TY - JOUR A1 - Riedmüller, Stephanie A1 - Lindner, Niels T1 - Column Generation for Periodic Timetabling N2 - Periodic timetabling for public transportation networks is typically modelled as a Periodic Event Scheduling Problem (PESP). Solving instances of the benchmark library PESPlib to optimality continues to pose a challenge. As a further approach towards this goal, we remodel the problem by a time discretization of the underlying graph and consider arc-based as well as path-based integer programming formulations. For the path-based case, we use cycles on the graph expansion of the operational lines as variables and, therefore, include more of the problem inherent structure into the model. A consequence is the validity of several known inequalities and a lower bound on the LP-relaxation, that is the best known to date. As an extension we integrate passenger routing into the new model. The proposed models have an advantage in the linear programming relaxation, on the one hand, but have an increased problem size, on the other hand. We define the corresponding pricing problems for the use of column generation to handle the size. Both models are practically tested on different problem instances. Y1 - 2025 ER - TY - GEN A1 - Lindner, Niels A1 - Mehl, Lukas A1 - Bartoszuk, Karolina A1 - Berendes, Sarah A1 - Zittel, Janina T1 - Demand Uncertainty in Energy Systems: Scenario Catalogs vs. Integrated Robust Optimization N2 - Designing efficient energy systems is indispensable for shaping a more sustainable society. This involves making infrastructure investment decisions that must be valid for a long-term time horizon. While energy system optimization models constitute a powerful technique to support planning decisions, they need to cope with inherent uncertainty. For example, predicting future demand on a scale of decades is not only an intricate challenge in itself, but small fluctuations in such a forecast might also largely impact the layout of a complex energy system. In this paper, we compare two methodologies of capturing demand uncertainty for linear-programming based energy system optimization models. On one hand, we generate and analyze catalogs of varying demand scenarios, where each individual scenario is considered independently, so that the optimization produces scenario-specific investment pathways. On the other hand, we make use of robust linear programming to meet the demand of all scenarios at once. Since including a multitude of scenarios increases the size and complexity of the optimization model, we will show how to use warm-starting approaches to accelerate the computation process, by exploiting the similar structure of the linear program across different demand inputs. This allows to integrate a meaningful number of demand scenarios with fully-fledged energy system models. We demonstrate the practical use of our methods in a case study of the Berlin-Brandenburg area in Germany, a region that contains both a metropolitan area and its rural surroundings. As a backbone, we use the open-source framework oemof to create a sector-coupled optimization model for planning an energy system with up to 100% reduction of greenhouse gas emissions. This model features a fine-grained temporal resolution of one hour for the full year 2050. We consider uncertainty in demand for electricity, hydrogen, natural gas, central, and decentral heat. Based on our computations, we analyze the trade-offs in terms of quality and computation time for scenario catalogs and the robust optimization approach. We further demonstrate that our procedure provides a valuable strategy for decision makers to gain insight on the robustness and sensitivity of solutions regarding demand variability. T3 - ZIB-Report - 25-19 Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-102404 SN - 1438-0064 ER - TY - GEN A1 - Lindner, Niels T1 - A Multi-Commodity Flow Heuristic for Integrated Periodic Timetabling for Railway Construction Sites N2 - Rescheduling a railway system comprises many aspects, such as line planning, timetabling, track allocation, and vehicle scheduling. For periodic timetables, these features can be integrated into a single mixed-integer program extending the Periodic Event Scheduling Problem (PESP) with a routing component. We develop a multi-commodity-flow-based heuristic that allows to compute better solutions faster than a black-box MIP approach on real construction site scenarios on the S-Bahn Berlin network. T3 - ZIB-Report - 25-02 KW - Railway Timetabling KW - Periodic Timetabling KW - Rescheduling KW - Railway Track Allocation Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-99449 SN - 1438-0064 ER - TY - CHAP A1 - Lindner, Niels A1 - Mehl, Lukas A1 - Bartoszuk, Karolina A1 - Berendes, Sarah A1 - Zittel, Janina T1 - Demand Uncertainty in Energy Systems: Scenario Catalogs vs. Integrated Robust Optimization T2 - Proceedings of the 38th International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy Systems N2 - Designing efficient energy systems is indispensable for shaping a more sustainable society. This involves making infrastructure investment decisions that must be valid for a long-term time horizon. While energy system optimization models constitute a powerful technique to support planning decisions, they need to cope with inherent uncertainty. For example, predicting future demand on a scale of decades is not only an intricate challenge in itself, but small fluctuations in such a forecast might also largely impact the layout of a complex energy system. In this paper, we compare two methodologies of capturing demand uncertainty for linear-programming based energy system optimization models. On one hand, we generate and analyze catalogs of varying demand scenarios, where each individual scenario is considered independently, so that the optimization produces scenario-specific investment pathways. On the other hand, we make use of robust linear programming to meet the demand of all scenarios at once. Since including a multitude of scenarios increases the size and complexity of the optimization model, we will show how to use warm-starting approaches to accelerate the computation process, by exploiting the similar structure of the linear program across different demand inputs. This allows to integrate a meaningful number of demand scenarios with fully-fledged energy system models. We demonstrate the practical use of our methods in a case study of the Berlin-Brandenburg area in Germany, a region that contains both a metropolitan area and its rural surroundings. As a backbone, we use the open-source framework oemof to create a sector-coupled optimization model for planning an energy system with up to 100% reduction of greenhouse gas emissions. This model features a fine-grained temporal resolution of one hour for the full year 2050. We consider uncertainty in demand for electricity, hydrogen, natural gas, central, and decentral heat. Based on our computations, we analyze the trade-offs in terms of quality and computation time for scenario catalogs and the robust optimization approach. We further demonstrate that our procedure provides a valuable strategy for decision makers to gain insight on the robustness and sensitivity of solutions regarding demand variability. Y1 - 2025 ER -