A proactive-reactive framework for collaborative truck-drone pickup-and-delivery routing under uncertain customer presence

In traditional last-mile attended home delivery, stochastic service failures, primarily driven by uncertain customer presence, incur additional operational costs for the logistics provider and cause customer inconvenience. This stochasticity also poses a major challenge to collaborative truck-drone routing with simultaneous pickup and delivery. In such systems, retained payloads from service failures accelerate drone energy consumption, thereby disrupting vehicle synchronization and compromising flight feasibility. In this paper, we introduce a new problem, the collaborative truck-drone pickup-and-delivery routing under uncertain customer presence (CTD-PDRUCP). To capture the non-linear payload-energy-uncertainty coupling, we model and solve this problem through a unified two-stage, proactive-reactive framework. Specifically, the offline proactive stage constructs risk-averse routes utilizing an expectation-based surrogate recourse operator, whereas the online reactive stage performs rapid dynamic route re-optimization upon service failures. This framework is efficiently powered by the integration of Ant Colony Optimization and Adaptive Large Neighborhood Search (ACO-ALNS). Extensive computational experiments, including a real-world case study, and Monte Carlo simulations demonstrate the effectiveness of the proposed framework in terms of solution quality and robustness. Finally, our sensitivity analyses reveal that expanding the drone-eligible customer ratio yields diminishing returns and that higher drone speeds offer negligible cost savings due to payload and endurance bottlenecks, providing valuable managerial insights for collaborative last-mile delivery.