关键词: 应急血浆配送, 车辆–无人机协同, Benders分解算法, 分支定价切割算法

Abstract: Major emergencies such as earthquakes and floods can cause mass casualties and severe disruptions to transportation systems, creating an urgent need for timely and reliable emergency blood plasma delivery. Unlike conventional relief supplies, plasma is a time-critical medical resource characterized by limited availability, uncertain demand, temperature-control requirements, and blood-type compatibility constraints. This study investigates a vehicle–drone collaborative emergency plasma delivery problem under uncertainties in plasma supply, demand, and vehicle travel times. The problem jointly determines demand-point service decisions, plasma allocation quantities, and coordinated vehicle–drone routes. Each vehicle carries multiple drones that can be launched from designated stops to serve eligible demand points and must return before the vehicle departs. The formulation incorporates delivery deadlines, vehicle and drone capacity limits, drone endurance, vehicle–drone synchronization, temperature-control packaging loads, and plasma substitution rules. A two-stage mixed-integer robust convex programming model based on a discrete scenario set is developed to minimize a weighted sum of shortage penalties and worst-case delivery disutility. To solve the resulting large-scale problem, a logic-based Benders decomposition framework is developed. The Benders routing subproblem is reformulated as a path-based set-partitioning problem and solved using a branch-and-price-and-cut algorithm. Label-based exact pricing, subset-row cuts, and heuristic pricing strategies are further incorporated to improve computational efficiency while preserving exactness. Computational experiments are conducted on instances adapted from the Solomon benchmark dataset and on a real-world case involving one blood center and seven hospitals in Chengdu, China, with disaster scenarios constructed from historical earthquake data. The results show that the proposed algorithm solves more instances to proven optimality and achieves better overall computational performance than the benchmark Benders method. Vehicle–drone collaboration improves delivery efficiency and enables service to demand points that may be inaccessible to ground vehicles. In out-of-sample tests with 5,000 generated scenarios, the robust model achieves a constraint violation rate of 20.04%, compared with 61.40% for the deterministic model and 39.46% for the stochastic model, while requiring a higher planned objective value. These results demonstrate the value of explicitly accounting for uncertainty when reliability is a primary concern in emergency medical logistics. This study extends international research on humanitarian logistics and truck–drone routing by integrating plasma-specific operational requirements, multiple sources of uncertainty, and coordinated multi-drone operations within a unified optimization framework. In contrast to studies primarily concerned with commercial delivery or simplified emergency settings, the proposed framework explicitly incorporates plasma substitution relationships, temperature-control packaging requirements, unmet-demand penalties, and disrupted ground accessibility. The modeling and decomposition methods provide a methodological basis for other time-critical medical delivery problems involving uncertain demand, limited resources, and multimodal transportation.

Key words: Emergency plasma delivery, Vehicle-drone collaboration, Benders decomposition algorithm, Branch-and-price-and-cut algorithm