In this work, we consider the problem of scheduling a set of trains (i.e., determining their departure and arrival times at the visited stations) and simultaneously deciding their stopping patterns (i.e., determining at which stations the trains should stop) with constraints on passenger demand, given as the number of passengers that travel between an origin station and a destination station. In particular, we face the setting in which demand can be uncertain, and propose Mixed Integer Linear Programming (MILP) models to derive robust solutions in planning, i.e., several months before operations. These models are based on the technique of Light Robustness, in which uncertainty is handled by inserting a desired protection level, and solution efficiency is guaranteed by limiting the worsening of the nominal objective value (i.e., the objective value of the problem in which uncertainty is neglected). In our case, the protection is against a potential increased passenger demand, and the solution efficiency is obtained by limiting the train travel time and the number of train stops. The goal is to determine robust solutions in planning so as to reduce the passenger inconvenience that may occur in real-time due to additional passenger demand. The proposed models differ in the way of inserting the protection, and show different levels of detail on the required information about passenger demand. They are tested on real-life data of the Wuhan–Guangzhou high-speed railway line under different demand scenarios, and the obtained results are compared with those found by solving the nominal problem. The comparison shows that robust solutions can handle uncertain passenger demand in a considerably more effective way.

在这项工作中，我们考虑安排一组火车的问题（即确定它们在拜访的车站的出发和到达时间），同时确定其停靠方式（即确定火车应该在哪个车站停靠），并限制了乘客的问题。需求，以始发站与目的地站之间旅行的乘客数量表示。特别是，我们面临着需求可能不确定的环境，并提出了混合整数线性规划（MILP）模型以在规划中（即在运行前几个月）得出可靠的解决方案。这些模型基于光健技术，其中通过插入所需的保护措施来处理不确定性通过限制标称目标值（即，不确定性被忽略的问题的目标值）的恶化来保证解决方案的效率。在我们的案例中，这种保护措施是针对潜在的乘客需求增长而提供的，而解决方案的效率是通过限制火车的行驶时间和火车停靠的次数来获得的。目标是确定规划中的可靠解决方案，以减少由于额外的乘客需求而可能实时发生的乘客不便。提出的模型在插入保护的方式上有所不同，并且在有关乘客需求的所需信息上显示了不同的详细程度。在不同需求情况下，对武汉至广州高铁的真实数据进行了测试，并将获得的结果与通过解决名义问题发现的结果进行比较。比较表明，可靠的解决方案可以以更有效的方式处理不确定的乘客需求。