Exact resolution of a simultaneous vehicle routing and crew scheduling problem in long-haul transport

This work focuses on exact methods for a simultaneous vehicle routing and crew scheduling problem in long-haul transport. Pickup-and-delivery requests with time windows must be fulfilled over a multi-day planning horizon. Unlike some classic approaches, the correspondence between trucks and drivers is not fixed and they can be exchanged in some locations and at any time. Drivers can also travel for free as truck passengers or take external taxis for an additional cost. The objective is to minimise the truck and taxi travel costs and the penalties for late deliveries. Routes for trucks and drivers are represented separately as directed paths in certain digraphs and then synchronised in time and space. Three compact integer linear programming formulations are proposed, and many families of valid inequalities are described. Extensive computational experiments are conducted on randomly generated instances. The formulations are experimentally compared, and the effectiveness of the proposed valid inequalities as cutting planes in a branch-and-cut algorithm is evaluated.