Hierarchical siting of macro fire station and micro fire station

Abstract

With the rapid increase of city building density, public emergency service system for providing fire services faces increasing challenge in reducing the loss of lives and property, especially for the reduction of massive casualties in fire accidents. For obtaining a higher benefit from public service facilities, GIS-based techniques such as location optimization are commonly used. However, as a special facility, fire emergency facilities are quite particular in siting and providing services, and they have their unique demands including specific response time, benefit maximization, workload balancing and cost minimization; traditional optimization methods for fire facility siting are difficult to account for all of these objectives. Furthermore, the public emergency services agencies in China are implementing a plan to establish a hierarchical fire service system by siting fire stations with different capacities, and under this context, the general covering models with the same level of facilities are limited in their effectiveness. Therefore, this paper proposes a hierarchical covering model which takes into account the different characteristics of different levels of fire facilities (i.e. macro fire station and micro fire station). The case study of Nanjing city proves that our model is effective in practical applications of emergency services optimization.

Keywords

Built environment emergency facilities covering model fire station

Introduction

China’s cities have enjoyed over 30 years of fast growth, but their further development faces energy, sustainability and public safety constraints. The dense buildings and expanding urban areas make the emergency events occur more frequently and widely, leading to the increasing demands of public emergency services in cities (Dong et al., 2018). Compared to the dynamic change of emergency service demands, most of the relevant supplies have remained unchanged since they were installed many years ago. The current supply of emergency facilities is hard to meet the growing demand for urban emergency services (Farahani et al., 2019). Thus, strengthening the ability of emergency management and establishing an urban emergency response system have become an urgent issue in the current urban management.

Generally, there are two main parts in the urban emergency response system including safety planning and emergency management. The former is to prevent the occurrence of accidents from the source, and has the prospective and initiative; the latter involves the process of reducing the impact of accident, with the immediacy and passivity (Chen, 2009). As the essential link between the two parts, emergency facilities (e.g. shelters, fire facilities and hospitals) have onerous responsibilities to provide public emergency services in large-scale urban environment and need to be optimally allocated and distributed to improve the effectiveness and efficiency of services (Paul et al., 2017).

As a vital emergency facility, fire control construction (e.g. fire station, fire communication facilities, and water supply facilities) has been recognized as one of the standards to measure the modernization and civilization of a city (Chevalier et al., 2012; Yao et al., 2019). With the rapid increase of high-rise buildings, densely populated areas, inflammable and explosive units and other high-risk places, the fire security and stability of urban environments are facing great challenges (Wuschke et al., 2013). Specifically, the fire stations (squadrons) that undertake the main fire safety works usually lack the reasonable planning of location and function in China’s cities. For example, most of the responsibility areas of fire stations are simply divided according to administrative division, which could lead to the unbalanced workload problem and bring great difficulties to fire rescue. Besides, considering the increasing population and intensive land utilization, the volume of current fire management infrastructure is insufficient, and there is a huge gap between fire service supplies and demands (Chen, 2009). In recent years, a lot of research works have been carried out on how to improve the efficiency of emergency facility services from the above aspects (e.g. dividing service areas of facilities) (Chen et al., 2019). Among them, the core issue is to optimize the location of fire stations.

With different objectives, many different location models are developed in the literature, e.g. $p$ ‐median problem (PMP), $p$ ‐center problem (PCP) and covering location problems (e.g. location set covering problem (LSCP) and maximal covering location problem (MCLP) (Church and ReVelle, 1976). However, all these models are designed for general purpose use, while the locational efficiency of fire emergency facilities is constrained by the following specific aspects:

Response time. For fire emergency facilities, the speed of emergency response determines the quality of service to a great extent (Murray, 2013). The Chinese government has set a specific constraint for response time of fire stations. More specifically, after receiving call order, the fire squadron should reach the location of fire incident within 5 minutes, which contains 1 minute to prepare and 4 minutes to drive to the destination. To meet this constraint, fire stations should be located near to fire high-risk places.

Maximum benefits. The benefits of fire emergency services are reflected in the protection of lives and property in accidents.

Balanced workload. Fire risk varies across space, and a reasonable plan should locate more fire stations in the relative high-risk areas. It is believed that the constraint of balanced workload can help improve the efficiency of the whole emergency response system.

Minimum cost. More new fire facilities can help reduce the risk of fire accidents, while this process is also constrained by cost budget. Generally, fire stations are established and operated with no profit in China. Considering the limited land space in urban environments, site selection of fire stations should take the minimum cost to play the largest role (Murray et al., 2012).

The first two factors (i.e. response time and maximum benefits) have been taken into account by most studies on emergency facilities siting. They suggest to use fixed service distance instead of varied service distance to build location models such as MCLP and LSCP. For example, Schilling et al. (1980) propose to use MCLP to maximize the coverage areas of fire rescue facilities. Yao et al. (2019) constructed LSCP to ensure the full coverage of historical fire incidents.

Furthermore, the two latter factors, balanced workload and minimum cost, are also important supports for the long-term and stable operation of a fire service system. However, considering the varied fire risk in urban environments, it is hard to obtain a balanced workload only through optimizing existing fire stations. Another potential way would be for the government to consume more land resources for building new fire stations (Chevalier et al., 2012; Dong et al., 2018). However, such a solution is costly within the limited public land space, especially in the well-developed cities such as Nanjing and Beijing. Therefore, the Chinese government recently puts forward a new strategy that aims at establishing a set of micro fire stations to serve the local communities and important units. Compared to the existing macro fire stations, the micro fire stations do not need additional large-size public space and associated buildings. They are usually attached to the existing community offices. Therefore, micro fire stations have low cost, and with close distance to communities, they are able to participate in fire control quickly. In this regard, micro fire station is an effective supplement to existing macro fire station, and it helps form a hierarchical functional system of public fire emergency services.

In addition to fire service, many public emergency services are organized as a hierarchical system, e.g. public healthcare facilities system (Ma et al., 2019). Thus, establishing a hierarchical location model is particularly useful in related applications. It should be noted that, compared to existing single-level location problems, our hierarchical location problem has the following two main particular objectives:

Macro fire station siting. As the main executive of fire rescue, high-level fire station (i.e. macro fire station) takes responsibility for ensuring fire safety in large-scale urban areas. Considering that adding new macro fire stations is costly, our model proposes to optimize the locations of existing fire stations to obtain a maximum coverage area. In this process, macro fire station provides its services within 4 minutes across large-scale urban areas according to risk variation.

Micro fire station siting. Second-level fire station (i.e. micro fire station) has clear restrictions on where they can be set up and who they should serve. The response time of micro fire station is set at 3 minutes. These characteristics are different from high-level fire station. Since micro fire station has low cost, our model focus on the covering of all the fire demands with the minimum amount of suppliers. It should be noted that regarding the micro fire station, its demand units correspond to local communities and associated fire risk.

Hierarchical location model

In this section, a hierarchical model is proposed to optimize both the locations of macro fire stations (fire squadrons) and micro fire stations, so as to make the whole fire management system more reasonable. More specifically, according to the different requirements of the two types of fire stations, MCLP is selected to solve the site selection of macro fire stations (i.e. the first level of our model), and LSCP is selected to solve the site selection of micro fire stations (i.e. the second level of our model). The two are then combined together to constitute the hierarchical model of fire emergency services. The detailed data including the community-related data (i.e., building age data, residential population data and community spatial data) and fire incident data are introduced to solve the proposed hierarchical location problem (please see Supplementary Figure 2). The next two sections will describe the two levels of the location model in detail.

Location model for macro fire station

Generally, establishing a new macro fire station requires a lot of manpower, material and financial resources, especially in the well-developed urban areas. Thus, under our context, it is better to optimize the effectiveness of public fire emergency service system with no new macro fire stations added. In other words, in the first level of our model, we need to improve the locational efficiency of fire emergency facilities by seeking new sites for existing fire stations. More specifically, this problem can be solved with the MCLP model, which aims at covering the maximum demands through reasonable location for a given number $p$ of facilities.

In our model, the plane for siting macro fire stations is considered as a continuous area. Since the objective of MCLP is to cover the maximum demands in such plane, analyzing the spatial variation of fire rescuing demands is essential to the fire stations’ siting. In general, we can use the fire risk to model demands in fire services, and a reasonable location of fire facility should cover as many high-risk places as possible. Compared to the micro fire stations that mainly serve the communities, the macro fire stations account for the demands across all the places, and thus our method uses the historical fire incidents point data to estimate the actual fire risk variations across space. Furthermore, considering that fire risk decreases with the increase of distance to the fire incident points, we propose to use the kernel density method to estimate the smooth surface of fire risk from fire incident points. In this way, the distribution of fire service demands can be accurately estimated. For convenience of calculation, the original continuous plane is divided into a square grid, in which the center point of each cell is used as a facility candidate location point.

The notations related to our model are presented as following:

$i$ = index of demand points

$j$ = index of potential facility locations

$a_{i} =$ the demand value at node $i$

$η_{i} =$ {set of potential facilities capable of covering/serving demand $i$ }

$η_{j} =$ {set of demand that can be covered by potential facilities $j$ }

$p$ = number of facilities to be located

$X_{j}$ = $\{\begin{array}{l} 1 i f p o t e n t i a l f a c i l i t y j i s s i t e d \\ 0 o t h e r w i s e \end{array}$

$Y_{i}$ = $\{\begin{array}{l} 1 i f d e m a n d i i s s u i t a b l y c o v e r e d / s e r v e d \\ 0 o t h e r w i s e \end{array}$

$η_{i}$ and $η_{j}$ are usually determined using a Euclidean distance threshold $R$ . A larger value of R means that macro fire stations can serve a larger urban area; in this respect, we should determine the value of R according to the prior knowledge of practical applications. More specifically, under our context, we first calculate the average speed of fire trucks and then introduce the constraint of response time of fire rescuing set by Chinese government to determine the threshold R of service area of macro fire stations (please see ‘Experiment and analysis’ section). In this way, the service area is more consistent with the actual condition. If $d_{i j}$ is the distance between demand $i$ and potential facility $j$ , the cover sets $η_{i}$ and $η_{j}$ can be formalized as $η_{i} = \{j| d_{i j} \leq R\}$ , $η_{j} = \{i| d_{i j} \leq R\}$ . Then the detailed model (i.e. MCLP) for macro fire stations siting is as follows

$Maximize$

\sum_{i} a_{i} Y_{i}

(1)

Subject t o

\sum_{j \in η_{i}} X_{j} \geq Y_{i} \forall i

(2)

\sum_{j} X_{j} = p

(3)

\begin{array}{l} X_{j} = \{0, 1\} \forall j \\ Y_{i} = \{0, 1\} \forall i \end{array}

(4)

The objective is to maximize the total demand covered by macro fire stations. Constraints (2) determine whether the demand i is covered by fire facilities. Constraint (3) specifies the number of fire facilities to be located. Finally, integer requirements are imposed in Constrains (4). The MCLP model emphasizes the prioritization of fire management resources through optimizing services according to the spatial intensity of fire risk. Specifically, with a limited number of macro fire stations, our model can improve the locational efficiency of fire services.

Location model for micro fire station

For China’s fire emergency service system, the second-level fire station is micro volunteer fire station which aims at serving all the communities in urban areas. Compared to the macro fire station, micro fire station has the advantages of low cost, small footprint and high efficiency. Thus, considering the limitation of large public space in well-developed cities, we can establish a sub-system of second-level fire services from micro fire stations to fill the gap left by limited number of macro fire stations. Specifically, in our model, the number of micro fire stations is not specified and the objective is to cover all the local demands using the minimum number of micro fire stations. Since the proposed model mainly focuses on the local regions (i.e. communities), the demand can be defined from the characteristics of communities related to fire risk, e.g. building age and population size in each community (please see ‘Experiment and analysis’ section). In addition, according to the requirement of China’s government, the potential location of micro fire stations also needs to be within communities. Therefore, the locational efficiency of micro fire stations should be evaluated from the perspective of local fire emergency service of communities.

Based on the abovementioned factors, LSCP model best fits the problem of micro fire stations siting in our hierarchical system. We use the central points of all the community polygons as demands and candidate micro fire station locations. The detail of the proposed model is as follows.

$Minimize$

\sum_{j} X_{j}

(5)

Subject t o

\sum_{j \in η_{i}} X_{j} \geq 1 \forall i

(6)

X_{j} = \{0, 1\} \forall j

(7)

η_{j} \leq s \forall i

(8)

The objective (5) is to minimize the number of micro fire stations to be located. Constraints (6) ensure that each demand point is covered by at least one micro fire station point. Constraint (7) limits the decision variable $X_{j}$ to be an integer value. Constraint (8) is related to the workload limit s of micro fire stations.

Among various existing applications of the traditional LSCP model, a basic underlying assumption is that the facilities to be sited are without workload limited (i.e. Constraint (8)). Under this assumption, the demands will be met as long as they are within the service coverage standard of any facility. However, it could also limit the application of coverage models. Many service facilities have limited workload to ensure acceptable levels of service and spatial equity (Liao and Guo, 2008; Yin and Mu, 2012). An example is presented in Supplementary Figure 3. When the service distance is set to a fixed value (e.g. 1400 m), the micro fire stations tend to have different workloads (Supplementary Figure 3(a)). Specifically, the left micro fire station needs to cover much more demands than the right one does. In the real world, due to the issue of personnel and equipment, the micro volunteer fire stations usually have workload limitation. Therefore, we propose to use the LSCP with capacitated micro fire stations (Constraint (8)) to solve the location problem of micro fire stations. As presented in Supplementary Figure 3(b), this constrained model can help to balance the workloads of micro fire stations, and improve the fairness and efficiency of the whole service system. Please see Supplementary file for our implementation.

Experiment and analysis

Study area

The research area is located in the center of Nanjing, China (Figure 1). Nanjing is one of the megalopolises in the Yangtze delta of east China. According to the Nanjing Municipal Bureau Statistics, the average population density of Nanjing in 2015 is about 1250 people per square kilometer (NMBS, 2016). Such a high density of population brings great pressure to fire risk prevention in Nanjing, and there is urgent need to improve the urban fire emergency services. Our experiments obtain the fire station points data (Figure 1) and the fire risk data (Supplementary Figure 4) from the Fire Department of Public Security of Nanjing. Specifically, the fire risk for macro fire stations is related to the historical fire event points across the whole city from 2013 to 2015 (Supplementary Figure 4(a)), and that for micro fire stations is related to the community properties including building age (Supplementary Figure 4(b)) and resident population size (Supplementary Figure 4(c)). There are a total of 8595 historical fire incident points, 24 existing fire stations and 3891 communities. In the case study, the hierarchical model is used to re-plan the locations of existing macro fire stations and at the same time to determine the effective locations for new micro fire stations. In order to provide an applicable choice for urban management department, the actual data of fire incidents and communities are used to estimate fire risk variations across space.

Figure 1.

The study area and the distribution of existing fire stations.

Siting of macro fire stations

First, from the historical fire incident points, we used kernel density method to estimate the spatial variation of fire risk across the whole city, as presented in Supplementary Figure 5. It can be observed that the high-risk areas are located in the center and eastern parts of the city. Then, we used 4 minutes as the coverage threshold of macro fire stations. From the track data of fire engines of Nanjing, we calculate that the average speed of fire engines is about 32 km/h. Thus, we can take the circular buffer with 2133-m radius as the service area of macro fire stations. The first observation from Supplementary Figure 5(a) is that the existing macro fire stations do not cover all the areas with high fire risk. The distribution of these fire stations is unbalanced and crowded in the central areas. In this respect, many places in the city have to take the risk of needing longer time than that specified by the government to get fire rescuing from neighboring fire stations. In emergency events, this could lead to larger damages and more deaths. In addition, there are some fire stations located in the eastern areas, which have few workloads. This could lead to a great waste of public emergency service resources. Therefore, the first level of our hierarchical model is to re-site the existing fire stations without new established macro fire stations. In this way, the government does not have to increase the size of land space for macro fire stations. As presented in Supplementary Figure 5(b), the new distribution of macro fire stations is more balanced, which can help to improve the locational efficiency of public fire emergency facilities.

As presented in Supplementary Figure 5, we classified the fire risks into four levels. If we treat the areas with fire risk equal to or larger than Level 2 as high-risk area (i.e. 1570 cells), our calculated result is able to cover more high-risk cells. Specifically, compared to 926 high-risk cells that the existing fire stations can cover, our calculated fire station sites can serve 1208 high-risk cells. That is, the existing macro fire stations can only cover 58.98% of fire-risk cells, while the coverage ratio of the calculated result can reach 76.94%. Thus, the new fire station sites are arranged more neatly and effectively. In the real world, such increase of fire risk area coverage would also affect the safety management of the city.

In addition, the location optimization would have a large impact on the number of fire incident points covered (Supplementary Figure 6(a)) and the total area of cells covered (Supplementary Figure 6(b)). The proposed method also reduced the overlapping effects including the total number of fire incident points that are covered repeatedly (Supplementary Figure 7(a)) and the total area of cells that are covered repeatedly (Supplementary Figure 7(b)). With limited resources, our location method would enable each fire station to fully play its role and improve the fire rescuing service of the whole system. Besides, for each station, we take the sum of fire incident points that can be served in an effective manner (that is the demand point can be arrived from fire station within 4 minutes) as its workload, and then calculate the mean square error to measure the workload balance of facilities. As presented in Supplementary Figure 8, compared to the mean square error of the existing fire stations, our result is smaller, which means that our method is able to generate a more balanced workload for macro fire stations.

Then, we assigned each fire incident point to its nearest macro fire station (Supplementary Figure 9(a) and (b)). In this way, we can evaluate the effectiveness of location model from the perspective of travel cost. Besides, we calculated the sum of the service distances from all the fire incident points to their corresponding nearest fire stations, as presented in Supplementary Figure 9(c). Service distance that often represents the efficiency of fire rescuing is the intuitive consideration of evaluating emergency services. The smaller the travel distance, the better the service provided by facilities. From Supplementary Figure 9(c), it can be observed that the new location result could greatly shorten the overall distance and improve the rescuing efficiency for the whole city. Nevertheless, our method could also lead to the concentration of fire stations in some local areas with high fire risk and that makes some remote places are difficult to receive fire services. For example, the red lines in Supplementary Figure 9(a) and (b) represent the longest service distance in the entire region. We can observe that some places still lack the effective fire services from neighboring macro fire stations. Actually, in the first level of our hierarchical system, the MCLP model focuses more on the covering of high-risk areas but not the equity issue. Therefore, we propose to use micro fire stations with lower capacity to cover the remaining areas with low demand. This is particularly useful in practical applications, as fire stations of different levels are assigned differently according to the efficient allocation of resources. Specifically, we allocate macro fire stations with high capacity to the areas with high demand, while assigning micro fire stations with low capacity to the other areas with low demand.

Siting of micro fire stations

Micro fire station is the assistant and supplementary force of macro fire station, and it is modeled as the second-level fire station in our research. Chinese government stipulates that micro fire stations should be built in communities or important units and their response time should be within 3 minutes (www.119.gov.cn). Taken this into account, we used circle buffer with a radius of 1.6 km (i.e. $3 \times 32 / 60$ ) as the maximum service area for each micro fire station. According to the regulation, all the communities in the city should be covered by micro fire stations, and thus we used the LSCP model to solve the second-level problem of hierarchical fire stations siting.

Without considering the spatial heterogeneity of fire risk across communities, we obtained 90 facility sites for covering all the communities by using LSCP model, as presented in Supplementary Figure 10. It can be observed that all the micro fire stations have same service area. For macro fire stations, their rescue personnel are full-time, and equipped with a high standard. Thus, most of the macro fire stations are able to cover a neighborhood with a fixed scope (i.e. 4-minutes coverage). However, for micro fire stations, their capacities are usually limited due to insufficient equipment and unprofessional team. Thus, in high-risk communities, the micro fire stations should have a relatively smaller coverage. In this respect, we propose to assign different service areas to micro fire stations in different communities. Specifically, each micro fire station is assigned a limited workload in covering demands. The LSCP model with workload limitation can help generate balanced system for fire emergency service.

In local communities, fire risk is closely related to building condition and resident population size. Thus, we combined the data of building age and population to estimate fire risk in different communities. As presented in Tables 1 and 2, we first ranked the fire risk levels of communities from the two aspects of building age and population size, and then combined them into a unified indicator $R$ according to equation (9), which represents the overall fire risk of a community. The weight $a$ determines the importance that planners attach to these two aspects. For general purposes, we can adopt the weight of 0.5. Then, in our study region, the total fire risk of all the communities is 8382.5. As presented in Supplementary Figure 10, the number of micro volunteer fire stations is 90; then, we calculated the average fire risk (i.e. workload) for individual micro fire station as 93. Such value is then taken as the upper limit of workload for micro fire stations. Then, by using the constrained LSCP model (please see ‘Location model for micro fire station’ section), 145 fire stations are obtained to cover all the communities (Figure 2). It can be observed that the densely distributed communities in the center of the city have a relatively high fire risk. Thus, the corresponding micro fire stations obtain a relatively smaller service area and are densely distributed within the local regions. This can help generate a balanced system for second-level fire services.

R = a \cdot r_{b} + (1 - a) \cdot r_{p}

(9)

Table 1.

The fire risk level of communities in terms of building age.

Building age	The number of communities	Risk level $r_{b}$
1900–1990	714	4
1990–1999	1044	3
2000–2009	1369	2
2010–2019	764	1

Table 2.

The fire risk level of community in terms of population size.

Population size p	The number of communities	Risk level $r_{p}$
$0 < p \leq 1000$	2609	1
$1000 < p \leq 2000$	929	2
$2000 < p \leq 4000$	742	3
$p \geq 4000$	418	4

Figure 2.

The location of micro fire stations optimized by LSCP model with workload limitation.

These 145 micro fire stations and the re-planned 24 macro fire stations form the whole hierarchical model of urban fire protection system (Supplementary Figure 11). There are two main advantages in such result. First, within the high-risk areas, both the macro fire stations and micro fire stations are densely distributed to share intensive local fire rescuing duties. Note that the two types of fire stations focus on different levels of fire events. The macro fire station mainly serves high-cost fire incidents, while the micro fire station mainly serves low-cost fire incidents. Since micro fire station has a much larger spatial density than macro fire station, it can reach the places of fire incidents more quickly and help macro fire stations to slow the spread speed of sudden fire damages. Furthermore, compared to the result in single-level fire service system (Supplementary Figure 5), the hierarchical system can cover most of the demands, especially in the western areas of the city. More specifically, as presented in Figure 3, our coverage rate in high-risk areas reaches 97.32% (i.e. 1528 grids). Besides, our system can cover 95.22% of the fire incidents (i.e., 8184 incidents), which is significantly higher than the original rate of 60.64% (i.e. 5212 incidents). The effective service area also increases from 276.89 square kilometers to 609.49 square kilometers. Therefore, with our hierarchical model, the locational efficiency of fire stations can be significantly improved.

Figure 3.

Coverage of fire risk places by using the combined fire stations.

Movable resource allocation for micro fire stations

Some researchers deduce that urban fire events are highly dynamic, which means that fire rescue demands change with time (Kumar et al., 2020; Spatenkova and Virrantaus, 2013). It should be noted that in China siting a fire facility usually comes with a new building for parking the fire resources and supporting the daily training of firefighters; in this regard, the site of fire stations does not support changing location in a short time period. Nevertheless, for adapting to the dynamic demand of fire rescuing, we propose to allocate movable resources (e.g. fire extinguishers) dynamically for the micro stations with an acceptable travel cost. This strategy is particularly useful for the emergency service planning in China.

In the experiment, we first used random forest (RF) and geographical weighted regression (GWR) to predict the fire vulnerability across space (Kumar et al., 2020). To be specific, we consider two time periods, day-time (07:00–19:00) and night-time (19:00–07:00), based on the work shift of firefighters in China. The study area was divided into a square grid with cell size of 1000 m × 1000 m, and the fire vulnerability for each cell was then calculated using the methods of RF and GWR. Specifically, we use the variables listed in Table 3 to build the RF model. We classify the buildings by their usage and number of floors. According to the usage, buildings are divided into four categories: R (residential), C (commercial), I (industrial) and O (other); according the height, buildings are divided into three categories: L (low rise, number of floors <=3), M (medium rise, 3<number of floors <=9) and H (high rise, number of floors >9). Then, we count the buildings of different categories contained in each cell to obtain the building height (X2) and the building usage (X3), as presented in Table 3. Building age (X4) is calculated as the mode (the most frequent value) of building ages in a cell. Building count (X5) is the number of buildings in a cell. The variables X6–X20 represent the percentage of each category in the grid cells.

Table 3.

Variables considered in the modeling.

Variable	Unit
Fire vulnerability (Y)	Continuous numerical
Population (X1)	Continuous numerical
Buildings height (X2)	L, M, H, LM, LH, MH, LMH (Categorical)
Buildings usage (X3)	R, C, I, O, RC, RI, RO, CI, CO, IO, RCI, RCO, RIO, CIO, RCIO (Categorical)
Buildings age (X4)	Continuous numerical
Buildings count (X5)	Continuous numerical
Low rise residential percentage (X6)	Continuous numerical
Low rise commercial percentage(X7)	Continuous numerical
Low rise industrial percentage (X8)	Continuous numerical
Low rise other percentage (X9)	Continuous numerical
Low rise mix percentage (X10)	Continuous numerical
Medium rise residential percentage (X11)	Continuous numerical
Medium rise commercial percentage (X12)	Continuous numerical
Medium rise industrial percentage (X13)	Continuous numerical
Medium rise other percentage (X14)	Continuous numerical
Medium rise mix percentage (X15)	Continuous numerical
High rise residential percentage (X16)	Continuous numerical
High rise commercial percentage (X17)	Continuous numerical
High rise industrial percentage (X18)	Continuous numerical
High rise other percentage (X19)	Continuous numerical
High rise mix percentage (X20)	Continuous numerical

After testing the parameters of the model, we calculate the normalized variable importance values by using the RF of day-time and night-time (Supplementary Figure 12), and choose those above 0.02 to construct geographical weighted regression (GWR), as recommended by Kumar et al. (2020). The R-square value of the day-time GWR model is 0.85 and the night-time GWR model is 0.83. From the spatial distribution of local R-square in the two time periods (Supplementary Figure 13), the model has a good fit for the central urban area. According to the predicted fire vulnerability of day-time and night-time (Figure 4), there are differences between the two time periods. In the day-time, the high fire vulnerability values are more clustered in the central area. When entering in the night-time period, the predicted fire vulnerability values increase significantly in the periphery of the study area.

Figure 4.

The predicted fire vulnerability for the day-time (a) and the night-time (b).

Then, we calculate the sum of fire vulnerability values within the service areas of micro station ( $i$ ) as the fire vulnerability in the day-time ( ${d f}_{i}$ ) and in the night-time ( ${n f}_{i}$ ) (Supplementary Figure 14). Allocating the resources according to the fire vulnerability in different time periods will improve the efficiency of services. Note that the transport cost ( $C_{j}$ ) for moving resources ( $j$ ) between the sites of micro fire stations should also be considered in our model. Therefore, we take a linear combination of these three objectives by weights ( $w_{1}, w_{2}, w_{3}$ ) as follows

$Minimize$

w_{1} * \frac{\sum \frac{{d f}_{i}}{d_{i}}}{n} + w_{2} * \frac{\sum \frac{{n f}_{i}}{n_{i}}}{n} + w_{3} * \sum C_{j}

(1)

Subject to

\sum d_{i} = \sum n_{i} = m \forall i

(2)

m \geq n

(3)

d_{i}, n_{i} \geq 1 and d_{i}, n_{i} \in N \forall i

(4)

C_{j} = {dis}_{j} * p \forall j

(5)

where

n

is the total number of micro stations (i.e. 145) obtained from our LSCP model (‘Siting of micro fire stations’ section);

m

is the total number of the movable resources, which depends on the input of the government;

d_{i}

and

n_{i}

are the numbers of resources allocated for micro station

i

for day-time and night-time, respectively;

\frac{{d f}_{i}}{d_{i}}

is the fire vulnerability to be serviced at micro station

i

, and the first item in equation (1) means maximizing resource utilization for day-time;

{dis}_{j}

is the shortest distance to move resource

j

in different time periods and

p

is the transportation cost per kilometer. Note that all the

{d f}_{i}

{n f}_{i}

and

{dis}_{j}

are normalized. Constraint (2) specifies the total number of the resources is

m

, Constraints (3) and (4) require at least one resource to be allocated to each micro station and Constraint (5) identifies the transport cost.

In our experiment, we set $w_{1} = w_{2} = w_{3} = 1$ , and $p = 0.6$ for general application purpose. Then, we use genetic algorithm (GA) to give the resource allocation plan with $m = 200$ (Figure 5). In the two time periods, the allocation of resources basically follows the distribution of fire vulnerability, and the regions with a higher vulnerability level get more resources. Compared to the night-time, the distribution of resources in the day-time is more uneven, and some central locations obtain eight resource items. Generally, the resources are concentrated in the central area in both periods, where the fire vulnerability is higher than that in other areas. This distribution plan can not only improve resource utilization but also minimize the transportation cost for adjusting resources dynamically.

Figure 5.

The distributions of movable resource items for micro stations in the day-time (a) and night-time (b) (the total number of resources are set to 200).

Conclusion and future work

Fire emergency service is a critical part to the urban public health and safety system, as it has a significant impact on people injury, death and property destruction. It is recognized that GIS-enabled modeling and analysis can help plan and manage urban public emergency services such as healthcare service, police patrol and pollution regulation. However, compared to these common services, urban fire service has its own characteristics including specific response time, benefit maximization, workload equalization and cost minimization. The common location methods that only consider one or two of these aspects are hard to generate a reasonable result for urban fire stations siting. In addition, traditional research models all the fire stations as the same level, without consideration of the true hierarchical structure of fire service system. According to the Chinese government requirement (www.119.gov.cn), a series of micro fire stations shall be established in local communities to help cover fire service demands in the city. Different from the high cost of macro fire station, micro fire station consumes few human, physical, and financial resources, and can deliver services easily. In this regard, our paper proposes a new hierarchical location model for two-level fire stations, by taking into account their own unique aspects. Specifically, in the first level of our hierarchical model, MLCP is suitable for macro fire stations siting, as it only optimizes the locations of existing fire stations and does not add new macro fire stations. Then, in the second level of the hierarchical model, LSCP can be used as the number of micro fire stations is not the main concern. With the siting of micro fire stations, our system can cover all the demands, including those not covered by macro fire stations. In order to assess the urban environment as accurately as possible, our experiments used geospatial big data (e.g. historical fire incident data, community building age data and population data) to estimate the spatial variation of fire risk across city.

In addition, the rapid change of urban life leads to a highly dynamic demand for rescue services. Therefore, the use of dynamic resource allocation in fire protection systems would help to improve the resources utilization. Considering the application background of firefighting construction in China, the macro fire stations have fixed configuration, while micro fire stations are more flexible; thus we choose to dynamically allocate resources to micro fire stations in our model. Specifically, we used random forest (RF) and geographical weighted regression (GWR) methods to detect fire vulnerability in day-time and night-time, respectively. Then, with the goal of maximizing resources utilization and minimizing transportation costs, a location model is proposed to recommend a dynamic resource allocation scheme under a certain mobile cost. The result proves that the proposed model can largely improve the locational efficiency of fire stations in different time periods.

In the future, we plan to apply the hierarchical model to other types of emergency services such as police stations siting. In addition, our model only considers the Euclidean distance as the service radius of fire stations. In the future, we can further add constraints of road network, such as network distance, traffic congestion, multiple lanes and road direction to build a more detailed model (Yu et al., 2020).

Supplemental Material

sj-pdf-1-epb-10.1177_2399808320958424 - Supplemental material for Hierarchical siting of macro fire station and micro fire station

Supplemental material, sj-pdf-1-epb-10.1177_2399808320958424 for Hierarchical siting of macro fire station and micro fire station by Wenhao Yu, Yujie Chen and Menglin Guan in EPB: Urban Analytics and City Science

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China [41701440]; Natural Science Foundation of Hubei Province [2018CFB513]; Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) [CUG170640]; National Key Research and Development Program of China [2017YFB0503500]; Opening Fund of Key Laboratory of Geological Survey and Evaluation of Ministry of Education [GLAB2019ZR02]; a grant from State Key Laboratory of Resources and Environmental Information System [201801].

Supplemental material

Supplemental material for this article is available online.

Wenhao Yu received the B.S. and Ph.D. degrees in Geoinformatics from the Wuhan University, Wuhan, China, in 2010 and 2015, respectively. He is an associate professor at China University of Geosciences, Wuhan, China (CUG). His research interests include urban planning, map generalization, and spatial data mining. He has published more than 30 peer-reviewed papers in scientific journals such as applied geography, journal of transport geography, IJGIS, TGIS, CEUS, and IEEE TITS. He is an editorial board member of PLOS ONE.

Yujie Chen is a master student in China University of Geosciences, Wuhan, China (CUG). Her research interests include urban planning and spatial analysis. Menglin Guan received the B.S. degree in Geoinformatics from the Southwest University, China, in 2018. His research interests include urban planning and spatial analysis.

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