Urban rail transit (URT) demand often exhibits tidal or centripetal shapes during peak/off-peak hours. Inefficiency occurs when the supply of service is not adjusted to the fluctuating demand. This optimization can be realized by redesigning the URT timetables and/or through operational strategies. Certainly, implementation of the optimal/best-adjusted timetables must be feasible in order to accommodate efficient operations planning. This work develops a new methodology to derive an optimal timetabling design procedure for multiphase demands on a bi-directional URT line. It consists of three operational policies: marshaling, skip-stop operation, and robustness. The order of service is determined by the departure times. Following these considerations, this work develops a hybrid model formulated as a mixed-integer programming framework. The case study demonstrates the ability of the modeling framework to assess integrated effects, guarantee its robustness and to bring about 13% saving of the total cost associated with passengers, operations and reliability.

中文翻译：

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使用编组计划和跳过站操作的稳健和优化的城市轨道时刻表

城市轨道交通 (URT) 需求在高峰/非高峰时段通常表现出潮汐或向心形状。当服务供应没有适应波动的需求时，就会出现低效率。这种优化可以通过重新设计 URT 时间表和/或通过运营策略来实现。当然，最佳/最佳调整时间表的实施必须是可行的，以适应有效的运营计划。这项工作开发了一种新方法，可以为双向 URT 线路的多相需求推导出最佳时间表设计程序。它由三个操作策略组成：编组、跳过停止操作和健壮性。服务顺序由出发时间决定。根据这些考虑，这项工作开发了一种混合模型，该模型被制定为混合整数编程框架。