Truck and Unmanned Vehicle Routing Problem with Time Windows: A Satellite Synchronization Perspective

Abstract

We consider an important feature of satellite synchronization in the practical scenario of using unmanned vehicles (UVs) carried by trucks for “last-meter” delivery and introduce the truck and UV routing problem with time windows (TUVRP-TW) for optimizing the routes of a homogeneous fleet of truck-UV combinations. A UV that has been dispatched from its truck must be picked up by the same truck or must return by itself to the depot. Customers with time windows are classified into two types: truck-UV customers (TUCs) and UV customers (UCs). The TUCs where trucks dispatch or pick up the carried UVs are regarded as satellites. Fleet coordination and satellite synchronization are essential for modelling the TUVRP-TW. We classify satellite synchronization into inner-satellite synchronization and intersatellite synchronization. The inner-satellite synchronization generally considered in the literature focuses on synchronization operations at the same satellite. Intersatellite synchronization, which focuses on synchronization operations at various satellites, allows UVs to not return to the dispatched locations, if necessary. In the mixed-integer linear programming model of the TUVRP-TW, both binary variables for identifying the appointed satellites and continuous variables for time continuity constraints are introduced to ensure the interaction between truck routes and UV routes. A hybrid algorithm based on a greedy randomized adaptive search procedure (GRASP) and a variable neighborhood search (VNS) is provided. Based on generated instances and benchmark instances, computational experiments are conducted to evaluate the performance of the intersatellite synchronization, the performance of the developed formulation, and the applicability of the hybrid algorithm.