Abstract: Many epidemic outbreaks have occurred worldwide in recent years, which have not only seriously jeopardized people’s health and life safety, but also caused significant losses to the country’s economic and social development. Public health emergencies have become one of the most critical concerns of the public due to their suddenness, urgency, harmfulness and epidemic. The increase in large-scale epidemic outbreaks, for example, the COVID-19 epidemic, has significantly impacted society. The research on optimizing the siting of emergency facilities in the field of public health has gradually increased. However, much is on focused on the planning of the siting of medical institutions and the optimization of the emergency logistic network, and there is insufficient research on the siting of the testing institutions for large-scale epidemic outbreaks. Diagnostic testing is essential for controlling an epidemic, and nucleic acid testing, as a standard pathogen detection method, has been widely used in various outbreaks. In an outbreak, the scientific design of the site selection of nucleic acid testing facilities, the design of testing capacity and the distribution strategy of testing samples are crucial for curbing the spread of the virus. Therefore, this paper investigates the siting and capacity decision-making of nucleic acid testing facilities in large-scale outbreaks, intending to provide a reference for similar outbreaks that may occur in the future.
In this paper, we consider the location, capacity and allocation decisions for nucleic acid testing facilities in a region under the government’s provision of subsidized funding for nucleic acid testing capacity building in the event of an outbreak, including determining the capacity expansion plan for medical institutions with testing capacity and existing testing facilities, the location and capacity level of the additional testing facilities and the allocation of testing samples. It is assumed that (1)the location of nucleic acid sampling sites in the region and the number of samplers are known; (2)the location and initial testing capacity of healthcare facilities with nucleic acid testing capacity and existing nucleic acid testing facilities in the region are known; (3)the location of candidate additional nucleic acid testing facilities is known; (4)different mixing methods are used for different types of samplers; (5)samples collected at each sampling site can be allocated to multiple nucleic acid testing facilities for testing, and each nucleic acid testing facility can receive samples from multiple sampling sites for testing. The ultimate goal is to achieve the two objectives of minimizing government subsidy expenditure and minimizing time spent on nucleic acid testing.
A mixed integer programming model is developed to solve the problem. By introducing the cost preference weights of government subsidy expenditures and adopting the weighting method based on the membership function, the multi-objectives are transformed into a single objective for the solution. The solution is then performed using the Gurobi solver and the designed genetic algorithm. A capacity reduction step is added to the genetic algorithm to reduce the waste caused by excess capacity. Moreover, the fitness value calculation introduces a penalty function for violating the time constraint. We first verify the validity of the model and algorithm through numerical analysis. Then, we use the designed genetic algorithm to study the optimization problem of nucleic acid testing organization layout in 12 municipal districts of Chengdu with the background of the new coronary pneumonia epidemic. The information on nucleic acid testing sampling points and nucleic acid testing organizations in the region is obtained through the Health Commission of Chengdu. The layout of nucleic acid testing organizations in 12 municipal districts of Chengdu is finally given. The effects of different values of cost preference weights for government subsidy expenditures on the final cost are analyzed. With the gradual increase in cost preference weights, the government subsidy cost shows a decreasing trend, while the total testing time shows an increasing trend. Roughly, the results can correspond to the early, middle and late stages of a large-scale outbreak. In the future, decision-makers can choose different weighting schemes for various periods. In addition, the influence of time limits and government budgets on the results is also analyzed.
There are some shortcomings in this paper. Although we have identified issues such as the expansion of existing nucleic acid testing facilities, the location of additional nucleic acid testing facilities and the allocation of sampling points, we have only investigated the optimization of the layout of a single cycle in various parameter determination scenarios. In the case of an actual outbreak, data such as the number of people sampled at a sampling point is constantly changing. Therefore, future research can further explore the problem of optimizing the layout of multi-period dynamic nucleic acid testing facilities under the uncertainty of the sampling population to better adapt to the complex reality.

Key words: epidemic outbreak, nucleic acid testing, site selection, genetic algorithm

摘要： 诊断检测是控制突发疫情的重要环节。本文考虑大规模突发疫情爆发时,在政府提供核酸检测能力建设补助资金的情况下对核酸检测机构进行选址定容,包括确定对具有检测能力的医疗机构和现存检测机构的容量扩展方案,新增检测机构的位置和容量水平以及检测样本的送检方案。以实现政府补助资金支出最小化和核酸检测总时间最短为目标,建立了一种混合整数规划模型,通过引入政府补助支出成本偏好权重,采取基于隶属度函数的加权方法将多目标转化为单目标,然后使用Gurobi求解器和设计的遗传算法进行求解。通过数值分析验证了模型和算法的有效性,以新冠疫情期间成都市核酸检测机构布局优化问题进行了实例验证。最后,讨论分析了政府补助资金支出成本偏好权重取值、检测时间上限以及政府预算变化对结果的影响,以期为大规模疫情检测提供参考。

关键词: 突发疫情, 核酸检测, 选址, 遗传算法