This work addresses the Locomotive Scheduling Problem with Maintenance Constraints (LSPM). The basic Locomotive Scheduling Problem (LSP), which depicts one of the most crucial optimization problems occurring in the railway industry, aims at assigning a fleet of locomotives to a set of scheduled trains such that the overall costs are minimized. As the rolling stock represents one of the main costs of a rail company, the focus lies on maximizing the utilization of the locomotives. This requires the incorporation of special maintenance constraints that increase the computational difficulty of the problem significantly. In our previous work, we proposed a Mixed-Integer Linear Programming formulation for solving the LSPM and continue in this paper by investigating different heuristic solution approaches, i.e., an Overlapping Rolling Horizon Approach and a Two-Stage Matheuristic (2SMH). In the objective function, realistic costs for deadheading, the number of used locomotives and maintenance jobs are taken into account. An extensive computational study is conducted on instances with up to 2,290 trains derived from real-world data provided by RCA, the largest Austrian rail company for freight transportation. All solution approaches are analyzed in detail and compared against each other in order to show their benefits and disadvantages. We show that our approaches are capable of delivering high-quality solutions within short computation times. In fact, the performance of the 2SMH qualifies it to form the basis of a large scale real-time application to support railroad managers in their daily operations.

这项工作解决了具有维护约束 ( LSPM )的机车调度问题。基本的机车调度问题 ( LSP ) 描述了铁路行业中发生的最重要的优化问题之一，旨在将机车车队分配给一组预定的列车，从而使总成本最小化。由于机车车辆是铁路公司的主要成本之一，因此重点在于最大限度地利用机车。这需要结合特殊的维护约束，这会显着增加问题的计算难度。在我们之前的工作中，我们提出了一个混合整数线性规划公式来解决LSPM并在本文中继续研究不同的启发式解决方案方法，即重叠滚动地平线方法和两阶段数学 ( 2SMH )。在目标函数中，考虑了空头的实际成本、使用的机车和维护工作的数量。对多达 2,290 列火车的实例进行了广泛的计算研究，这些实例来自奥地利最大的货运铁路公司RCA提供的真实世界数据。所有解决方案都经过详细分析并相互比较，以显示其优缺点。我们表明我们的方法能够在很短的计算时间内提供高质量的解决方案。事实上，2SMH的性能 使其成为大规模实时应用程序的基础，以支持铁路管理人员的日常运营。