Because of the long planning periods and their long life cycle, railway infrastructure has to be outlined long ahead. At the present, the infrastructure is designed while only little about the intended operation is known. Hence, the timetable and the operation are adjusted to the infrastructure. Since space, time and money for extension measures of railway infrastructure are limited, each modification has to be done carefully and long lasting and should be appropriate for the future unknown demand. To take this into account, we present the robust network design problem for railway infrastructure under capacity constraints and uncertain timetables. Here, we plan the required expansion measures for an uncertain long-term timetable. We show that this problem is NP-hard even when restricted to bipartite graphs and very simple timetables and present easier solvable special cases. This problem corresponds to the fixed-charge network design problem where the expansion costs are minimized such that the timetable is conductible. We model this problem by an integer linear program using time expanded networks. To incorporate the uncertainty of the future timetable, we use a scenario-based approach. We define scenarios with individual departure and arrival times and optional trains. The network is then optimized such that a given percentage of the scenarios can be operated while minimizing the expansion costs and potential penalty costs for not scheduled optional trains.

翻译：由于规划周期长、生命周期久，铁路基础设施需要提前进行长远规划。目前，基础设施的设计往往在对运营方案知之甚少的情况下展开，因此时间表和运营方案需要根据基础设施进行调整。鉴于铁路基础设施扩建的空间、时间和资金有限，每项改造都必须审慎且持久，并应适应未来未知的需求。为此，我们提出了考虑容量约束和不确定时间表的铁路基础设施鲁棒网络设计问题。在该问题中，我们针对不确定的长期时间表规划所需的扩建措施。研究表明，即使限制为二分图且采用非常简化的时间表，该问题仍为NP难问题，并提出了若干易于求解的特殊情形。该问题对应固定费用网络设计问题，目标是最小化扩建成本，使得时间表可执行。我们利用时间扩展网络将该问题建模为整数线性规划。为纳入未来时间表的不确定性，我们采用基于场景的方法：定义具有个体到发时间和可选列车班次的场景，并在最小化扩建成本与未排入可选列车的潜在惩罚成本的前提下，对网络进行优化，使得给定比例的运营场景可被执行。