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A vehicle routing and crew scheduling problem (VRCSP) consists ofsimultaneously planning the routes of a fleet of vehicles and scheduling thecrews, where the vehicle-crew correspondence is not fixed through time. Thisallows a greater planning flexibility and a more efficient use of the fleet,but in counterpart, a high synchronisation is demanded. In this work, wepresent a VRCSP where pickup-and-delivery requests with time windows have to befulfilled over a given planning horizon by using trucks and drivers. Crews canbe composed of 1 or 2 drivers and any of them can be relieved in a given set oflocations. Moreover, they are allowed to travel among locations withnon-company shuttles, at an additional cost that is minimised. As our problemconsiders distinct routes for trucks and drivers, we have an additionalflexibility not contemplated in other previous VRCSP given in the literaturewhere a crew is handled as an indivisible unit. We tackle this problem with atwo-stage sequential approach: a set of truck routes is computed in the firststage and a set of driver routes consistent with the truck routes is obtainedin the second one. We design and evaluate the performance of a metaheuristicbased algorithm for the latter stage. Our algorithm is mainly a GRASP with aperturbation procedure that allows reusing solutions already found in case thesearch for new solutions becomes difficult. This procedure together with otherto repair infeasible solutions allow us to find high-quality solutions oninstances of 100 requests spread across 15 cities with a fleet of 12-32 trucks(depending on the planning horizon) in less than an hour. We also conclude thatthe possibility of carrying an additional driver leads to a decrease of thecost of external shuttles by about 60% on average with respect to individualcrews and, in some cases, to remove this cost completely.

A metaheuristic for crew scheduling in a pickup-and-delivery problem with time windows