@misc{BorndoerferErolGraffagninoetal.2010, author = {Bornd{\"o}rfer, Ralf and Erol, Berkan and Graffagnino, Thomas and Schlechte, Thomas and Swarat, Elmar}, title = {Aggregation Methods for Railway Networks}, organization = {Zuse Institut Berlin}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11881}, number = {10-23}, year = {2010}, abstract = {In this paper a bottom-up approach of automatic simplification of a railway network is presented. Starting from a very detailed, microscopic level, as it is used in railway simulation, the network is transformed by an algorithm to a less detailed level (macroscopic network), that is sufficient for long-term planning and optimization. In addition running and headway times are rounded to a pre-chosen time discretization by a special cumulative method, which we will present and analyse in this paper. After the transformation we fill the network with given train requests to compute an optimal slot allocation. Then the optimized schedule is re-transformed into the microscopic level and can be simulated without any conflicts occuring between the slots. The algorithm is used to transform the network of the very dense Simplon corridor between Swiss and Italy. With our aggregation it is possible for the first time to generate a profit maximal and conflict free timetable for the corridor across a day by a simultaneously optimization run.}, language = {en} } @misc{BorndoerferErolGraffagninoetal.2010, author = {Bornd{\"o}rfer, Ralf and Erol, Berkan and Graffagnino, Thomas and Schlechte, Thomas and Swarat, Elmar}, title = {Optimizing the Simplon Railway Corridor}, organization = {Zuse Institut Berlin}, issn = {1438-0064}, doi = {10.1007/s10479-012-1260-9}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11892}, number = {10-24}, year = {2010}, abstract = {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.}, language = {en} } @article{SchlechteBorndoerferEroletal.2011, author = {Schlechte, Thomas and Bornd{\"o}rfer, Ralf and Erol, Berkan and Graffagnino, Thomas and Swarat, Elmar}, title = {Micro-macro transformation of railway networks}, volume = {1}, journal = {Journal of Rail Transport Planning \& Management}, number = {1}, doi = {10.1016/j.jrtpm.2011.09.001}, pages = {38 -- 48}, year = {2011}, abstract = {In this paper a bottom-up approach of automatic simplification of a railway network is presented. Starting from a very detailed, microscopic level, as it is used in railway simulation, the network is transformed by an algorithm to a less detailed level (macroscopic network), that is sufficient for long-term planning and optimization. In addition running and headway times are rounded to a pre-chosen time discretization by a special cumulative method, which we will present and analyse in this paper. After the transformation we fill the network with given train requests to compute an optimal slot allocation. Then the optimized schedule is re-transformed into the microscopic level and can be simulated without any conflicts occuring between the slots. The algorithm is used to transform the network of the very dense Simplon corridor between Swiss and Italy. With our aggregation it is possible for the first time to generate a profit maximal and conflict free timetable for the corridor across a day by a simultaneously optimization run.}, language = {en} } @article{BorndoerferErolGraffagninoetal.2012, author = {Bornd{\"o}rfer, Ralf and Erol, Berkan and Graffagnino, Thomas and Schlechte, Thomas and Swarat, Elmar}, title = {Optimizing the Simplon railway corridor}, volume = {218}, journal = {Annals of Operations Research}, number = {1}, edition = {Annals of Operations Research}, publisher = {Springer US}, doi = {10.1007/s10479-012-1260-9}, pages = {93 -- 106}, year = {2012}, language = {en} } @article{BorndoerferSchlechteSwarat2012, author = {Bornd{\"o}rfer, Ralf and Schlechte, Thomas and Swarat, Elmar}, title = {Railway Track Allocation -- Simulation, Aggregation, and Optimization}, volume = {2}, journal = {Proc. 1st International Workshop on High-speed and Intercity Railways (IWHIR 2011)}, number = {148}, doi = {10.1007/978-3-642-27963-8}, pages = {53 -- 70}, year = {2012}, abstract = {Today the railway timetabling process and the track allocation is one of the most challenging problems to solve by a railway company. Especially due to the deregulation of the transport market in the recent years several suppliers of railway traffic have entered the market in Europe. This leads to more potential conflicts between trains caused by an increasing demand of train paths. Planning and operating railway transportation systems is extremely hard due to the combinatorial complexity of the underlying discrete optimization problems, the technical intricacies, and the immense size of the problem instances. In order to make best use of the infrastructure and to ensure economic operation, efficient planning of the railway operation is indispensable. Mathematical optimization models and algorithms can help to automatize and tackle these challenges. Our contribution in this paper is to present a renewed planning process due to the liberalization in Europe and an associated concept for track allocation, that consists of three important parts, simulation, aggregation, and optimization. Furthermore, we present results of our general framework for real world data.}, language = {en} } @inproceedings{SchwartzSchlechteSwarat2017, author = {Schwartz, Stephan and Schlechte, Thomas and Swarat, Elmar}, title = {Designing Inspector Rosters with Optimal Strategies}, booktitle = {Operations Research Proceedings 2016}, doi = {10.1007/978-3-319-55702-1_30}, pages = {217 -- 223}, year = {2017}, abstract = {We consider the problem of enforcing a toll on a transportation network with limited inspection resources. We formulate a game theoretic model to optimize the allocation of the inspectors, taking the reaction of the network users into account. The model includes several important aspects for practical operation of the control strategy, such as duty types for the inspectors. In contrast to an existing formulation using flows to describe the users' strategies we choose a path formulation and identify dominated user strategies to significantly reduce the problem size. Computational results suggest that our approach is better suited for practical instances.}, language = {en} } @misc{SchwartzSchlechteSwarat2016, author = {Schwartz, Stephan and Schlechte, Thomas and Swarat, Elmar}, title = {Designing Inspector Rosters with Optimal Strategies}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61123}, year = {2016}, abstract = {We consider the problem of enforcing a toll on a transportation network with limited inspection resources. We formulate a game theoretic model to optimize the allocation of the inspectors, taking the reaction of the network users into account. The model includes several important aspects for practical operation of the control strategy, such as duty types for the inspectors. In contrast to an existing formulation using flows to describe the users' strategies we choose a path formulation and identify dominated user strategies to significantly reduce the problem size. Computational results suggest that our approach is better suited for practical instances.}, language = {en} } @misc{SagnolBorndoerferSchlechteetal.2014, author = {Sagnol, Guillaume and Bornd{\"o}rfer, Ralf and Schlechte, Thomas and Swarat, Elmar}, title = {The Price of Spite in Spot-checking games}, issn = {1438-0064}, doi = {10.1007/978-3-662-44803-8}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-52775}, year = {2014}, abstract = {We introduce the class of spot-checking games (SC games). These games model problems where the goal is to distribute fare inspectors over a toll network. Although SC games are not zero-sum, we show that a Nash equilibrium can be computed by linear programming. The computation of a strong Stackelberg equilibrium is more relevant for this problem, but we show that this is NP-hard. However, we give some bounds on the \emph{price of spite}, which measures how the payoff of the inspector degrades when committing to a Nash equilibrium. Finally, we demonstrate the quality of these bounds for a real-world application, namely the enforcement of a truck toll on German motorways.}, language = {en} } @misc{BorndoerferSchlechteSwarat2011, author = {Bornd{\"o}rfer, Ralf and Schlechte, Thomas and Swarat, Elmar}, title = {Railway Track Allocation - Simulation, Aggregation, and Optimization}, issn = {1438-0064}, doi = {10.1007/978-3-642-27963-8}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14031}, number = {11-35}, year = {2011}, abstract = {Today the railway timetabling process and the track allocation is one of the most challenging problems to solve by a railway company. Especially due to the deregulation of the transport market in the recent years several suppliers of railway traffic have entered the market in Europe. This leads to more potential conflicts between trains caused by an increasing demand of train paths. Planning and operating railway transportation systems is extremely hard due to the combinatorial complexity of the underlying discrete optimization problems, the technical intricacies, and the immense size of the problem instances. In order to make best use of the infrastructure and to ensure economic operation, efficient planning of the railway operation is indispensable. Mathematical optimization models and algorithms can help to automatize and tackle these challenges. Our contribution in this paper is to present a renewed planning process due to the liberalization in Europe and an associated concept for track allocation, that consists of three important parts, simulation, aggregation, and optimization. Furthermore, we present results of our general framework for real world data.}, language = {en} } @misc{BorndoerferReutherSchlechteetal.2015, author = {Bornd{\"o}rfer, Ralf and Reuther, Markus and Schlechte, Thomas and Schulz, Christof and Swarat, Elmar and Weider, Steffen}, title = {Duty Rostering in Public Transport - Facing Preferences, Fairness, and Fatigue}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-56070}, year = {2015}, abstract = {Duty rostering problems occur in different application contexts and come in different flavors. They give rise to very large scale integer programs which ypically have lots of solutions and extremely fractional LP relaxations. In such a situation, heuristics can be a viable algorithmic choice. We propose an mprovement method of the Lin-Kernighan type for the solution of duty rostering problems. We illustrate its versatility and solution quality on three different applications in public transit, vehicle routing, and airline rostering with a focus on the management of preferences, fairness, and fatigue, respectively.}, language = {en} } @article{BorndoerferSagnolSchlechteetal.2016, author = {Bornd{\"o}rfer, Ralf and Sagnol, Guillaume and Schlechte, Thomas and Swarat, Elmar}, title = {Optimal duty rostering for toll enforcement inspectors}, volume = {252(2)}, journal = {Annals of Operations Research}, edition = {252}, publisher = {Springer US}, doi = {10.1007/s10479-016-2152-1}, pages = {383 -- 406}, year = {2016}, abstract = {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, we developed a personalized crew rostering model, to schedule the crews of the tours. 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 main focus of this paper extends our previous publications on how different requirements for the rostering can be modeled in detail. The second focus is on a bi-criteria analysis of the planning problem to find the balance between the control quality and the roster acceptance. Finally, computational results on real-world instances show the practicability of our method and how different input parameters influence the problem complexity.}, language = {en} } @inproceedings{SagnolBorndoerferSchlechteetal.2014, author = {Sagnol, Guillaume and Bornd{\"o}rfer, Ralf and Schlechte, Thomas and Swarat, Elmar}, title = {The Price of Spite in Spot-checking games}, volume = {8768}, booktitle = {7th International Symposium on Algorithmic Game Theory (SAGT'2014)}, editor = {Lavi, Ron}, publisher = {Springer}, isbn = {978-3-662-44802-1}, doi = {10.1007/978-3-662-44803-8}, pages = {293}, year = {2014}, abstract = {We introduce the class of spot-checking games (SC games). These games model problems where the goal is to distribute fare inspectors over a toll network. Although SC games are not zero-sum, we show that a Nash equilibrium can be computed by linear programming. The computation of a strong Stackelberg equilibrium is more relevant for this problem, but we show that this is NP-hard. However, we give some bounds on the \emph{price of spite}, which measures how the payoff of the inspector degrades when committing to a Nash equilibrium. Finally, we demonstrate the quality of these bounds for a real-world application, namely the enforcement of a truck toll on German motorways.}, language = {en} } @inproceedings{BorndoerferReutherSchlechteetal.2015, author = {Bornd{\"o}rfer, Ralf and Reuther, Markus and Schlechte, Thomas and Schulz, Christof and Swarat, Elmar and Weider, Steffen}, title = {Duty Rostering in Public Transport - Facing Preferences, Fairness, and Fatigue}, booktitle = {Proceedings of Conference on Advanced Systems in Public Transport 2015 (CASPT2015)}, year = {2015}, abstract = {Duty rostering problems occur in different application contexts and come in different flavors. They give rise to very large scale integer programs which ypically have lots of solutions and extremely fractional LP relaxations. In such a situation, heuristics can be a viable algorithmic choice. We propose an mprovement method of the Lin-Kernighan type for the solution of duty rostering problems. We illustrate its versatility and solution quality on three different applications in public transit, vehicle routing, and airline rostering with a focus on the management of preferences, fairness, and fatigue, respectively.}, language = {en} } @misc{BorndoerferSagnolSchlechteetal.2013, author = {Bornd{\"o}rfer, Ralf and Sagnol, Guillaume and Schlechte, Thomas and Swarat, Elmar}, title = {Optimal Toll Enforcement - an Integration of Vehicle Routing and Duty Rostering}, issn = {1438-0064}, doi = {10.1007/s10479-016-2152-1}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-45107}, year = {2013}, abstract = {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.}, language = {en} } @inproceedings{GamrathReutherSchlechteetal.2021, author = {Gamrath, Gerwin and Reuther, Markus and Schlechte, Thomas and Swarat, Elmar}, title = {An LP-based heuristic for Inspector Scheduling}, volume = {1}, booktitle = {Proceedings of the 13th International Conference on the Practice and Theory of Automated Timetabling - PATAT 2021: Volume I}, pages = {77 -- 86}, year = {2021}, abstract = {We present a heuristic based on linear programming (LP) for the integrated tour and crew roster planning of toll enforcement inspectors. Their task is to enforce the proper paying of a distance-based toll on German motorways. This leads to an integrated tour planning and duty rostering problem; it is called Toll Enforcement Problem (TEP). We tackle the TEP by a standard multi-commodity flow model with some extensions in order to incorporate the control tours. The heuristic consists of two variants. The first, called Price \& Branch, is a column generation approach to solve the model's LP relaxation by pricing tour and roster arc variables. Then, we compute an integer feasible solution by restricting to all variables that were priced. The second is a coarse-to-fine approach. Its basic idea is projecting variables to an aggregated variable space, which is much smaller. The aim is to spend as much algorithmic effort in this coarse model as possible. For both heuristic procedures we will show that feasible solutions of high quality can be computed even for large scale industrial instances.}, language = {en} }