Robust and Cost-Efficient Integrated Multiple Depot Vehicle and Crew Scheduling with Controlled Trip Shifting

For vehicle and crew scheduling in public bus transport, two concepts are intensively studied to reduce resource usage and minimize operational costs: Integrated, that is, simultaneous scheduling of vehicles and drivers, and resource scheduling with simultaneous trip shifting, that is, slightly modifying departure and arrival times of particular trips without changing their duration. Applying these two concepts can lead to highly cost-efficient and tight schedules. Unfortunately, such schedules are more susceptible to delays during operations. Furthermore, shifting of particular trips may have an unwanted impact on the original timetable structure as, for example, headways between consecutive trips of a line might be changed. In this work, we develop an integrated vehicle and crew scheduling approach with the possibility to shift scheduled trips controllably within small defined time windows. It is a Lagrangian heuristic based on column generation. In addition to minimizing planned costs, the approach aims at two further objectives: building robust schedules by minimizing the expected overall propagation of delays through the transport network and minimizing timetable alteration. To reduce the possible propagation of delays, the mutual dependencies between vehicle and crew schedules are taken into account during integrated scheduling. To increase both robustness and cost-efficiency, the possibility to shift trips within small defined time windows is used. Robust and cost-efficient vehicle itineraries and crew duties are generated in the column-generation pricing problems. Computational experiments on data sets from the real world show that resource usage can be further reduced compared with pure cost-efficient integrated scheduling, whereas resource schedules remain robust and timetable alterations can be minimized.