  We study the allocative challenges that governmental and nonprofit
organizations face when tasked with equitable and efficient rationing of a
social good among agents whose needs (demands) realize sequentially and are
possibly correlated. As one example, early in the COVID-19 pandemic, the
Federal Emergency Management Agency faced overwhelming, temporally scattered, a
priori uncertain, and correlated demands for medical supplies from different
states. In such contexts, social planners aim to maximize the minimum fill rate
across sequentially arriving agents, where each agent's fill rate is determined
by an irrevocable, one-time allocation. For an arbitrarily correlated sequence
of demands, we establish upper bounds on the expected minimum fill rate
(ex-post fairness) and the minimum expected fill rate (ex-ante fairness)
achievable by any policy. Our upper bounds are parameterized by the number of
agents and the expected demand-to-supply ratio, yet we design a simple adaptive
policy called projected proportional allocation (PPA) that simultaneously
achieves matching lower bounds for both objectives (ex-post and ex-ante
fairness), for any set of parameters. Our PPA policy is transparent and easy to
implement, as it does not rely on distributional information beyond the first
conditional moments. Despite its simplicity, we demonstrate that the PPA policy
provides significant improvement over the canonical class of non-adaptive
target-fill-rate policies. We complement our theoretical developments with a
numerical study motivated by the rationing of COVID-19 medical supplies based
on a standard SEIR modeling approach that is commonly used to forecast pandemic
trajectories. In such a setting, our PPA policy significantly outperforms its
theoretical guarantee as well as the optimal target-fill-rate policy.
