Abstract: Once a COVID-19 epidemic breaks out, regular nucleic acid testing becomes a major measure for epidemic prevention and control in various regions. Through regular nucleic acid testing, the government can effectively achieve the goal of “early detection, early reporting and early isolation” of infected persons and reduce the risk of epidemic transmission. Taking Suzhou City as an example, since the COVID-19 broke out in February 2022, the government fully launched normalized nucleic acid testing policy, requiring residents to undergo nucleic acid testing every 48 hours and present a test certificate before entering or leaving the community. However, due to the sudden onset of the epidemic, large sampling demand and lack of staff, it is easy to cause disorder in the sampling process if there is no reasonable sampling site location and personnel allocation plan in advance. In this situation, how to locate testing stations? How are residential areas allocated? How many “sampling booths” should be set up at each testing station? How to configure testing personnel and set their working hours? These are all decision-making issues faced by epidemic prevention and control departments.
Obviously, the optimal layout of testing stations belongs to the facility location problem. As a kind of classical combinatorial optimization problem, facility location problem has been widely concerned by scholars in the field of management science. However, the existing location models mainly focus on the p-median, p-center, set covering and maximum covering models, and they are mainly applied to the location of commercial facilities. At present, there is very little literature on the location of testing stations. Different from the traditional facility location model, thetesting station location not only has the common characteristics of traditional location-allocation problem but also needs to further determine service capacity (e.g., the number of testing booth in every testing station), optimize personnel allocation (e.g., how to allocate residents and doctors to every testing station?) and determine working hours(how many hours is each testing station open every day?). Therefore, according to the current policy of “dynamic zero clearing”, this paper proposes a new model of the nucleic acid sampling location problem to improve the sampling efficiency. Different from the traditional location-allocation problem, this model extends the traditional location-allocation problem, and further considers the optimization decisions of service capacity, staffing and working hours, as well as related constraints. The above problem is formulated as a nonlinear mixed integer model, which can be transformed into linear equivalence by adding variables and constraints.
Finally, the above linear equivalent model is solved by commercial software such as Cplex. In particular, in order to test how large a problem our solution method can solve in an acceptable time, we perform a grid test. The results show that: 1)As the problem size increases, the computational time continues to increase. The reason is that the expansion of the problem size leads to an increase in model constraints and variables, greatly increasing the computational time cost of the branch and bound algorithm in Cplex. 2)In a given time of 3,600 seconds, the largest problem we can solve with the Cplex software contains 525 nodes, which indicates that our model has certain applicability in real-world scenarios. Furthermore, our model is also applied to the nucleic acid sampling case of Shuangta Street in Suzhou City. The calculation results not only help the government obtain an optimal testing station location and personal allocation plan, but also verify the feasibility and effectiveness of our model.

Key words: COVID-19 epidemic, nucleic acid sampling, location, staffing, working time

摘要： COVID-19疫情背景下,常态化核酸检测可以有效实现感染者“早发现、早报告、早隔离”的目标,现已成为各地疫情防控的主要措施。通过核酸采样点布局优化,可以更好地提高核酸采样效率。首先,结合疫情防控实际要求提出一类全新的核酸采样点布局问题,其在传统“选址-分配”问题上,进一步集成考虑了采样点的服务能力、人员配置和工作时长等优化决策。其次,将该问题构建为一类非线性混合整数模型,进一步通过添加变量和约束的方法对其线性等价转换。再者,采用Cplex软件求解模型,进一步通过网格测试发现,在3600秒内最多可求解出包含525个节点的中等规模问题;最后,结合苏州市双塔街道核酸采样相关数据进行仿真分析,算例结果验证了模型的有效性。

关键词: COVID-19疫情, 核酸采样, 选址, 人员配置, 工作时长