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

TL;DR

This paper compares stochastic and robust optimization methods for resource distribution during disease outbreaks, focusing on balancing costs, demand coverage, and fairness amid spatiotemporal uncertainties, with applications to COVID-19 vaccine and test kit distribution.

Contribution

It introduces a comparative analysis of stochastic and distributionally robust optimization models for resource distribution under disease spread uncertainties, highlighting their trade-offs and practical implications.

Findings

DRO prioritizes worst-case demand coverage despite higher costs.

SP offers intermediate solutions balancing cost and demand coverage.

Both models outperform deterministic plans in uncertain scenarios.

Abstract

We consider the problem of optimizing locations of distribution centers (DCs) and plans for distributing resources such as test kits and vaccines, under spatiotemporal uncertainties of disease spread and demand for the resources. We aim to balance the 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, to compare SP and DRO models with a deterministic formulation using estimated demand and with the current resource distribution plans implemented in the US. 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. Our results further indicate that if the worst-case unmet demand is prioritized, then the DRO approach is preferred despite of its higher overall cost. Nevertheless, the SP approach can provide an intermediate plan under budgetary restrictions without significant compromises in demand coverage.