大规模灾害中基于聚类的医疗物资联合运送优化

应急响应中，往往出现救援物资供应节点与需求节点距离太远、关键道路损毁导致难以及时通过车辆运送物资到灾区等情景，此时直升飞机逐渐被用来运送关键应急资源（如医疗物资及医护人员）。然而，大规模灾害中难以使用直升飞机运送医疗物资到每个医疗救助点，通常考虑灾民的聚集性选择一定数量的应急中转点，以接收直升飞机运送的医疗物资，之后采用车辆运送物资到其覆盖的医疗救助点。针对该问题，提出一种基于聚类的两阶段医疗物资联合运输方法：第一阶段根据医疗救助点分布，采用模糊C-均值算法（FCM）进行应急中转点选择和医疗救助点划分，并针对FCM划分中存在的剩余容量不均衡问题，考虑容量约束提出一种改进划分方法（FCMwCC），构建“直升飞机-车辆”医疗物资联合运输网络结构；第二阶段建立基于聚类的运送路线优化模型，确定从应急中转点到医疗救助点的具体运送路线。数值实验验证了提出方法和算法的有效性。

A Clustering-Based Approach for Medical Supplies Intermodal Transportation in Large-Scale Disasters

In real-world emergency responses, helicopters are gradually used to transport key relief resources such as medical supplies and personnel, due to the long distance between supply nodes and demand nodes or the difficulty to reach to affected areas by land in time. However, it is often impossible to transport relief supplies to every medical aid point (MAP) by helicopters in large-scale disasters. In general, considering the aggregation of residents in disasters, emergency distribution points (EDPs) are set up for receiving urgent medical supplies from helicopters and then delivering the supplies to each MAP by vehicles. In the work, a clustering-based two-stage approach is developed for medical supplies intermodal transportation in disasters. In the first stage, according to the locations of MAPs, Fuzzy C-Means (FCM) is used to select EDPs and partition MAPs, and importantly an improved FCM algorithm with capacity constraints (FCMwCC) is developed to overcome the unbalanced extra capacity in the FCM partitioning, which can determine the network of helicopters-vehicles intermodal transportation. In the second stage, a clustering-based routes optimization model is developed, which can determine the vehicle traveling routes from EDPs to their covered MAPs. Numerical experiments test the effectiveness of the developed approach and algorithms, and the following findings are obtained. Firstly, the MAPs partitioning by the classic FCM could minimize the total distance among MAPs and EDPs, but could result in big extra capacities due to lack of considering the capacity constraints. Further the MAPs adjustment by the improved FCMwCC could decrease the extra capacities and the number of used medical vehicles. The proposed model and algorithms could select proper emergency distribution points and arrange transportation routes for real-world intermodal transportation of medical supplies.