Resource Distribution Under Spatiotemporal Uncertainty of Disease Spread: Stochastic versus Robust Approaches

Speeding up testing and vaccination is essential for controlling the coronavirus disease 2019 (COVID-19) pandemic. We develop mathematical frameworks for optimizing locations of distribution centers DCs and plans for distributing resources such as test kits and vaccines, under spatiotemporal uncertainties of disease infections and demand for the resources. We aim to balance operational cost (including costs of deploying facilities, shipping, and storage) and quality of service (reflected by demand coverage), while ensuring equity and fairness of resource distribution across multiple populations. We compare a sample-based stochastic programming (SP) approach with a distributionally robust optimization (DRO) approach using a moment-based ambiguity set. Numerical studies are conducted on instances of distributing COVID-19 vaccines in the United States and test kits in Michigan, to compare SP and DRO with a deterministic model using demand estimates and with the current resource distribution implemented in the real world. We demonstrate the results over distinct phases of the pandemic to estimate the cost and speed of resource distribution depending on scale and coverage, and show the ``demand-driven'' properties of the SP and DRO solutions.