Optimization approaches for the urban delivery problem with trucks and drones

In this paper, we introduce an urban delivery problem with trucks and drones. The problem is to construct truck routings over a subset of parking points and customers, and drone deliveries from parking points to customers. The goal is to minimize the total costs, including the truck routing, drone delivery, and parking costs. To formulate the problem, three mathematical formulations are proposed: the mixed-integer, bi-level (BP), and three-level (TP) programming formulations. Two heuristics: bi-level (BH) and three-level heuristics (TH) are developed, inspired by the proposed BP and TP formulations. Finally, two classes of problems derived from TSPLIB are generated to test the formulations and heuristics. Results indicate that both heuristics take significantly less computational time than CPLEX, and BH found more best solutions. Thus, BH has the best performance in addressing the problem, followed by TH.