频繁发生的突发事件对人类社会产生了巨大的负面影响，尤其是2019年底全球爆发的新冠疫情，给民众生活和生命健康造成了巨大的损害，与此同时也触发了大量的应急医疗物资配送需求。该类物资具有对时效性要求较高、不确定性较强的特点。鉴于无人机具有配送速度快、不受道路交通条件限制等优势，本论文采用无人机进行医疗物资配送的方式，针对不同不确定条件，对应急物资配送中重要问题——选址、分配展开研究。首先，本文针对随机需求下无人机应急物资配送拥塞型设施选址问题开展研究，考虑了无优先级、静态优先级、动态优先级三种优先级策略。建立了以无人机为移动服务台，具有一般服务时间分布的排队-选址模型。该模型以最小化最大响应时间为目标保障公平性，同时对设施选址、需求分配、无人机数量进行决策。然后将三种策略下的非凸非线性模型分别成功转换为二阶锥规划。最后，通过数值试验验证模型并分析比较了三种策略下的系统表现，为决策者针对实际应急配送不同紧急程度，选择合适的优先级策略，制定选址和分配决策提供理论指导。 随后，本研究对静态优先级策略下的拥塞型设施选址问题进行扩展，考虑了模糊化的需求到达率以及无人机续航能力参数，建立了模糊规划排队-选址模型。首次针对该问题考虑成本、系统效率、公平响应时间三个目标函数。综合利用加权目标规划、二阶锥规划、模糊规划、机会约束规划方法将复杂模型重构为混合整数二阶锥规划。案例分析表明，该模型可以帮助决策者更好地平衡多个目标，得到理想的帕累托最优解，通过设置合理的模糊度做出更灵活的决策，并显著提高高优先级需求的服务水平。最后，论文研究了一类特殊的防疫应急物资——新冠疫苗的配送问题。首次考虑了疫苗配送问题中的供应不确定性，并基于无人机配送网络，建立了一个多周期的两阶段鲁棒优化模型。模型综合考虑了医疗服务安排和分配公平，对设施的选址、无人机的部署、两针剂疫苗分配安排进行决策，同时优化经济效益和社会效益。针对所提出的模型，本研究设计了两种分别基于顶点遍历和对偶方法的列与约束生成算法。通过案例分析验证了模型和算法有效性，说明了鲁棒模型的优势以及考虑供应不确定和公平的必要性，为现实不确定疫苗配送决策提供指导。
Frequent disasters and emergencies have had a severe impact on human society. For example, the global outbreak of the novel coronavirus disease 2019 (COVID-19) has caused immense damage to people‘s lives and health. This has led to an increases demand for emergency medical delivery service, such as medication, blood, and exam kits， which are time-sensitive and subject to high uncertainty. According to the fast delivery and reduced traffic restrictions of drones, this thesis proposes the use of drones for delivering emergency medical materials. The study investigates the facility location-allocation problems under different uncertainties which have a significant impact on distribution efficiency. Firstly, we study the stochastic congested facility location-allocation problem with drones as mobile servers in emergency medical delivery. We employ queues to model the system congestion of drone requests and consider three queuing disciplines: non-priority, static priority, and dynamic priority. The model jointly optimizes the location of facilities, the capacity of drones deployed at opened facilities, and the allocation of demands, with an objective of equitable response time among all demand sites. The non-linear model under each discipline is further recast as a mixed-integer second-order conic program (MISOCP). We conduct extensive computational experiments to demonstrate the effectiveness and accuracy of our approach, and compare the system performance under the three queuing disciplines. Important managerial insights are also provided for decision-makers to help choose the appropriate priority strategy and make optimal facility location and allocation decisions based on actual emergency situations.Subsequently, we extend the congested facility location problem with static priority by considering fuzzy demand arrival rates and drone endurance. A multi-objective fuzzy queuing-location model is proposed, which simultaneously optimizes cost, system efficiency, and equitable response time for the first time. We apply chance-constrained, second-order conic, fuzzy, and weighted goal programming approaches to recast the complex model as a crisp MISOCP. Results based on a case study show that our method can help decision-makers better balance various objectives by producing an appropriate Pareto optimal solution, make more flexible decisions with desirable fuzzy degrees, and significantly improve the service level of high priority demands.Finally, we explore the distribution problem of COVID-19 vaccines, which is a kind of preventive medical supply for public health emergencies. We for the first time consider the supply uncertainty in the vaccine distribution problem, and develop a multi-period two-stage robust optimization model based on a drone delivery network. The model jointly optimizes the location of facilities, the capacity of deployed drones, and the assignment of the two-dose vaccine, taking into account social and economic benefits. We propose two tailored column-and-constraint generation (C\&CG) algorithms, where the subproblems are solved via the vertex traversal and the dual methods, respectively. The performance of these two methods is further compared. Real-world data is used to demonstrate the superiority of the robust model and the necessity of addressing uncertain supply and distribution equity, and to provide guidance for actual vaccine distribution under uncertainty.
