A bi-level programming model for the location-allocation of medical testing facilities with cross infection risk during pandemics

The COVID-19 pandemic has placed unprecedented pressure on healthcare systems worldwide, emphasizing the critical need for timely identification and isolation of infected individuals during public health emergencies. However, when large-scale testing is poorly organized, it may inadvertently increase the risk of cross-infection by concentrating potentially infected individuals at testing sites. This study is among the first to investigate the location-allocation problem of medical testing facilities with a specific focus on minimizing cross-infection risk. To address this challenge, we develop a novel bi-level mathematical programming model that aims to minimize a comprehensive cross-infection risk index, which jointly considers the potential spread magnitude and congestion levels at testing sites. In this framework, the upper-level model determines the optimal locations for medical testing facilities, and the lower-level model characterizes individual travel behaviour through an equilibrium approach, thereby capturing the interaction between facility placement and population movement. To solve the proposed model efficiently, we design a hybrid algorithm that combines the genetic algorithm with the Frank–Wolfe algorithm, taking advantage of the respective strengths of metaheuristic and exact optimization methods. The effectiveness of the model and solution algorithm is demonstrated through a real-world case study in Beijing, China. The results show that strategic placement of testing facilities can facilitate more orderly testing participation and significantly mitigate the risk of cross-infection. Furthermore, sensitivity analyses on budget constraints, testing durations, and testing requirements provide valuable insights for policymakers in designing effective testing strategies.