A Comparison of Two Models for Rolling Stock Scheduling

A major step in the planning process of passenger railway operators is the assignment of rolling stock, that is, 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 two distinct problem settings, an NS setting and DB-light setting and consider different model variants to tune the models to these settings. We prove that in both of these settings, the linear programming bounds of the two models are equally strong as long as a number of reasonable assumptions are met. However, through a numerical evaluation on NS and DB-light instances, we show that the numerical performance of the models strongly depends on the instances. Although the composition model is the most compact and fastest model for the NS instances, an adjusted version of this model grows quickly for the DB-light instances and is then outperformed by the considered hypergraph model variants. Moreover, we show that a depot-extended version of the hypergraph model is able to combine strengths of both models and show good performance on both the NS and DB-light instances.