Railway capacity is a vague concept, related to the possibility to run a maximal transport performance given a set of available resources. While most approaches focus only on infrastructure resources (i.e. availability of train paths), we include both infrastructure and vehicle resources in a capacity estimation problem. We study the railway capacity estimation problem applying an associated timetable saturation method; in other words, the capacity is related to a timetable where no additional trains can be added. We use optimization methods to find such a timetable integrating explicitly variables and constraints from vehicle circulation. A hybrid time–space network describes the integrated timetabling and vehicles scheduling problem, based on which an integer programming model can be formulated, to maximize the overall transportation performance. A Lagrangian relaxation-based decomposition algorithm is proposed to solve the problem, and is shown able to scale to large instances efficiently. The integrated scheduling problem is decomposed into a timetabling sub-problem and a vehicle circulation sub-problem by dualizing the consistency constraints linking the two. A new heuristic, based on the concept of timetable intensity, is employed to improve the quality of the feasible (non-relaxed) solution found. The experimental result shows the benefit of the approach, which can evaluate transportation performance and relate it to various fleet sizes, vehicle depot locations, and minimum headways.

铁路运力是一个模糊的概念，与在给定一组可用资源的情况下运行最大运输性能的可能性有关。尽管大多数方法仅关注基础设施资源（即火车路径的可用性），但是我们将基础设施和车辆资源都包含在容量估计问题中。我们使用关联的时间表饱和方法研究铁路运力估算问题；换句话说，容量与时间表有关，在该时间表中不能添加其他火车。我们使用优化方法来找到这样一个时间表，该时间表将车辆循环中的变量和约束条件进行了明确整合。时空混合网络描述了集成的时间表和车辆调度问题，可基于此制定整数规划模型，以最大程度地提高整体运输性能。提出了一种基于拉格朗日松弛的分解算法来解决该问题，并证明了该算法能够有效地扩展到大型实例。通过对链接两者的一致性约束进行双重化，将综合调度问题分解为时间表子问题和车辆流通子问题。基于时间表强度的概念，采用了一种新的启发式方法来提高找到的可行（非松弛）解决方案的质量。实验结果表明了该方法的好处，该方法可以评估运输性能并将其与各种车队规模，车辆仓库位置和最小车距相关联。通过对链接两者的一致性约束进行双重化，将综合调度问题分解为时间表子问题和车辆流通子问题。基于时间表强度的概念，采用了一种新的启发式方法来提高找到的可行（非松弛）解决方案的质量。实验结果表明了该方法的好处，该方法可以评估运输性能并将其与各种车队规模，车辆仓库位置和最小车距相关联。通过对链接两者的一致性约束进行双重化，将综合调度问题分解为时间表子问题和车辆流通子问题。基于时间表强度的概念，采用了一种新的启发式方法来提高找到的可行（非松弛）解决方案的质量。实验结果表明了该方法的好处，该方法可以评估运输性能并将其与各种车队规模，车辆仓库位置和最小车距相关联。