The location routing problem for cooling shelters during heat waves

Abstract

Given the increasing frequency, duration, and intensity of heat waves around the globe, more research is needed on the allocation and operations of cooling shelters for efficient heat mitigation. To address this need, this study considers a cooling shelter operating system that uses shuttle buses to transport heat-vulnerable people and presents a binary integer programming model for the multi-depot location routing problem (LRP) that decides optimal locations of cooling shelters and routes of shuttle buses simultaneously with the objective of minimizing the total operating cost for full accommodation of the heat-vulnerable population. Since the LRP is NP-hard, we further present the simulated annealing to efficiently derive a near-optimal solution. We then validate the proposed methodology with an application to the 14 administrative regions of Ulsan Metropolitan City in the Republic of Korea to assign heat-vulnerable residents and provide them with ride services to the associated cooling shelters. The overall results demonstrate the proposed methodology's competitive performance compared with the traditional two-phased solution approach that separately solves the location problem and routing problem. In particular, our results show that the proposed methodology can save up to 49,000 USD in addressing the cooling shelter location routing problem compared to the two-phased solution approach. Subsequently, a sensitivity analysis is conducted regarding three factors that are likely to impact the effectiveness and efficiency of cooling shelter operations: shuttle bus capacity, traveling cost, and maximum walking distance. Our research provides recommendations for policymakers to carry out the best heat mitigation strategy for their unique circumstances and reduce heat-related illness and death.