Routing of carrier-vehicle systems with dedicated last-stretch delivery vehicle and fixed carrier route

Abstract

We examine a routing problem that arises when an unmanned aerial vehicle (UAV), or drone, is used in the last-stretch of parcel delivery to end customers. In the scenario that we study, a delivery truck is dispatched carrying a shipment of parcels to be delivered to customers. While the truck is following a predetermined route, a drone is charged with making the last-stretch delivery of a parcel from the truck to a customer’s doorstep. Given a set of customers to be served and a set of rendezvous points where the drone can meet with the truck to pick up a parcel, we ask what the quickest way is of delivering all parcels to the end customers. We model this problem as a problem of finding a special type of a path in a graph of a special structure, and show that the graph problem is NP-hard even when all edge weights are restricted to be 1 or 2. Furthermore, we identify a special instance type that can be solved optimally in polynomial time. Finally, we propose a polynomial-time approximation algorithm for the graph problem in metric graphs, and show that its approximation ratio is bounded above by 2 in restricted metric graphs.