AI 中文总结
针对低空空域的无人机物流容量规划问题，构建两阶段随机规划并通过带列生成子问题的Benders分解求解，经实验验证其在中等及更大网络上的有效性，深圳案例显示预留集中于核心走廊。
AI 中文摘要
中国、美国和欧盟的监管机构如今将低空空域准入作为按定价、分时段的走廊授权提供，需提前预订，未使用则作废。我们研究无人机物流规划者应在需求实现前的每个走廊-时间单元上预留多少容量，以最大化扣除预留成本后的预期利润。预留容量无法在走廊或时间窗口间转移，且会沿时间相关路径共同消耗，因此预留通过网络耦合，这是具有 exogenous 空域容量的模型无法捕捉的。我们构建了一个两阶段随机规划，其 recourse 会在时间扩展网络上选择并路由已接受的请求，证明其基于弧的形式与路径打包形式等价，并通过带列生成子问题的 Benders 分解求解。该分解基于 LP 松弛操作，所有报告的预留与路由决策均作为整数计划恢复。计算实验在中等规模网络上实现了个位数的 LP-Benders 间隙，并通过截断路径方法扩展到更大实例。深圳案例研究显示，预留集中在结构上的核心走廊，需求水平和预留价格对预留容量数量的影响大于走廊选择。
英文摘要
Regulators in China, the United States, and the European Union now provide low-altitude airspace access as priced, time-windowed corridor authorizations, booked in advance and forfeited if unused. We ask how much capacity a UAV logistics planner should reserve on each corridor--time unit before demand is realized, to maximize expected profit net of reservation cost. Reserved capacity cannot be transferred across corridors or time windows and is consumed jointly along time-respecting paths, so reservations are coupled through the network in ways that models with exogenous airspace capacity cannot capture. We formulate a two-stage stochastic program whose recourse selects and routes accepted requests on a time-expanded network, prove its arc-based and path-packing forms equivalent, and solve it by Benders decomposition with column-generated subproblems. The decomposition operates on the LP relaxation, and all reported reservation and routing decisions are recovered as integer plans. Computational experiments achieve single-digit LP-Benders gaps on moderate-sized networks and extend to much larger instances through a truncated-path approach. A Shenzhen case study shows reservations concentrating on structurally central corridors, with demand level and reservation price having more influence on the quantity of capacity reserved than the selection of corridors.
