Facility location and capacity planning for sampling and testing processes under demand uncertainty

Abstract

During an outbreak, nucleic acid testing is essential for early infection detection and virus transmission control. In this study, we aim to location and capacity planning of testing facilities, balancing minimal costs with maximum population coverage during public health emergencies. We propose a novel two-stage robust optimization model that addresses uncertainties in sampling demand during an epidemic, with distinct phases for sampling and testing. Applying this model to medium and high-risk areas in Beijing during COVID-19, we use the column-and-constraint generation (C&CG) algorithm and compare its performance with three meta-heuristic algorithms: Differential Evolution (DE), Genetic Algorithm (GA), and Simulated Annealing (SA). Our findings reveal that the C&CG algorithm reduces sampling costs by 31.10% compared to DE, 26.77% to GA, and 21.17% to SA. It also lowers testing costs by 7.48%, 79.79%, and 60.63%, respectively, and achieves a higher completion rate for sampling and testing volumes, ranging from 93.12% to 100%. In addition, C&CG outperforms the other algorithms in handling large sample sizes by 43.98% to 61.84%. Despite its longer computational time, C&CG is more efficient in cost reduction and demand satisfaction. Furthermore, we analyze the impact of uncertainty set parameters, including a unified value of the demand risk parameter, and assess different cases. The corresponding location and capacity solutions can offer decision support for emergency agencies managing public health crises.