A Multi-Period Spatial Optimization Model for Equal and Equitable Access in Emergency Logistics

Abstract

This study develops a multi-period location-allocation model for mobile Points of Distribution (PODs) to enhance both spatial equality and spatial equity in emergency relief distribution. Traditional fixed-site PODs often fail to ensure equitable access, particularly in low-density, underserved, or transportation-disadvantaged areas. To address these limitations, we propose a bi-objective mixed-integer linear programming model that determines optimal mobile POD placements and demand assignments across multiple time periods. The model simultaneously aims to (i) maximize population coverage within a defined travel distance threshold and (ii) minimize total travel burden by accounting for disparities in transportation access, such as vehicle ownership and income levels, across demand groups. The proposed model is validated using real-world data from Flint, Michigan, including road networks, demographics, and socioeconomic status. Compared to fixed-site PODs, our mobile POD strategy reduces average travel time by up to 59.03% and achieves full population coverage at 61.68% lower operational cost. Vulnerable communities, particularly those with limited transportation access, benefit the most from this approach. Our sensitivity analysis reveal that travel distance thresholds have a greater impact on accessibility than budget levels, highlighting the need for context-specific strategies reflecting the spatial and socioeconomic characteristics of each ward. Our results demonstrate that mobile PODs offer a scalable and policy-relevant solution for improving access to emergency supplies in disadvantaged areas. These findings underscore the importance of integrating both spatial equality and equity into disaster relief logistics and position mobile PODs as a viable strategy for strengthening community resilience in the face of increasing disaster risk.