Multi-depot bus schedule assignment with parking and maintenance constraints for intercity transportation over a planning period

This article introduces the schedule assignment problem for public transit, which aims to assign vehicle blocks of a planning period to buses in the fleet of a transportation company. This assignment has to satisfy several constraints, the most important of which is compatibility, meaning that certain blocks can only be serviced by buses belonging to given types. Other constraints come from the fact that the problem considers a long-term plan for several days or weeks, which means that daily parking and periodic maintenance activities also have to be taken into account. We give a state-expanded multi-commodity flow network for the above problem. This model takes parking constraints into account, and also assigns preventive maintenance tasks to buses after serving blocks for a fixed amount of time. The solutions of this model are presented for real-life and randomly generated instances.