A relaxation-based Voronoi diagram approach for equitable resource distribution

Abstract

This paper introduces a methodology designed to reduce cost, improve demand coverage, and ensure equitable vaccine distribution during the initial stages of the vaccination campaign when demand significantly exceeds supply. We formulate an enhanced maximum covering problem as a mixed integer linear program, aiming to minimize the total vaccine distribution cost while maximizing the allocation of vaccines to population blocks under equity constraints. Block-level census data are employed to define demand locations, identifying gender, age, and racial groups within each block using population data. A Lagrangian relaxation technique integrated with a modified Voronoi diagram is proposed to solve the location–allocation problem efficiently. Empirical case studies in Pennsylvania, using real-world data from the Centers for Disease Control and Prevention and health department websites, were conducted for the first 4 months of the COVID-19 vaccination campaign. Preliminary results show that the proposed solution algorithm effectively solves the problem, achieving a 5.92% reduction in total transportation cost and a 28.15% increase in demand coverage. Moreover, our model can reduce the deviation from equity to 0.07 (∼50% improvement).