中断恢复对货运航空公司的运营起到至关重要的作用。为扩大货运航班网络的应用场景，引入强制节点和外部弧等元素，在通常情况下，飞机和货物均被定义在相互独立的网络中，并通过顺序求解的方法依次恢复，为挖掘各研究对象之间的关联性，并同时完成各项恢复操作，引入实体流将不同类型的实体集成在同一网络中；为解决机组的恢复问题，在模型中添加机组执勤、飞行资质等有关约束，并基于改进的航班网络构建混合整数线性规划模型，该模型能够实现飞机、货物和机组的一体化恢复；为准确评估货机的容量限制，以标准托盘表示货物量，并改进有关的容量约束模型；为降低问题的复杂度，采用实体聚合的方法来缩减网络中实体的数量。使用小规模货运航空公司所提供的运行数据进行模型验证。结果表明：模型提出的恢复方案能够减少42%的延误时间；在进一步的仿真测试中，针对两个具备多机队的货运航空公司，分别设置6种不同的中断场景，随着中断率的提高，中型货运航空公司的恢复策略以重新规划货机路径和机组排班为主，而大型货运航空公司的恢复策略以航班延误为主。提出的基于改进航班网络的航空货运综合调度恢复模型能够在有限时间内求得所有算例的精确解，并且平均误差为0.47%。

The disruption recovery is regarded as a crucial role in the operation of freighter airlines. To expand the application scenarios of the freight flight network, elements such as mandatory nodes and external arcs were introduced to enhance the applicability of the network. In general, aircraft and cargo were defined in separate networks and are recovered using a sequential solving method. To explore the correlation between each research object and to complete each recovery action, the entity flow was defined to integrate different types of entities in the same network. To solve the problem of crew recovery, constraints such as crew duty and flight qualifications were added to the model, and a mixed integer linear programming model was constructed based on an improved flight network. This model can achieve integrated recovery of aircraft, cargo, and crew. To accurately evaluate the capacity constraints of the cargo aircraft, a unit load device was used to represent the volume of cargo and to improve the relevant models of capacity constraints. An entity aggregation approach was employed to reduce the number of entities to control the model complexity. The model evaluation was performed using operational data provided by a small freighter airline. The results show that the recovery solution causes a 42% reduction in the delay time. In the subsequent simulation experiments, six different disruption scenarios were established for two freighter airlines with multiple fleets. As the disruption rate increases, medium freighter airlines adopt the strategy of re-routing aircraft and rescheduling crew, while large freighter airlines focus on flight delays. The proposed integrated air cargo schedule recovery model based on an improved flight network can solve all the cases exactly in limited time, and the average error is 0.47%.