay of the first one always affects the subsequent train. We present extensions of the integer programming formulation in [BorndoerferSchlechte2007] for solving (TTP). These models can incorporate both aspects, because of the additional track configuration variables. We discuss how these variables can directly be used to measure a certain type of robustness of a timetable. For these models which can be solved by column generation techniques, we propose so-called scalarization techniques, see [Ehrgott2005], to determine efficient solutions. Here, an efficient solution is one which does not allow any improvement in profit and robustness at the same time. We prove that the LP-relaxation of the (TTP) including an additional $\epsilon$-constraint remains solvable in polynomial time. Finally, we present some preliminary results on macroscopic real-world data of a part of the German long distance railway network. T3 - ZIB-Report - 08-22 KW - Train Timetabling Problem KW - Bicriteria Optimization KW - Column Generation Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10763 SN - 1438-0064 ER -