Daily Distribution of Duties for Crew Scheduling with Attendance Rates: A Case Study

Abstract

The railway crew scheduling problem with attendance rates is particularly relevant for the planning of conductors in German regional passenger transport. Its aim is to find a cost-minimal set of duties. In contrast to other crew scheduling problems, only a given percentage of trains has to be covered by personnel. As a result, existing solution approaches for this complex planning task often generate schedules in which the number of duties per day varies significantly. However, schedules with an uneven distribution are often not applicable in practice, as an proper assignment of duties to conductors becomes impossible. Therefore, we discuss several ways how an even distribution can be considered in a column generation solution method, namely post-processing and integrated approaches. In addition, the daily distribution is also examined for each depot, where a given number of conductors may be assigned to. In a case study the presented approaches are examined and compared for three real-world transportation networks. It is shown that without much additional computational effort and only a minor increase of costs schedules with evenly distributed duties can be gained. Especially the depot-based integrated approaches show promising results. Hence, this study can contribute to an improved applicability in practice of automated railway crew scheduling.