Exact and heuristic approaches to Truck–Drone Delivery Problems

Collaborative delivery employing drones in last-mile delivery has been an extensively studied topic in recent years. In this paper, it is studied Truck–Drone Delivery Problems (TDDPs) in which a traditional delivery truck is gathered with a drone to cut delivery times and costs. The vehicles work together in a hybrid operation involving one drone launching from a larger vehicle that operates as a mobile depot and a recharging platform. The drone launches from the truck with a single package to deliver to a customer. Each drone must return to the truck to recharge batteries, pick up another package, and launch again to a new customer location. This work proposes a novel Mixed Integer Programming (MIP) formulation and a heuristic approach to address the problem. The proposed MIP formulation yields better linear relaxation bounds than previously proposed formulations for all instances, and was capable of optimally solving several unsolved instances from the literature. A hybrid heuristic based on the General Variable Neighborhood Search metaheuristic combining Tabu Search concepts is employed to obtain high-quality solutions for large-size instances. The efficiency of the algorithm was evaluated on 1415 benchmark instances from the literature, and over 80% of the best known solutions were improved.