Planning robust drone-truck delivery routes under road traffic uncertainty

In this paper, we show the potential of a drone-truck logistics system to provide fast last-mile delivery services. In the system, a truck and a drone work in tandem to serve customers within pre-specified delivery time windows. Since the uncertainty in the ground traffic network can not only fail a service promise but also expose the drone to danger, we focus on mitigating such risks when designing the routing plan. In particular, we investigate the robust drone-truck delivery problem (RDTDP) that seeks a robust joint route for the truck-and-drone tandem to maximize the profit. We develop an exact branch-and-price (B&P) solution approach that can solve RDTDP instances, both randomly generated and collected from real-life data, with up to 40 service requests. In a numerical study, we demonstrate that the solution obtained with our proposed B&P approach is significantly more robust than the one obtained without considering any uncertainty. In particular, while maintaining a comparable mean value in the solution quality measures, the robust solution features a variance up to 58% smaller and a feasibility ratio (i.e., on-time performance) up to 90% higher than the deterministic solution. These insights suggest that the robust route can be carried out much more frequently in practical usage.