  Speeding up testing and vaccination is essential to controlling the
coronavirus disease 2019 (COVID-19) pandemic that has became a global health
crisis. In this paper, we develop mathematical frameworks for optimizing
locations of distribution centers and plans for distributing resources such as
test kits and vaccines under spatiotemporal uncertainties of infection and
demand trends. We aim to balance between operational cost (including costs of
deploying facilities, shipping and storage) and quality of service (reflected
by delivery speed and demand coverage), while ensuring equity and fairness of
resource distribution based on historical infection data and demographics of
estimated demand. Using weighted multiple objectives, we formulate a stochastic
integer program and also seek robust solutions against the distributional
ambiguity of demand. For the latter, we propose a distributionally robust
optimization model using a moment ambiguity set, and derive monolithic
reformulations depending on specific forms of this set. We compare different
approaches by solving instances generated using real COVID-19 infection data
for distributing vaccines and test kits over the United States and the State of
Michigan, respectively. We demonstrate results over distinct phases of the
pandemic to estimate cost and speed of resource distribution depending on the
scales and coverage. approaches always outperform the deterministic one. If we
prioritize the worst-case performance in terms of unmet demand (i.e., untested
or unvaccinated people who qualify), then the distributionally robust approach
is preferred despite of its higher overall cost. Nevertheless, the stochastic
programming approach can provide an intermediate plan under budgetary
restrictions without significant compromises in demand coverage.
