列车编组调度模型的比较
A Comparison of Models for Rolling Stock Scheduling
AI总结：
本文比较了两种列车调度模型，探讨了其在铁路运营商运营差异下的适用性，并提出改进方法以适应荷兰铁路公司的需求。
摘要：
乘客铁路运营商规划过程中的关键步骤是将列车单元分配到时刻表中的行程。大量数学优化模型被提出以支持此任务，本文讨论并论证这些模型的合理性，以最有效的方式应对铁路运营商之间的运营差异和不同的规划需求。我们的研究重点是两种常用模型，即组成模型和超图模型，分别由荷兰铁路公司（NS）和DB长途客运公司（DB）开发。我们在类似NS的列车调度设置中比较了这些模型，证明该问题在计算上是强NP难的，并提出不同的超图模型变体以适应NS的设置。我们证明，在此设置下，只要选择足够表达力的超图模型变体，两种模型的线性规划界强度相等。然而，通过在NS实例上的数值评估，我们发现组成模型在实践中通常更紧凑，并且可以在最短的运行时间内找到最优解。
英文摘要：
A major step in the planning process of passenger railway operators is the assignment of rolling stock, i.e., train units, to the trips of the timetable. A wide variety of mathematical optimization models have been proposed to support this task, which we discuss and argue to be justified in order to deal with operational differences between railway operators, and hence different planning requirements, in the best possible way. Our investigation focuses on two commonly used models, the Composition model and the Hypergraph model, that were developed for Netherlands Railways (NS) and DB Fernverkehr AG (DB), respectively. We compare these models in a rolling stock scheduling setting similar to that of NS, which we show to be strongly NP-hard, and propose different variants of the Hypergraph model to tune the model to the NS setting. We prove that, in this setting, the linear programming bounds of both models are equally strong as long as a Hypergraph model variant is chosen that is sufficiently expressive. However, through a numerical evaluation on NS instances, we show that the Composition model is generally more compact in practice and can find optimal solutions in the shortest running time.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
