Optimal cooling shelter assignment during heat waves using real-time mobile-based floating population data

Highlights

• Real-time floating population data and temperature-humidity index are used.

• Demands are categorized and prioritized based on heat vulnerability index.

• A mathematical model is proposed to allocate cooling shelters during heat waves.

• Two conflicting objectives: maximize demand coverage and minimize operating cost.

• We apply the proposed model and conduct sensitivity analysis in Ulsan, Korea.

Abstract

As the frequency, duration, and intensity of heat waves have been increasing in recent decades, the effective and efficient allocation of cooling shelters has become a significant issue in many cities. This study presents an integer programming model for allocating cooling shelters with the two conflicting objectives of maximizing coverage for the heat-vulnerable population and minimizing total operating cost of the cooling shelters. The temperature-humidity index is included in the model to reflect the weather conditions that affect heat waves. We also introduce data analysis procedures using real-time floating population data so as to track the hourly number and locations of individuals in the heat-vulnerable population. The proposed model is then validated with an application to Ulsan Metropolitan City in the Republic of Korea in which heat-vulnerable people are assigned to existing and potential cooling shelters. Given the condition of restricted budgets, we categorize and prioritize heat-vulnerable people into several groups using a clustering method and heat vulnerability index, and we suggest effective policy recommendations, so the most vulnerable people are provided cooling services first. In addition, we perform a sensitivity analysis on weather conditions, travel distance, electricity cost, and percentage of heat-vulnerable population served by cooling shelters, so policy makers can be prepared to respond quickly to the various factors that can change during a heat wave and ultimately reduce heat-related morbidity and mortality.

Introduction

According to the fifth synthesis report by the Intergovernmental Panel on Climate Change (IPCC), the last three decades have experienced the greatest increase in the Earth's surface temperature since 1850 (IPCC, 2014; IPCC, 2019). As a result of this increasing temperature, heat waves have become more intense and are one of the most dangerous atmospheric risks, causing significant heat-related morbidity and mortality across the globe (Anderson and Bell, 2011; Bradford et al., 2015; O'Neill and Ebi, 2009). For example, in the Republic of Korea, heat waves have been increasing in terms of their intensity and duration and are projected to occur with higher frequency in the future, as shown in Fig. 1.

To cope with this natural disaster, local governments and communities have made economic investments in establishing policies and devising plans for emergency response and adaptation and hazard mitigation, including cool roofs, cool pavements, and urban forestry (U.S. Environmental Protection Agency, 2013; Li et al., 2014; Middel et al., 2015). Cooling shelters have been demonstrated to be an effective solution in alleviating the impacts of heat waves for heat-vulnerable people (Centers for Disease Control and Prevention, 2012; Widerynski et al., 2017). However, there are several challenges associated with cooling shelters, including optimizing their number, location, and accessibility (Ahn and Chae, 2018; Berisha et al., 2017; Nayak et al., 2019). For instance, in the Republic of Korea, local governments have operated cooling shelters for heat-vulnerable people every summer since 2006. Since then, the number of cooling shelters across the country has gradually increased and totaled around 4,700 in 2019. Despite the increasing number of cooling shelters available, the Korea Disease Control and Prevention Agency (KDCA) predicts the number of heat-related patients will continue to increase, as shown in Fig. 2. To better prepare for future extreme heat events, it is essential to make more efficient use of existing cooling shelters and to determine additional locations for potential cooling shelters.

To effectively and efficiently resolve the issues above, spatial optimization problems can be applied. In the last decade, spatial optimization problems have been further extended and applied to a variety of service industries, such as determining the location of shelters and emergency medical supplies (Berman et al., 2013; Kim et al., 2021; Murali et al., 2012); multi-depot emergency facilities location-routing planning (Zhang et al., 2018); nonemergency healthcare, such as searching for the possible location of hospitals, organ transplant centers, and medical screening facilities (Beliën et al., 2013; Guerriero et al., 2016; Mestre et al., 2012; Ratick et al., 2016); transportation systems, such as locating fueling/charging stations for alternative-fuel vehicles (Abbaas and Ventura, 2021; Hwang et al., 2015, Hwang et al., 2017, Hwang et al., 2020, Hwang et al., 2021; Kweon et al., 2017; Ventura et al., 2015, Ventura et al., 2017), to name a few. Spatial optimization problems have been similarly applied to explore potential locations for cooling shelters to optimize the public health response to extreme heat. More recently, Bradford et al. (2015) investigated the factors that mainly contribute to heat vulnerability and searched for the potential location for additional cooling shelters. To address these concerns in Pittsburgh, Pennsylvania, they used population information from the 2010 U.S. census, ArcGIS geospatial modeling, and statistical analysis. Similarly, Fraser et al. (2018) presented an iterative heuristic method of the maximal covering location problem to deploy cooling center facilities that improve access for people who are more vulnerable to heat waves and without access to other alternatives. To this end, they generated random points within each census tract for every 100 residents in Los Angeles County, California and Maricopa County, Arizona from the 2010 U.S. census data.

In contrast to the papers searching for the potential locations of cooling shelters, some researchers have focused on factors related to the heat-vulnerable population. Cutter et al. (2008) defined a conceptual model for hazard vulnerability with three components: environmental exposure, physical sensitivity of the population to that exposure, and adaptive capacity of the population to actively cope with the exposure. A number of heat vulnerability indexes (HVI) have been developed based on Cutter et al.'s (2008) model. For example, Reid et al. (2009) utilized 10 vulnerability variables (e.g., vegetation, age, social isolation, poverty, education) and computed an HVI using factor analysis techniques, including principal components analysis. A large number of studies (e.g., Harlan et al., 2013; Mallen et al., 2019; Nayak et al., 2018; Wolf and McGregor, 2013) have applied similar techniques and used similar variables to derive an HVI as well as map various regions.

The research in this area has focused on factors related to existing cooling shelters, heat vulnerability of people, and the potential location of cooling shelters. This research primarily relied on census data, which are less accurate in identifying the distribution of heat-vulnerable residents due to (1) data gaps that are common in traditional collection methods, such as door-to-door surveys and national census counts; (2) limitations associated with large-scale government data collection efforts, which are expensive and too infrequent to measure demographics in highly spread out populations; and (3) changes in population densities, which lead to different sized census blocks depending on the region (i.e., the size of a census block is determined by the population density of an area, and as a result, rural areas with lower population density have larger census blocks than urban areas, which makes it hard to estimate the exact locations of the heat-vulnerable population). With the development of information and communications technology and big data, people are now increasingly involved in producing a new type of data that is useful for spatial analysis. This study extends the previous research by incorporating new methods for massive real-time floating population data collection, integration, and analysis in spatially explicit formats. Floating population is defined as “population movements that do not involve a change in household registration” by Goodkind and West (2002) and can be acquired through mobile phones in real-time. As Fig. 3 and Fig. 4 present, the floating population data reflects the real-time population movement based on the constant grid-cell unit, while the census data only shows the static population of each census block at a fixed time point. Therefore, we utilize the mobile phone-based floating population data to track the hourly locations of mobile phone users and resolve the less-accurate data issue produced by using census data.

Also, while previous studies commonly used ArcMap's location-allocation tool that relies on its own heuristic and thus does not guarantee an optimal solution (Bradford et al., 2015; Fraser et al., 2018), we formulated and solved a bi-objective integer programming model to find optimal allocation strategies for existing and potential cooling shelters considering both a temperature-humidity index (THI) and HVI. This is another distinction that can contribute to the literature. The proposed model is then validated with an application to Ulsan Metropolitan City (hereinafter referred to as Ulsan), the industrial capital of the Republic of Korea, and derives the numbers, locations, and assignment results for both existing and potential cooling shelters under a variety of cases. We also suggest a method that categorizes and prioritizes heat-vulnerable populations to provide cooling services to those most in need. Applying our proposed optimization model to a sensitivity analysis is another interesting part of this study and further quantifies the impact of a variety of factors that can change during a heat wave and impact the allocation and operations of cooling shelters.

Through this study we aim to suggest systematic and comprehensive solutions to ensure efficient use of government resources and effective protection of the heat-vulnerable population during heat waves. The results of this study can be used as guidance in the future operations of cooling shelters by federal and local governments and ultimately contribute to a decline in heat-related mortality and morbidity.

The remainder of this article is organized as follows. Section 2 presents a formulation of the cooling shelter location-allocation problem during heat waves, with the bi-objectives of maximizing coverage of heat-vulnerable people and minimizing total operating cost. Also, to provide phased cooling services, we propose a method for categorizing and prioritizing the heat-vulnerable people using a clustering method, as well as a priority-based model. To validate the proposed models, Section 3 introduces the case study of Ulsan in the Republic of Korea, which is experiencing a heat wave crisis, and describes the data preprocessing techniques of the relevant data, including 2018 floating population data, cooling shelter data, and geographic data of the study areas. Using the proposed models and methodologies, as well as the preprocessed data from previous sections, in Section 4 we apply the proposed model to the case study and analyze the results. Furthermore, to quantify the impact of a variety of factors that can change during a heat wave and affect the allocation and operations of cooling shelters, a sensitivity analysis for various criteria is also presented. Lastly, in Section 5 we draw conclusions and provide effective policy recommendations for federal and local governments regarding the number, location, and allocation of cooling shelters for various heat wave situations in order to ultimately reduce heat-related morbidity and mortality.