• train scheduling;
  • timetabling;
  • periodic event scheduling problem;
  • flexibility


This article addresses the problem of generating conflict-free periodic train timetables for large railway networks. We follow a two-level approach, where a simplified track topology is used to obtain a macrolevel schedule, and the detailed topology is considered locally on the microlevel. To enlarge the solution space in the interface of the two levels, we propose an extension of the well-known periodic event scheduling problem (PESP) such that it allows to generate flexible time slots for the departure and arrival times instead of exact times. This flexible periodic event scheduling problem (FPESP) formulation increases the chance to obtain feasible solutions (exact train routings) subsequently on the microlevel, in particular for stations with dense peak traffic. Total trip time and the time slot sizes are used as multiple objectives and weighted and/or constrained to allocate the flexibility where it is most useful. Tests on medium-size instances of the Swiss Federal Railways' 2007 service intention demonstrate the advantage of the FPESP model, while it only moderately increases its solution time in most cases. A trade-off analysis of the two conflicting objectives is presented and discussed for different scenarios. Finally, we present the Flexbox model, which generalizes the single event flexibilities of the FPESP to arbitrary subsets of events. These Flexboxes can make use of natural dependencies in the timetable and can considerably increase the total flexibility of the timetable. © 2010 Wiley Periodicals, Inc. NETWORKS, 2011