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.

鉴于全球热浪的频率、持续时间和强度不断增加，需要对冷却棚的分配和运营进行更多研究，以有效缓解热量。为了满足这一需求，本研究考虑了一个使用穿梭巴士运送易受热人群的冷却避难所操作系统，并提出了用于决定冷却避难所和路线的最佳位置的多仓库位置路由问题 (LRP) 的二进制整数规划模型穿梭巴士的同时，目标是最大限度地降低总运营成本，以充分满足热脆弱人群的需求。由于 LRP 是 NP 难的，我们进一步展示了模拟退火以有效地得出一个接近最优的解决方案。然后，我们通过应用到大韩民国蔚山广域市的 14 个行政区来验证所提出的方法，以分配易受热影响的居民，并为他们提供前往相关冷却避难所的乘车服务。总体结果表明，与分别解决位置问题和路由问题的传统两阶段解决方案方法相比，所提出的方法具有竞争力。特别是，我们的结果表明，与两阶段解决方案方法相比，所提出的方法可以节省高达 49,000 美元的冷却棚位置路由问题。随后，对可能影响冷藏室运营有效性和效率的三个因素进行了敏感性分析：穿梭巴士容量、旅行费用和最大步行距离。我们的研究为政策制定者提供了建议，以针对他们的独特情况实施最佳的热缓解策略，并减少与热相关的疾病和死亡。