The Single Truck and Drone Trailer Routing Problem

The rapid growth of e-commerce has substantially increased last-mile delivery volumes, intensifying the pressure on urban logistics systems with limited vehicle capacity. While truck-and-trailer configurations offer higher capacity, their operational flexibility is restricted, as trailers cannot access all customer locations. Thus, a truck decouples a trailer at designated satellite locations, delivers its own cargo, and subsequently picks up the trailer. During these truck delivery tours, the trailer remains unused. However, it can be used to automatically launch drones and serve as a flexible mobile hub. But, how efficient is this system in terms of delivery costs compared with a truck and trailer concept? <br> <br> To answer this question, we introduce the single Truck and Drone Trailer Routing Problem (TDTRP), a novel truck and trailer routing extension that integrates a single truck, a detachable trailer, and multiple drones launched from the trailer. The TDTRP is formulated as a mixed-integer linear program that explicitly captures heterogeneous vehicle capacities, trailer parking decisions, and drone operations. Furthermore, we develop a branch-and-cut algorithm that dynamically adds subtour elimination constraints via callbacks to efficiently solve larger instances. <br> <br> The computational results demonstrate that drone operations can reduce last-mile delivery costs by up to 3.7% or 10.3% dependent on the drone-to-truck cost ratio. In addition, we find that modeling the depot as a potential satellite location significantly amplifies the observed cost advantages.