A distributionally robust optimisation for COVID-19 testing facility territory design and capacity planning

COVID-19 has been a severe crisis for global health, which caused significant loss of life and property. One of the most effective ways to prevent the spread of the virus during an epidemic is to provide nucleic-acid tests for the population. Management of testing resources is both critical and challenging because outbreaks are irregular and resources are scarce. In this study, we develop a decision support tool for city governments by districting testing facilities and determining their capacities. Considering the stochastic testing demand during a disease outbreak, a set-partitioning model embedded with a two-stage distributionally robust optimisation is formulated. Tractable reformulations are derived to solve the problems efficiently and a conservative approximation method is introduced to achieve acceptable accuracy while reducing the computational burden. Compared with different benchmark models, the numerical analyses demonstrate the effectiveness of the proposed territory design, which realises a robust testing infrastructure network and saves the cost while pursuing capability.