The outbreak of coronavirus disease 2019 (COVID-19) has seriously affected the whole world, and epidemic research has attracted increasing amounts of scholarly attention. Critical facilities such as warehouses to store emergency supplies and testing or vaccination sites could help to control the spread of COVID-19. This paper focuses on how to locate the testing facilities to satisfy the varying demand, i.e., test kits, caused by pandemics. We propose a two-phase optimization framework to locate facilities and adjust capacity during large-scale emergencies. During the first phase, the initial prepositioning strategies are determined to meet predetermined fill-rate requirements using the sample average approximation formulation. We develop an online convex optimization-based Lagrangian relaxation approach to solve the problem. Specifically, to overcome the difficulty that all scenarios should be addressed simultaneously in each iteration, we adopt an online gradient descent algorithm, in which a near-optimal approximation for a given Lagrangian dual multiplier is constructed. During the second phase, the capacity to deal with varying demand is adjusted dynamically. To overcome the inaccuracy of long-term prediction, we design a dynamic allocation policy and adaptive dynamic allocation policy to adjust the policy to meet the varying demand with only one day's prediction. A comprehensive case study with the threat of COVID-19 is conducted. Numerical results have verified that the proposed two-phase framework is effective in meeting the varying demand caused by pandemics. Specifically, our adaptive policy can achieve a solution with only a 3.3% gap from the optimal solution with perfect information.
