Two echelon vehicle routing problem with drones in last mile delivery

In recent years, drone routing and scheduling has become a highly active area of research. This research introduces a new routing model that considers a synchronized truck-drone operation by allowing multiple drones to fly from a truck, serve one or multiple customers, and return to the same truck for a battery swap and package retrieval. The model addresses two levels (echelons) of delivery: primary truck routing from the main depot to serve assigned customers and secondary drone routing from the truck, which behaves like a moveable intermediate depot to serve other sets of customers. The model takes into account both trucks' and drones’ capacities with the objective of finding optimal routes of both trucks and drones that minimizes the total arrival time of both trucks and drones at the depot after completing the deliveries. The problem can be solved by formulated mixed integer programming (MIP) for the small-size problem, and two efficient heuristic algorithms are designed to solve the large-size problems: Drone Truck Route Construction (DTRC) and Large Neighborhood Search (LNS). Numeric results from the experiment compare the performance of both heuristics against the MIP method in small/medium-size instances from the literature. A sensitivity analysis is conducted to show the delivery time improvement of the proposed model over the previous truck-drone routing models.