Collaborative truck-and-drone delivery for inventory-routing problems

With the retail market more competitive than it has ever been and with profit margins razor-thin, it has become of the essence that business operations are conducted as cost-efficiently as possible. With traditional methods exhausted, companies now see it worthwhile to explore fundamentally paradigm-shifting methods to create savings. For the logistics industry, one such approach is the incorporation of unmanned aerial vehicles (UAVs), or drones, into the delivery cycle, whose per-mile transportation costs are much lower than those of trucks, the traditional mode of transportation for deliveries. Yet despite the long-standing promise of drones to revolutionize the supply chain, realistic proposals for the exact ways in which UAVs would be introduced into delivery operations have only recently begun to appear in the operations research literature. Particularly noteworthy among these proposals is the concept of collaborative truck-and-drone operation, which captures the advantages of each of the two modes of delivery involved while attenuating their respective downsides. Over the past five years, collaborative delivery has been studied extensively in the classical contexts of the traveling salesman problem and the vehicle-routing problem. In this paper, we offer a first incursion into studying the incorporation of tandem truck–drone delivery into the inventory-routing problem (IRP)–a more realistic and more challenging operations model. After presenting a mixed integer-linear programming formulation for the IRP with drone (IRP-D), we propose an exact branch-and-cut solution approach for it. Additionally, a heuristic for the problem is designed based on the solution of the basic (i.e., droneless) IRP. Extensive computational results show that the heuristic is effective both as a standalone algorithm and as a warm-starting agent for the branch-and-cut IRP-D algorithm. We also demonstrate the contrast between the IRP-D and the basic IRP.