Interpretable Vaccine Administration and Inventory Replenishment Policies via Smooth-in-Expectation Decision Rules

The effective management of vaccine administration and inventory is critical for achieving widespread immunization coverage, yet developing policies that are both optimal and interpretable remains a significant challenge. We address this by proposing a novel, flexible multistage stochastic programming model that handles realistic operational complexities like patient queueing and early clinic closures. To overcome the black-box nature of typical solutions, we employ smooth-in-expectation decision rules—a first-of-its-kind application, also extended to handle integer first-stage decisions—to generate interpretable policies as intuitive flowcharts. Our solution algorithm combines batch stochastic gradient descent with a rounding heuristic and is warm-started by our novel two-stage stochastic program, which also provides a strong lower bound and is orders of magnitude faster than comparable models. Numerical experiments demonstrate our flowchart policies are near-optimal, while our Pareto frontier analysis offers practical insights into policy trade-offs.