Abstract: The outbreak of COVID-19 poses a significant threat to the emergency management system of public health emergencies in China. The pertinence weakness of the emergency rescue plan has led to a lag in the organization and coordination of epidemic response and resources scheduling, which has affected patient care and epidemic prevention and control. In the actual emergency rescue process, medical resources are showing random changes due to unforeseen uncertainties, resulting in the failure of supply and even interruption, which affects the effective arrangement of rescue and disposal activities. In addition, the current use status of medical resources will affect the use of medical resources in the next stage. Therefore, how to scientifically arrange emergency rescue activities in a highly uncertain environment and improve the response efficiency of rescue disposal has become an important issue worthy of attention in the public health emergency management.
The supply of medical resources is one of the main factors that affect the cost of emergency response to public health events. Due to uncertain factors such as the unclear laws of epidemic transmission, the supply of medical resources presents dynamic changes due to difficulty in accurately estimating them, and the current state of medical resource usage will affect the next stage of medical resources usage, which may lead to difficulties in smoothly executing activities such as patient treatment. Considering the correlation of the use status of medical resources, this paper studies the reactive scheduling optimization problem of public health emergencies under the dynamic change of medical resources, that is, when the random change of medical resources in each stage leads to the interruption of rescue activities, how do we optimize and adjust the rescue plan in time through reactive scheduling strategy, so as to minimize the activity adjustment cost and resource waiting cost in the whole emergency disposal process? Firstly, the reactive project scheduling optimization model of public health emergency under the change of resource correlation is constructed. Secondly, according to the NP-hard of the research problem, a tabu search heuristic algorithm is designed, and two improvement measures are proposed to improve the efficiency of the algorithm. These algorithms are compared and tested on a randomly generated standard instances set, and the results show that TS_LA3 algorithm combining the two improvement measures can obtain a better satisfactory solution. Finally, the influences of key parameters on project costs are analyzed.
The results show that the total cost of emergency rescue project decreases with an increase in resources strength and resources availability probability, and increases with an increase in resources factor and resources transfer probability to interruption state. The adjustment cost of emergency rescue project increases with an increase in resources factor and resources transfer probability to interruption state, and decreases with an increase in resources strength and resources availability probability. The project resources waiting cost decreases with an increase in resources strength and resources availability probability, first increases and then decreases with an increase in resources factor, and increases with an increase in the resources transfer probability to interruption state. The increase in medical resources strength has a marginally decreasing effect on the adjustment cost of emergency rescue projects, the impact of resources waiting costs, and the total cost, and an increase in medical resources factors has a marginally decreasing effect on the total cost of projects. When the probability of medical resources usage transitioning to an interrupted state is low, the cost of project adjustment decreases with an increase in medical resources intensity and increases with an increase in medical resources factors. The resources waiting cost and total cost, first decrease and then increase with the increase in medical resources strength, and then increases and then decreases with an increase in medical resources factors. When the probability of interruption is moderate, the project adjustment cost, resources waiting cost, and total cost rapidly decrease as the intensity of medical resources increases. The cost of project adjustment increases rapidly with an increase in medical resources factors, and the waiting cost and total cost of resources also increase and tend to stabilize.
This paper can provide effective decision support for the reactive scheduling of emergency rescue project in reality. Firstly, in the process of emergency disposal, when the rescue activities are interrupted, the measure of gathering the existing resources to the activities of high importance can effectively reduce an increase in the project adjustment cost caused by an uncertain change in resources. Then, the optimal selection of different resources supply strategies can effectively reduce the possibility of interruption of rescue plan, which can improve the stability of plan implementation and reduce the total cost of emergency rescue project. Finally, resources dependence fluctuations make the supply of resources and the types of resources demand have a marginal decreasing effect on the emergency rescue cost. The project decision-maker should reasonably evaluate the degree of uncertainty, and arrange the combination and supply intensity of different types of resources in different periods, which can improve the efficiency of resources utilization and reduce the cost of project adjustment.

Key words: public health emergencies, reactive project scheduling, dynamic resource fluctuation, optimization model, tabu search algorithm

摘要： 医疗资源的稳定供给是突发公共卫生事件应急处置顺利执行的重要保障。本文考虑医疗资源动态变化特点,研究如何通过反应性调度对应急救援活动进行优化安排,最小化应急处置成本。首先,界定研究问题,构建医疗资源动态变化下的应急救援反应性调度优化模型;然后,根据问题NP-hard属性设计禁忌搜索算法,并提出两个改进措施提升算法搜索效率;最后,利用随机生成标准算例测试算法,并分析关键参数对应急救援成本的影响。结果表明:应急救援成本随着医疗资源强度和医疗资源可用量概率增大而下降,随着医疗资源因子和医疗资源转移到中断状态概率增大而上升。本研究为突发公共卫生事件应急救援过程中的资源利用与救援活动调度优化提供了有效的决策支持。

关键词: 公共卫生事件, 反应性项目调度, 资源动态变化, 优化模型, 禁忌搜索算法