Robust drone delivery with partial recharging strategy in urban medical logistics

The rapid development of smart cities has prompted the upgrading of drone transport services. This study examines a new variant of the drone routing problem (DRP), which considers a homogeneous group of drones transporting medical supplies to multiple hospitals or medical centers with pre-specified deadlines. On each trip, the drone is allowed to land on existing charging platforms, with decisions made regarding when and where to recharge, as well as the duration of each charging session. We also consider that the drone flight time is uncertain, and the drone power consumption is nonlinearly dependent on its payload. To address this problem, we first propose a robust optimization model grounded in the well-known budgeted uncertainty set. Subsequently, we design a tailored branch-and-price (B&P) algorithm. This algorithm employs a variable neighborhood search (VNS) strategy to effectively solve the subproblem. In VNS, we develop four kinds of neighborhood structures to explore the solution space effectively. Also, to avoid falling into a local optimum, a shaking operation is introduced. Extensive numerical experiments are conducted to evaluate the algorithm’s effectiveness, highlight the advantages of robustness in handling uncertainty, and examine how critical model parameters influence the resulting solutions. Finally, we also use the real data of the blood center in Chongqing, China, to illustrate the application of the model.