Collaborative truck multi-drone routing and scheduling problem: Package delivery with flexible launch and recovery sites

Abstract

This paper deals with the problem of coordinating a truck and multiple heterogeneous unmanned aerial vehicles (UAVs or drones) for last-mile package deliveries. Existing literature on truck–drone tandems predominantly restricts the UAV launch and recovery operations (LARO) to customer locations. Such a constrained setting may not be able to fully exploit the capability of drones. Moreover, this assumption may not accurately reflect the actual delivery operations. In this research, we address these gaps and introduce a new variant of truck–drone tandem that allows the truck to stop at non-customer locations (referred to as flexible sites) for drone LARO. The proposed variant also accounts for three key decisions — (i) assignment of each customer location to a vehicle, (ii) routing of truck and UAVs, and (iii) scheduling drone LARO and truck operator activities at each stop, which are always not simultaneously considered in the literature. A mixed integer linear programming model is formulated to jointly optimize the three decisions with the objective of minimizing the delivery completion time (or makespan). To handle large problem instances, we develop an optimization-enabled two-phase search algorithm by hybridizing simulated annealing and variable neighborhood search. Numerical analysis demonstrates substantial improvement in delivery efficiency of using flexible sites for LARO as opposed to the existing approach of restricting truck stop locations. Finally, several insights on drone utilization and flexible site selection are provided based on our findings.