Increasing Delay-Tolerance of Vehicle and Crew Schedules in Public Transport by Sequential, Partial-Integrated and Integrated Approaches

Document Type

Journal Article

Publication Date


Subject Area

mode - bus, operations - scheduling, organisation - workforce planning, place - europe


vehicle and crew scheduling, public transport, delay-tolerance, robustness, time-space-network


In public bus transport delays occur frequently during execution of vehicle and crew schedules. Delayed busses not only affect the vehicle schedule but also the associated crew schedule. Delayed drivers cause similar effects the other way round. Thus planned schedules can become infeasible and the operations control has to initiate expensive recovery actions. To avoid these undesirable effects possible disruptions can already be considered in the planning phase. We present different offline approaches to increase delay-tolerance of both vehicle schedules and crew schedules. Thereby we consider sequential, partial-integrated and integrated planning methods for vehicle and crew scheduling.

We propose two different types of approaches: approaches using no information about possible delays, and approaches using historical delay data. Within these approaches the main focus is on providing buffer times at appropriate positions in the vehicle and crew schedules. Buffer times should be distributed that way that minor disruptions are absorbed and delay propagation can be limited. Further, planned costs should not be increased significantly compared to cost-optimal scheduling. We use different flow decomposition strategies for cost-optimal flows of the underlying time-space-network model in order to redistribute buffer times. In addition, we apply different strategies to select timetabled trips that might be susceptible to delays. After these trips a certain minimum buffer time is guaranteed. The approaches are compared with regard to planned costs and delay-tolerance using real-life timetables from German cities for the experiments.


Permission to publish the abstract has been given by Elsevier, copyright remains with them.


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