An integrated approach to ex-urban crew and vehicle scheduling

Scheduling of vehicles and crews, traditionally performed sequentially by scheduling vehicles prior to crews, has to be carried out simultaneously in particular settings such as the ex-urban mass transit, where crews are tightly dependent on vehicles' activity or crews' dead-headings are highly constrained. In this paper we propose an integrated approach to vehicle and crew scheduling which exploits the network structure of the problem. A heuristic method based on Lagrangean relaxation is presented, which determines a set of pieces of work suitable for both vehicle activities as well as for crew duties. Crew duties are fixed step by step, while vehicles are scheduled once all the trips have been partitioned into pieces. Extended use is made of Bundle methods for polyhedral functions and algorithms for constrained shortest paths and assignment within a dual greedy heuristic procedure for the set partitioning problem. Computational results are provided for Italian public transit operators, which show some improvements over the results of the sequential approach.