Robust Efficiency in Urban Public Transportation: Minimizing Delay Propagation in Cost-Efficient Bus and Driver Schedules

Bastian Amberg and Boris Amberg and Natalia Kliewer
Transportation Science
Articles in Advance
This work examines combined vehicle and crew scheduling in public bus transit in the context of both robust and cost-efficient resource allocation. Cost-efficiency in terms of minimal planned costs for resource usage is already addressed in numerous contributions providing increasingly sophisticated optimization approaches that are able to compute highly efficient resource schedules. Unfortunately, during operations the resulting tight resource schedules are generally more susceptible to disruptions causing delays or even cascades of delays. Because of dependencies between scheduled vehicles and drivers, even small delays may propagate through the entire network. However, to date there is only little research assessing schedule robustness against disruptions and delays, affecting both vehicle and crew schedules. We consider the mutual dependencies between vehicle and crew schedules and propose solution approaches that are able to consider the propagation of possible delays. The approaches are used to create cost-efficient resource schedules simultaneously capable to absorb delays and to prevent delay propagation. In particular, we present a fully integrated vehicle and crew scheduling approach. To analyze problem characteristics we investigate to what extent sequential, partially integrated, and integrated vehicle and crew scheduling lead to schedules with different quality. Numerical experiments using real-world problem instances examine the influence of these different scheduling schemes on robustness and cost-efficiency. The results stress the relevance of incorporating possible delay propagation when scheduling resources in (especially urban) public transportation. Compared to pure cost-efficient scheduling, the expected delay propagation can be decreased drastically without additional costs. The online appendix is available at
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Published by
Boris Amberg