Heterogeneity Analysis of Resident Demands and Public Service Facilities in Megacities of China from the Perspective of Urban Health Examination

Abstract

Public service facilities are the cornerstone of urban development and further expansion, and their spatial distribution fairness is closely related to the quality of life of urban residents. Existing research tends to focus on coverage analysis of a single city or a single type of public service facility, lacking a macro perspective at a medium-to-large scale and consideration of residents’ public service needs. To improve the monitoring of urban public service facility coverage and supply–demand patterns, this paper adopts an urban diagnostic perspective, using 14 megacities from nine urban agglomerations in China as the study area. By integrating spatial and temporal social sensing big data, including road networks, population, and points of interest (POI) data, and employing spatial analysis methods including coverage rate calculation, supply–demand matching efficiency, spatial heterogeneity, and sp{atial stability analysis, this study reveals the spatial distribution patterns of various facilities within cities, as well as the heterogeneity, balance, and equity of supply–demand matching efficiency between different cities. The results show that the spatial distribution of public service facilities in different cities generally tends to concentrate in the central areas, although there are some variations due to local topographical influences. The coverage rate of transportation and education facilities is relatively high, while that of healthcare facilities is generally lower. This study provides information support for urban planning and the optimization of public service facility allocation, contributing to the achievement of sustainable urban development through the comprehensive analysis and comparison of 14 megacities.

1. Introduction

Public service facilities, as essential infrastructure underpinning urban development, play a pivotal role in sustaining urban operations and residents’ well-being. These facilities encompass transportation, healthcare, education, commerce, and cultural amenities that directly fulfill citizens’ daily needs [1]. Achieving their balanced spatial allocation and supply–demand equilibrium constitutes a critical pathway for enhancing urban livability and advancing sustainable development [2]. At the global level, this equilibrium aligns with the United Nations’ Sustainable Development Goals—particularly SDG 11 on sustainable cities—while nationally, it resonates with China’s new urbanization priorities emphasizing inclusive public services [3]. By providing emergency response systems, waste management, and equitable service distribution, optimized facility allocation not only strengthens urban resilience but also simultaneously advances multiple goals, including health (SDG 3), education (SDG 4), infrastructure innovation (SDG 9), and inequality reduction (SDG 10) [4,5].

Against the backdrop of China’s rapid urbanization, the diversification of residents’ public service demands and the prominent imbalance in facility supply distribution have necessitated advanced analytical approaches. Spatiotemporal big data-driven spatial heterogeneity analysis, statistical modeling, and indicator systems have emerged as critical methodologies for monitoring coverage and supply–demand dynamics. Recent advances focus on three key directions: spatial heterogeneity modeling (e.g., hierarchical living circle evaluation in Lanzhou [6] and mobile signaling-based density impacts in Shanghai [7]); intelligent algorithm integration (e.g., graph convolutional network-enhanced coverage optimization [8] and the DeepMCLP framework for automated layout planning [9]); and cross-disciplinary GIS and spatial statistics techniques for measuring inequality [10]. These innovations collectively enhance decision-making precision for facility allocation [11]. However, three limitations hinder broader applicability: (1) oversimplified metrics—an overreliance on population parameters neglects multidimensional resident needs [6,7]; (2) fragmented spatial scales—research is largely confined to single cities or facility types, lacking comprehensive multi-city or agglomeration-level assessments [6,8,9,10]; and (3) limited algorithmic generalizability—existing models struggle with heterogeneous multi-city data [8,9].

To address these gaps, this study develops a cross-scale, multidimensional framework that integrates variability indices and supply–demand efficiency metrics under an urban diagnostics paradigm. Specifically, we selected 14 representative megacities from nine major urban agglomerations in China, covering regions with varying economic levels and development characteristics. The analysis encompasses six subcategories of public service facilities—education, healthcare, transportation, commerce, culture and sports, and leisure—chosen for their relevance to residents’ daily lives and policy importance. By coupling parcel-level coverage with demand assessments and applying supply–demand matching efficiency alongside variability indicators, we aim to (a) quantify spatial heterogeneity and equity of facility distribution across multiple scales, and (b) provide a resident-centered diagnosis of supply–demand imbalances to inform targeted optimization strategies.

This study expects to provide theoretical and technical references in the following three aspects: (1) a cross-scale evaluation framework that bridges macro-level urban agglomeration comparisons and micro-level parcel analyses to reveal scale-dependent allocation patterns; (2) a diagnostic indicator system balancing coverage, equity, and supply–demand efficiency to objectively assess disparities between and within cities; and (3) insights into the coupling between public service facility allocation and urbanization processes, offering theoretical support and practical guidance for future planning and policy formulation in Chinese megacities.

2. Related Works

2.1. Monitoring Methods for Public Service Facility Coverage

Accurately assessing the spatial coverage of public service facilities constitutes a fundamental scientific challenge in urban planning, driven by the need to reconcile facility supply with heterogeneous resident demands. Public service facilities—spanning education, healthcare, transportation, commerce, culture, and recreation—serve as critical infrastructure for equitable urban development [12]. Their spatial distribution directly impacts social equity, accessibility, and quality of life [13], necessitating robust methodologies to quantify coverage and optimize allocation [14,15,16,17,18]. Current approaches for monitoring facility coverage primarily focus on supply-side quantification through accessibility metrics and spatial modeling [19,20]. Accessibility evaluations, such as two-step floating catchment area (2SFCA) analysis [21], coverage rate calculations [22], and walkability assessments [3], dominate the field. While these methods prioritize spatial proximity, they often oversimplify demand dynamics by relying on population density as a proxy [23,24]. For instance, population-based models identify gaps in service provision [24] but neglect nuanced factors such as socioeconomic disparities, age-specific needs, and temporal variations in usage patterns [6,7], limiting their applicability to complex urban systems.

Recent algorithmic advancements aim to address these limitations. Commercial solvers [25] and heuristic algorithms [26] optimize facility layouts under predefined constraints, while deep reinforcement learning frameworks [11,27] enable dynamic, data-driven solutions. Innovations like graph convolutional networks [8] and automated planning tools [9] exemplify progress in spatial optimization, yet they face scalability challenges when applied to multi-city or multi-facility contexts. These methods excel in single-city analyses but struggle with heterogeneous data across urban agglomerations, hindering their generalizability [8,9]. A critical scientific gap lies in the fragmentation of spatial scales: Most studies focus on isolated cities or facility types [6,8,9,10], failing to account for inter-city disparities or regional synergies within urban agglomerations. This narrow scope inhibits holistic assessments of spatial equity and supply–demand matching across diverse urban contexts. Furthermore, existing metrics often prioritize efficiency over equity, overlooking the multidimensional needs of vulnerable populations [23,24,25,26,27,28].

To bridge these gaps, our study introduces a cross-scale diagnostic framework that integrates variability indices (e.g., coverage balance, coefficient of variation) and supply–demand efficiency metrics. By analyzing 14 megacities across China’s major urban agglomerations, we address the limitations of single-city analyses while accounting for regional economic and developmental heterogeneity. This approach advances the scientific discourse on spatial equity by linking facility allocation patterns to urbanization stages and functional zoning principles [15,16], thereby enhancing methodological rigor and offering scalable solutions for equitable urban planning.

2.2. Analyzing Methods for Supply and Demand of Public Service Facility

The analysis of supply–demand dynamics for public service facilities hinges on resolving a core scientific dilemma: how to reconcile spatially fragmented service provision with the multidimensional needs of heterogeneous urban populations. Traditional approaches, often anchored in aggregate metrics like per capita facility counts, inadequately address the interplay between demographic diversity (e.g., age, income, mobility) and spatial equity—a gap magnified in rapidly urbanizing megacities [28,29]. Recent methodological advances aim to bridge this divide through heterogeneity analysis and big data integration [30]. For example, POI data enables granular mapping of facility distribution [31,32,33,34], while regression models quantify how socioeconomic factors and residential location shape service utilization [35,36,37]. These studies consistently highlight systemic imbalances: Even within megacities, core-periphery divides persist, with underserved populations in remote or densely populated areas facing exclusion [32,33,34,36,37,38]. Such findings expose the limitations of static, population-centric models, which overlook temporal demand fluctuations and fail to integrate policy drivers like zoning regulations or investment priorities [6,23].

Technological innovations, such as GIS-based deep mapping [39], refine spatial diagnostics by linking urban form to functional distribution. Yet, these tools often operate in isolation from socioeconomic and policy contexts. For instance, hierarchical urban planning frameworks allocate facilities based on administrative boundaries [40] but neglect cross-jurisdictional synergies, resulting in fragmented service networks. Similarly, policy evaluations prioritize infrastructure investment over operational inefficiencies, such as mismatches between facility placement and actual usage patterns [41]. This disconnect underscores a broader scientific gap: Existing models excel in single-city or single-facility analyses but struggle to address multi-scale interactions within urban agglomerations [8,9]. Few studies compare supply–demand efficiency across cities with divergent urbanization levels, limiting insights into regional equity.

To advance this field, our study proposes a multi-dimensional framework that unifies demand heterogeneity, spatial equity, and policy impacts. By analyzing 14 Chinese megacities across urban agglomerations, we (1) quantify demand drivers such as age, income, and mobility, (2) evaluate spatial mismatches using integrated POI and population data, and (3) assess how policy interventions shape cross-regional equity. This approach transcends isolated case studies, offering a scalable model to balance efficiency and equity in diverse urban contexts—a critical step toward equitable urban development.

3. Materials and Methods

3.1. Study Area

This study focuses on the urban development and health status of megacities in China, considering the current urbanization characteristics in China, where regional megacities serve as the main driving force for urban agglomeration. Based on the distribution and scale of urban agglomerations in China and the regional development strategy of “coastal areas, along the Yangtze River, and along the Yellow River”, 14 representative cities were selected from 9 urban agglomerations in northeast China, north China, central China, east China, south China, and southwest China. All these cities are super-large or ultra-large cities, and their built-up areas are selected as the study areas. In 2022, the GDP of these 14 megacities reached 30.79 trillion yuan, with a total population of 206 million, accounting for 24.42% and 14.61% of the national total, respectively.

Table 1. Selected megacities as study area and their urban agglomerations.

Regions	Urban Agglomerations	Selected Megacities as Study Area
Northeast China	Harbin–Changchun Urban Agglomeration	Harbin
North China	Beijing–Tianjin–Hebei Urban Agglomeration	Beijing
	Central Plains Urban Agglomeration	Zhengzhou
	Guanzhong Plain Urban Agglomeration	Xi’an
	Shandong Peninsula Urban Agglomeration	Jinan–Qingdao
East China	Yangtze River Delta Urban Agglomeration	Shanghai–Hangzhou–Nanjing
Central China	Urban Agglomeration of Middle Reaches of Yangtze River	Wuhan–Changsha
South China	Guangdong–Hong Kong–Macao Greater Bay Area	Guangzhou–Shenzhen
Southwest China	Chengdu–Chongqing Urban Agglomeration	Chengdu

shows the corresponding relationship between the selected cities and their urban agglomerations, and Figure 1 shows the administrative divisions and built-up areas of the 14 representative cities.

3.2. Data Acquisition and Preprocessing

3.2.1. Road Network

The road network data utilized in this study was obtained from OpenStreetMap (https://www.openstreetmap.org, accessed on 2 February 2024). Upon retrieving the vector data of the road network in China from OpenStreetMap, the road network corresponding to each area was first clipped based on the administrative boundaries of respective cities. Subsequently, road features were organized according to the road name field, with double line roads consolidated into single line roads. Concurrently, topological rules were established for the road network data, aimed at removing isolated road segments and dangling nodes.

3.2.2. City Boundary and Built-Up Area

The basic data used in this study include administrative boundary data, population data, road network data, and multi-source remote sensing imagery. The vector data of urban administrative boundaries were obtained from the 1:1,000,000 National Fundamental Geographic Database of the National Geographic Information Catalog Service (https://www.webmap.cn/commres.do?method=result100W, accessed on 2 February 2024). Population data were sourced from China’s Seventh National Population Census and retrieved from the statistical yearbooks of the 14 megacities. Road network data were acquired from the OpenStreetMap platform and categorized into highways, urban expressways, major arterial roads, minor arterial roads, branch roads, and other roads to facilitate subsequent urban parcel extraction.

Urban built-up area data, another foundational dataset for parcel extraction, were derived from Landsat 8, Sentinel-1/2, and Digital Elevation Model (DEM) imagery. After atmospheric correction of Sentinel-2 imagery using Sen2Cor, radiometric calibration and Lee filtering (5 × 5 window) of Sentinel-1 imagery, all remote sensing data were spatially aligned to 10 m resolution (WGS84 UTM) via bilinear resampling. Normalized Difference Built-up Index (NDBI), Normalized Difference Vegetation Index (NDVI), Modified Normalized Difference Water Index (MNDWI), Sentinel-1 VV mean texture (7 × 7 window), and DEM data were stacked as input features. A Random Forest classifier (100 trees, max depth = 15) was trained using 4000 samples (50% built-up and 50% non-built-up) to classify built-up areas. The classification results were refined through morphological opening (3 × 3 kernel) and removal of isolated patches (area < 500 m²). Validation against Google Earth imagery via random sampling achieved an overall accuracy of 85.16%, meeting the requirements for subsequent analysis.

After delineating urban built-up boundaries, road network data were intersected with built-up areas to partition them into “parcels”. Population data were then linked to the attribute tables of these parcels. Parcels with populations greater than 100 were selected as the final study areas [42].

3.2.3. Population

The population data in this study were obtained from the WorldPop website (https://www.worldpop.org/, accessed on 2 February 2024), specifically from the Unconstrained individual countries 2000–2020 UN adjusted data product, with a spatial resolution of 100 m × 100 m. The population data were projected onto the WGS 1984 UTM Zone 49N coordinate system to match the built-up area boundaries and were subsequently clipped according to the administrative boundaries of the selected super-large cities.

3.2.4. POI Data

The POI data of public facilities in this study were obtained using the Amap API (https://lbs.amap.com/, accessed on 2 February 2024). The coordinates of the POI data points were adjusted to latitude and longitude coordinates under the WGS 1984 coordinate system. The obtained POI data were then subjected to data cleaning, visualization, and analysis using ArcGIS 10.8. Additionally, the coordinate system was unified to WGS 1984 UTM Zone 49N to match the other data used in this study.

A combined method of grid-based search and keyword query was employed to obtain POI data, resulting in 6 types and 14 subtypes of POI data from the 14 megacities. Furthermore, using these POI data as centers, buffer zones were established based on the maximum travel time standards for public facility life circles outlined by the Ministry of Housing and Urban–Rural Development of China, as shown in

Table 2. Types and subtypes of POI data and their maximum traffic time of life circle.

Types	Subtypes	Code	Maximum Traffic Time of Life Circle
Education	Kindergartens	160101	5 min
	Primary schools	160102	10 min
	Secondary schools	160103	15 min
Medical care	General hospitals	170101	15 min
	Specialized hospitals	170102	15 min
	Nursing home and orphanage	170201	15 min
Transportation	Metro stations	230111	15 min
	Bus stations	230112	10 min
Commerce	Shopping malls	130102	15 min
	Supermarkets	130106	10 min
Culture and sports	Cultural activity center	160208	15 min
	Multifunctional sports courts	180100	15 min
Leisure	Parks	180304	15 min
	Squares	180306	15 min

.

3.3. Methods

3.3.1. Calculation of Coverage Level of Public Service Facilities

This study evaluates the coverage levels of public service facilities in each mega city by calculating facility coverage scores and facility coverage rates. These metrics quantitatively reflect the spatial heterogeneity of public service facility coverage at the plot scale within cities.

We calculated the total coverage of each type and subtype of public facility for each parcel, which served as the facility coverage score for that parcel [43]. This indicator reflects the overall coverage of public service facilities in each parcel of a megacity. The higher the number of different major types of facilities covering a parcel, the higher the facility coverage score [44,45]. The range of this indicator is [0, 6].

Simultaneously, we used the facility coverage rate to assess the coverage efficiency of each major category of public service facility in the 14 super-large cities. The expression is as follows:

$$R={\displaystyle \frac{\sum _{i=1}^n{A}_{cov}}{A}}$$

(1)

where $R$ represents the facility coverage rate; $A_{cov}$ represents the area covered by various types of public service facilities within each parcel; $n$ represents the total number of parcels; and $A$ represents the total area of the city.

3.3.2. Calculation of Coverage Balance of Public Service Facilities

This study employs the radar chart comprehensive evaluation method to measure the coverage balance of public service facilities in 14 megacities. Based on radar chart visualization, this method constructs perimeter evaluation values and area evaluation values to represent the overall coverage level and the balance level of public service facilities, respectively. The specific methodology is as follows:

(1) Extracting feature vectors. In this study, the feature vector $a_i$ of the i-th city consists of the perimeter $P_i$ and area $A_i$ of the radar chart, denoted as $a_i=[P_i,A_i]$.

(2) Computing the evaluation vector. Referring to Chen et al. [46], for this study, the radar chart evaluation vector $b_i$ of the i-th city consists of the perimeter evaluation value $b_1$ and area evaluation value $b_2$, denoted as $b_i=[b_1,b_2]$. $b_1$ is defined as the ratio of the area of the radar chart to the area of a circle with the same perimeter, reflecting the comprehensive coverage level of public service facilities in the i-th city; $b_2$ is defined as the ratio of the area enclosed by the radar chart of each super-large city to the maximum area of the radar chart, reflecting the balance of public service facilities in the i-th city. The expressions are as follows:

$$b_1={\displaystyle \frac{A_i}{\pi \cdot {\left(\frac{P_i}{2\pi }\right)}^2}}$$

(2)

$$R={\displaystyle \frac{\sum _{i=1}^n{A}_{cov}}{A}}$$

(3)

(3) Comprehensive evaluation function. Based on the calculation of the evaluation vector, the geometric mean of the two evaluation vectors is taken as the comprehensive evaluation value. The expression is as follows:

$$f\left(b_1,b_2\right)=\sqrt{b_1\cdot b_2}$$

(4)

3.3.3. Calculation of Supply–Demand Matching Efficiency of Public Service Facilities

This study utilizes the Supply–Demand Matching Efficiency Index (SDI) to reveal the supply–demand patterns of public service facilities in 14 mega cities. The Matching Efficiency Index is calculated based on the standardized difference between the supply and demand of urban public service facilities, reflecting the degree of alignment between facility supply and demand [47,48]. The index calculation is divided into three steps. Firstly, the total demand for public facilities in each super-large city is calculated based on the demand function model. Secondly, the total supply of public service facilities in the region is determined. Finally, the efficiency index of supply–demand matching for public service facilities is evaluated.

(1) Determining the demand for public facilities by residents. According to the demand function model, the total per capita demand for public service facilities in the region is linearly related to the proportion of female residents, average household size, per capita disposable income, and average age. Therefore, the total demand for public service facilities by residents in the region can be calculated as follows:

$$D=p\left(aFEM+bPOP+cDIN+dAGE\right)$$

(5)

where $D$ represents the total demand for public facilities by residents in the region; $p$ represents the total population of residents in the region; $FEM$, $POP$, $DIN$, and $AGE$ represent the proportion of female residents, average household size, per capita disposable income, and average age, respectively; and $a$, $b$, $c$, and $d$ are coefficients for these four indicators. In the calculation of supply–demand matching efficiency, we use the relative value of demand for residents, which has a range of [0, 1], calculated as follows:

$${RD}_i={\displaystyle \frac{D_i}{\sum _{i=1}^n{D}_i}}$$

(6)

where ${RD}_i$ represents the relative value of demand for public facilities by residents in the i-th city and $D_i$ represents the total demand for public facilities by residents in the i-th city.

(2) Calculating the supply of public service facilities. In this study, we use the parcel coverage score calculated in 3.3.1 as the supply of public service facilities for each super-large city. Similarly to the demand, in the calculation of supply–demand matching efficiency, we use the relative value of facility supply (with a range of [0, 1]) for calculation, as shown in the following formula:

$${RS}_i={\displaystyle \frac{S_i}{\sum _{i=1}^n{S}_i}}$$

(7)

where ${RS}_i$ represents the relative value of supply of public facilities in the i-th city and $S_i$ represents the total supply of public facilities in the i-th city.

(3) Calculating the efficiency index of supply–demand matching for public service facilities. The expression for the efficiency index of supply–demand matching for a single type of public facility is as follows:

$$SDI={\displaystyle \frac{2\left(RS-RD\right)}{RS+RD}}$$

(8)

where $SDI$ represents the supply–demand matching efficiency index and $RS$ and $RD$ respectively represent the relative values of supply and demand for public facilities. The range of SDI is [−2, 2]. When $SDI=0$, public service facilities in that parcel maintain supply–demand balance, and spatial efficiency is maximized; when $SDI>0$, the supply of public service facilities exceeds demand, indicating an oversupply of public facility resources; and when $SDI<0$, the supply of public service facilities is less than demand, indicating an inadequate supply of public facility resources. Generally, the smaller the absolute value of $SDI$, the higher the supply–demand matching efficiency of a certain type of facility within the parcel.

On this basis, the comprehensive spatial supply–demand matching efficiency of all types of public service facilities within each parcel is further calculated, as expressed below:

$$SDE=1-{\displaystyle \frac{\sum _{i=1}^n\left|SDI\right|}{n}}$$

(9)

where $SDE$ represents the comprehensive spatial supply–demand matching efficiency and $SDI$ represents the supply–demand matching efficiency index for the i-th type of public service facility. A higher $SDE$ indicates a higher comprehensive spatial supply–demand matching efficiency for all types of public service facility within that parcel.

3.3.4. Coefficient of Variation (CV)

This study uses the coefficient of variation to evaluate the stability of supply–demand matching efficiency. In this study, the coefficient of variation is calculated based on SDI. A larger CV indicates a greater degree of difference in the SDI of a certain type of public service facility within the region [49,50]. The CV is calculated as follows:

$$CV=\sqrt{{\displaystyle \frac{\sum _{i=1}^n{\left(SDI-\overline{SDI}\right)}^2}{n\cdot \overline{SDI}}}}$$

(10)

where $CV$ is the coefficient of variation for $SDI$; $\overline{SDI}$ is the average value of $SDI$ for all parcels; and $n$ is the number of parcels.

3.4. Research Framework

The research framework of this study is illustrated in Figure 2. Initially, parcel units are generated based on road network data, and these parcel units are filtered using population data to select those that meet the threshold criteria. The selected parcel units are then overlaid with various types of POI data for analysis, calculating their coverage of different types of POI points. Feature vectors are extracted from the coverage data of parcel units using radar charts, constructing a public service facility evaluation index to comprehensively assess their functionality and level. Furthermore, various dimensions of the evaluation index are analyzed to explore the directional characteristics of public service facilities in different parcel units. The coverage frequency of POI points for each parcel unit is statistically analyzed to calculate a supply–demand matching index, evaluating the level of supply–demand matching for public service facilities. The coefficient of variation is utilized to measure the differences in supply–demand matching among different cities and parcel units, providing a comprehensive analysis of the diversity in supply–demand matching.

4. Results

4.1. Spatial Distribution of Facility Coverage in Each Megacity

Figure 3 shows the spatial distribution of the coverage scores for public service facilities in the 14 megacities. From Figure 3, we can see that the spatial distribution of 0 to 6 types of public service facility coverage for all 14 cities is similar to the urban structure. Within the built-up areas of the 14 megacities, the area covered by all six categories of public service facilities is the largest and is in the core areas of the urban built-up area. Moving from the core to the edge of the built-up area, there is a decreasing trend in the number of types of public service facilities covered, indicating that the edge of the urban built-up area receives less coverage from public service facilities. This is mainly because the central areas of cities have high population density and strong socio-economic activities, resulting in a greater and more diverse demand for public service facilities. Therefore, public service facilities tend to concentrate in the core areas of the built-up area, covering the most types to support different types of human activities in the core areas, such as within the Fifth Ring Road in Beijing, along the Huangpu River in Shanghai, along the Pearl River in Guangzhou, along the Yangtze River in Wuhan and Hangzhou, and in the coastal areas of Qingdao. Moving from the core to the edge of the built-up area, the types of public service facilities gradually decrease, reflecting the decreasing intensity and diversity of human activities from the central area to the edge area, resulting in less coverage of public service facilities in the edge areas of the built-up area. From Figure 3, it can be observed that parcels covered by five types or fewer of public service facilities are distributed on the periphery of parcels covered by all six types of public facilities in all 14 megacities.

4.2. Facility Coverage Rate of Each Megacity

We calculated the coverage rates for each major category of public service facilities in the 14 megacities and plotted radar charts with the coverage rate for each category of public service facility as the axis. Based on the radar chart, we extracted the perimeter and area of each megacity’s radar chart to evaluate the overall coverage level and balance of each category and all types of public service facilities in the 14 megacities. The radar chart of public service facility coverage rates for the 14 cities is shown in Figure 4.

Looking at the coverage rates of each category of public service facilities in the 14 megacities, all six types of public service facilities have coverage rates of over 50% in these cities. For example, the coverage rate of transportation facilities in Changsha is 97.53%, while the coverage rate of leisure facilities in Qingdao is 57.53%. The coverage rates of all six types of public service facilities in Beijing are above 85%, in Shanghai and Guangzhou they are above 70%, and in Shenzhen, above 65%. By type, the coverage rates of educational, transportation, and commercial service facilities in the 14 megacities are all over 79%, 90%, and 75%, respectively. Medical and elderly care facilities in Beijing and Harbin have reached 86.22% and 81.79%, respectively, while in the other 12 megacities, the coverage rates range from 64% to 79%. The coverage rate of medical and medical care facilities in the first-tier city of Shenzhen is 68.54%, and in Zhengzhou, Hangzhou, Wuhan, and Qingdao, it is also below 70%. The coverage rates of cultural and sports service facilities in Beijing, Shanghai, and Shenzhen are 90.23%, 92.82%, and 91.61%, respectively. The coverage rates of leisure facilities in these three cities are 88.05%, 79.20%, and 96.35%, respectively. The coverage rates of cultural and sports, as well as leisure facilities in Qingdao, are the lowest among the 14 megacities, at 65.57% and 57.53%, respectively.

Table 3. Results of the radar chart comprehensive evaluation.

Megacities	${\mathit{P}}_{\mathit{i}}$	${\mathit{A}}_{\mathit{i}}$	$\mathit{f}\left({\mathit{b}}_1,{\mathit{b}}_2\right)$
Harbin	4.9368	1.7285	0.8911
Beijing	5.4314	2.1181	0.9843
Zhengzhou	4.9319	1.6930	0.8852
Xi’an	5.1391	1.8707	0.9273
Shanghai	5.2453	1.9625	0.9485
Hangzhou	4.9024	1.6864	0.8818
Wuhan	4.6402	1.5042	0.8335
Chengdu	5.0298	1.7946	0.9079
Guangzhou	5.3392	2.0196	0.9634
Shenzhen	5.5459	2.1549	0.9967
Nanjing	5.1261	1.8706	0.9264
Jinan	4.9658	1.7414	0.8952
Qingdao	4.5347	1.4179	0.8111
Changsha	5.3248	1.9988	0.9594

presents the evaluation indicators for public service facility coverage radar charts calculated based on the perimeter and area of the radar charts in the 14 megacities. From Table 3, we can see that the perimeter and area of the radar charts for public service facility coverage in Beijing, Guangzhou, and Shenzhen are both above 5.0 and 2.0. Therefore, the comprehensive evaluation values of these three cities rank in the top three among the 14 megacities, at 0.98, 0.96, and 0.99, respectively. This indicates that the overall coverage quality of public service facilities in these three cities is good, achieving a large coverage area of public facilities while maintaining relatively balanced coverage of different types of public service facilities. In addition to these three cities, there are eight cities with comprehensive evaluation values above 0.9, including Xi’an, Shanghai, Chengdu, Nanjing, and Changsha, totaling 57.14%.

The perimeter evaluation value and area evaluation value for Qingdao are 0.8665 and 0.7592, respectively, with a comprehensive evaluation value of 0.8111, which are the smallest among the 14 megacities. This indicates that the coverage and balance of public service facilities in Qingdao, especially for medical and elderly care, cultural and sports, and leisure facilities, are relatively low, all below 70%. The coverage rate of transportation service facilities is 95.60%. There is significant room for improvement in the coverage quality of public service facilities in Qingdao.

We conducted a statistical analysis on the proportion of areas covered by public service facilities of 1 to 6 types in the 14 megacities, and the results are shown in Figure 5. From Figure 5, we can see that the proportion of areas covered by classes 1–6 of public service facilities in the 14 cities increases sequentially. The proportion of areas covered by all six classes of service facilities exceeds 35% in all 14 cities. Among them, Beijing, Shanghai, Guangzhou, and Shenzhen, the four first-tier cities, rank in the top four in terms of the proportion of areas covered by all six classes of service facilities, with 71.73%, 62.55%, 66.20%, and 63.69%, respectively. Other cities where the proportion of areas covered by all six types of service facilities exceeds 60% include Nanjing and Changsha, with 62.24% and 61.91%, respectively. During the process of increasing coverage areas for 1 to 6 types of service facilities, cities where the area covered by one type of service facility exceeds 3% include Hangzhou, Wuhan, Chengdu, Nanjing, and Qingdao, with Shenzhen having only 0.21% in this indicator. Qingdao reaches 10% in the area covered by two types of service facilities; Harbin and Zhengzhou reach 10% in the area covered by class 3 service facilities; cities where the area covered by class 4 service facilities reaches 10% include Harbin, Zhengzhou, Xi’an, Hangzhou, Wuhan, Jinan, and Qingdao; and cities where the area covered by class 5 service facilities reaches 20% include Harbin, Hangzhou, and Shenzhen. It is worth noting that the proportion of areas covered by class 1–2 service facilities in Shenzhen is less than 1% and the proportion covered by class 3–4 service facilities is less than 10%, while the proportion covered by class 5 and 6 service facilities increases sharply to 25.23% and 63.69%, respectively. Meanwhile, Qingdao has the highest proportion of area covered by class 1 service facilities, reaching 6.02% among the 14 megacities. The areas covered by class 2–4 service facilities are all above 10%, but the proportions covered by class 5 and 6 service facilities are only 19.43% and 39.64%, respectively. This indicates that traditional first-tier cities like Shenzhen and Guangzhou have relatively high overall coverage efficiency of public service facilities, while emerging core-level cities like Qingdao, Wuhan, and Harbin need to improve the overall coverage efficiency of public service facilities in urban planning.

4.3. Supply–Demand Matching Efficiency Index of Public Service Facilities

We calculated the supply–demand matching efficiency index of public service facilities for the 14 megacities on a block-by-block basis to analyze the spatial differentiation characteristics of the supply–demand matching efficiency index of the six classes of public service facilities within the megacities, as shown in Figure 6. In the map, we use cool colors to represent blocks where the supply of public service facilities is less than the demand, and warm colors to represent blocks where the supply exceeds the demand. We use an interval of 0.2 for equal interval classification, with a total of 10 levels. From Figure 6, it can be observed that in traditional first-tier cities, such as Shanghai, Guangzhou, and Shenzhen, there are significantly more blocks where the supply of public service facilities is less than the demand than blocks where the supply exceeds the demand. Blocks where the supply exceeds the demand are scattered within the urban built-up areas. In Beijing, there are significantly more blocks where the supply of public service facilities exceeds the demand than in Shanghai, Guangzhou, and Shenzhen. These blocks occupy a slightly dominant position within the urban built-up areas and form a spatially balanced situation with blocks where the supply is less than the demand.

Among the other 10 core-level cities of urban agglomeration, parcels where the supply of public service facilities exceeds the demand also show a scattered distribution pattern. In Harbin and Qingdao, there are significantly more parcels where the supply of public service facilities is less than the demand, than blocks where the supply exceeds the demand, and they dominate. Blocks with a supply–demand matching index above 0.2 are only distributed in a few blocks near the city center. In Zhengzhou, Nanjing, Chengdu, Wuhan, and Hangzhou, the blocks where the supply of public service facilities is less than the demand are balanced with parcels where the supply exceeds the demand within the built-up area. In Xi’an and Jinan, there are more parcels where the supply of public service facilities exceeds the demand than blocks where the supply is less than the demand within the built-up area, and most of the parcels in the city center have a supply–demand matching index above 0.2.

4.4. Spatial Heterogeneity and Stationarity of Supply–Demand Matching Efficiency of Public Service Facilities

We calculated the CV of the SDI for each type and all types of public service facilities in the 14 megacities to quantitatively measure the spatial heterogeneity and stationarity of these indicators at the parcel level. The results are shown in

Table 4. The CV for the SDI of six types of public service facilities in 14 megacities.

	SDI						CV for SDI of All Types of Facility
	Education	Medical Care	Transportation	Commerce	Culture and Sports	Leisure
Harbin	0.5673	0.5511	0.5716	0.5674	0.5613	0.5511	0.5789
Beijing	0.6104	0.5992	0.5949	0.6032	0.5953	0.5868	0.5689
Zhengzhou	0.6207	0.5652	0.6039	0.6087	0.5990	0.5990	0.5649
Xi’an	0.6345	0.5802	0.6151	0.6294	0.5880	0.5729	0.5680
Shanghai	0.6090	0.5680	0.5874	0.5979	0.5934	0.5737	0.5685
Hangzhou	0.5896	0.5191	0.5766	0.5889	0.5841	0.5280	0.5785
Wuhan	0.5956	0.5433	0.5794	0.5923	0.5642	0.5400	0.5596
Chengdu	0.6219	0.5666	0.6013	0.6122	0.6082	0.5882	0.5676
Guangzhou	0.5410	0.4865	0.5365	0.5363	0.5294	0.5126	0.5514
Shenzhen	0.5914	0.5139	0.5766	0.5813	0.5833	0.5803	0.5764
Nanjing	0.6084	0.5703	0.5928	0.6123	0.6063	0.5909	0.5543
Jinan	0.6106	0.5626	0.5774	0.5918	0.5703	0.5597	0.5677
Qingdao	0.6040	0.5609	0.5704	0.5852	0.5448	0.5144	0.5567
Changsha	0.5889	0.5333	0.5722	0.5814	0.5732	0.5718	0.5665

. From Table 4, we can see that the CV values for the SDI of all types of public service facilities in 14 megacities range from 0.55 to 0.58. The lowest value is in the first-tier city of Guangzhou, with a CV of 0.5514 for all types of public facilities. Additionally, Wuhan, Nanjing, and Qingdao have a CV for the SDI of all types of public facilities below 0.56, at 0.5596, 0.5543, and 0.5567, respectively. The other three first-tier cities, Beijing, Shanghai, and Shenzhen, have values of 0.5689, 0.5685, and 0.5764, respectively. Apart from Shenzhen, Harbin and Hangzhou also have a CV of the SDI for all types of public facilities above 0.57, at 0.5789 and 0.5785, respectively. These three cities are the top three in terms of the CV for the SDI of all types of public facilities among 14 megacities.

In terms of the CV for the SDI of each type of public service facility, the first-tier city of Guangzhou has the lowest CV for the SDI of the education and medical care facilities, at 0.5410 and 0.4865, respectively, which are the lowest among the 14 megacities. Moreover, Guangzhou has a CV for the SDI of all six types of public facilities below 0.55. Beijing and Shanghai have a CV for the SDI of all six types of public facilities between 0.57 and 0.62, while Shenzhen, except for medical care facilities, which has a CV for the SDI as low as 0.5139, has a CV for the SDI of the other five types of public facilities between 0.57 and 0.60. Among the other 10 core-level cities of urban agglomerations, Zhengzhou and Chengdu have a CV for the SDI of all six types of public facilities above 0.56, while Xi’an has even higher values, above 0.57.

5. Discussion

5.1. Coverage Level of Public Service Facilities

The coverage rates of public service facilities reveal that first-tier cities (including Beijing, Shanghai, Guangzhou, and Shenzhen) lead in overall coverage levels, with rates exceeding 70% and facilities distributed evenly. Their comprehensive evaluation scores rank among the top. For instance, Beijing’s coverage rates for transportation, healthcare, and cultural facilities exceed 85%, while Shenzhen’s leisure facility coverage rate reaches 96.35%. In contrast, new first-tier cities (e.g., Qingdao, Wuhan, and Harbin) exhibit significant shortcomings in both coverage rates and distribution balance. Qingdao’s cultural and leisure facility coverage rates are only 65.57% and 57.53%, respectively, with the lowest comprehensive evaluation score and poor radar chart performance in terms of area and perimeter metrics. This disparity highlights the need for new first-tier cities to improve resource allocation and facility coordination. The deficiencies in the coverage and distribution equity of public service facilities in new first-tier cities, particularly provincial capital-level cities and sub-provincial regional hub cities beyond traditional first-tier cities, align with the findings of Xiao et al. [51] and Zhao et al. [52]. Xiao et al., while investigating the spatial allocation of public service facilities in Urumqi from the perspective of 15 min living circles, similarly highlighted that Urumqi—as a provincial capital—achieved over 95% coverage of public service facilities in densely populated central residential areas yet exhibited significantly insufficient coverage in peripheral areas and new urban districts. Zhao et al., when comparing the differentiation degree of public service facility allocation among cities in the Beijing–Tianjin–Hebei region, also emphasized the pronounced “core-periphery” spatial structure of public service facilities under the urban living circle framework.

From the vertical perspective of different facility types, transportation facilities generally have high coverage rates, such as Changsha reaching 97.53%, demonstrating their foundational role in supporting overall urban layouts. Healthcare and cultural facilities, however, display notable disparities. For example, Beijing’s healthcare facility coverage rate is 86.22%, compared to Shenzhen’s 68.54% and Qingdao’s even lower 64%, reflecting uneven regional allocation of healthcare resources. Cultural facility coverage in first-tier cities exceeds 90%, but new first-tier cities like Qingdao and Zhengzhou are significantly lacking. The leisure facility coverage follows a similar pattern, with high levels in first-tier cities but only 57.53% in Qingdao. These inter-facility differences reflect varied resource investment priorities and are closely linked to the developmental stages of different cities. Studies by Zhai et al. [53] and Zhang et al. [54] also demonstrate that significant disparities exist in the distribution of different types of public service facilities within cities or urban agglomerations, which are attributed to the interplay of multiple factors such as urbanization levels, urban planning practices, and resident demands.

In terms of the proportion of areas covered by all six types of facilities, Beijing, Shanghai, Guangzhou, and Shenzhen stand out with proportions of 71.73%, 62.55%, 66.20%, and 63.69%, respectively, showcasing high coverage efficiency and comprehensive planning capabilities. While Qingdao has the highest proportion of areas covered by at least one type of facility (6.02%), its coverage rates for five and six facility types drop significantly to 19.43% and 39.64%, indicating a pronounced gap in coverage levels. Shenzhen, on the other hand, demonstrates a concentrated resource distribution strategy, with areas covered by five and six facility types rapidly rising to 25.23% and 63.69%, respectively. This distribution trend indicates that first-tier cities possess stronger capabilities for comprehensive facility coverage, while new first-tier cities need to make continuous improvements in coverage comprehensiveness and resource coordination [55,56].

5.2. Supply–Demand Matching Patterns of Public Service Facilities

The supply–demand matching pattern of urban public service facilities is determined by the quality of supply and the scale of demand. The quality of public service facility supply is influenced by supply efficiency and supply equity. The fundamental factors affecting supply efficiency include the spatial distribution and coverage scale of facilities. When various types of public facilities are evenly distributed across urban areas and have extensive coverage, the supply efficiency of urban public service facilities is higher, effectively meeting demand. Wei et al. [56] and Yan et al. [57] highlighted this phenomenon in their respective case studies of Wuhan and Nanjing. Wei et al., through their investigation of urban public-service facility evaluation methodologies in Wuhan, proposed inter-regional circulation-based supply–demand matching relationships. They emphasized that the spatial heterogeneity of public service facility supply and demand scales constitutes a fundamental factor driving variations in urban supply–demand matching patterns and resident mobility behaviors. Meanwhile, Yan et al., in their research on optimizing age-friendly facility distribution in Nanjing, demonstrated that the spatial allocation and provision of urban public service facilities—particularly in central urban areas—should be tailored to accommodate the spatial heterogeneity of differentiated demands across various zones and facility categories.

The supply–demand matching patterns of public service facilities among the 14 megacities exhibit significant spatial similarities. The spatial distribution of public service facilities is characterized by concentrated clustering and gradual outward diffusion. Core areas, with higher population densities and economic activities, have greater demand for public service facilities, reflecting the imbalance in urban development. Among basic service facilities, the coverage rate of healthcare facilities is generally low, whereas among living support facilities, the coverage rate of commercial facilities is relatively high. Compared to other types of public service facilities, healthcare facilities involve higher construction and operational costs due to the need for substantial medical equipment and highly qualified medical personnel. In contrast, commercial facilities benefit from more flexible land use policies and higher investment returns, attracting significant social capital for their construction. Therefore, the spatial distribution pattern of public service facilities’ supply–demand matching is primarily influenced by the spatial structure of urban functions, which in turn is closely related to the population structure of the city. Core urban areas, as population hubs, generate substantial demand for public services, leading to greater mismatches between supply and demand. On the other hand, peripheral areas, with smaller populations, have lower demand for public service facilities, resulting in fewer supply–demand conflicts [58].

From a cross-city perspective, the supply–demand matching pattern of public service facilities is closely tied to the level of urbanization and urban functions. Among the 14 megacities, traditional first-tier cities like Shanghai, Guangzhou, and Shenzhen exhibit significantly more areas with supply deficits than surpluses. In contrast, Beijing has more areas with supply surpluses compared to Shanghai, Guangzhou, and Shenzhen. This indicates that traditional first-tier cities, with the highest levels of urbanization and densely concentrated populations (even attracting populations from surrounding regions), face notable shortages in public service supply relative to demand. As the capital, Beijing, benefits from its unique urban functions, which bring greater public service resources. Among the new first-tier cities, Harbin and Qingdao also show a trend of more supply-deficient areas, indicating significant urban expansion. Conversely, Xi’an and Jinan exhibit more supply-surplus areas, suggesting a stable urbanization state.

Urbanization levels also affect the spatial stability of the supply–demand matching pattern for public service facilities. The coefficient of variation for supply–demand matching efficiency shows that traditional first-tier cities like Guangzhou and Shenzhen have lower coefficients of variation, indicating relatively stable supply–demand matching efficiency in highly urbanized cities. In contrast, new first-tier cities like Harbin and Hangzhou demonstrate higher fluctuations in supply–demand matching efficiency [59].

5.3. Policy Suggestions and Future Research

To address the issues in public service facility coverage rates and supply–demand matching patterns, it is essential to optimize resource allocation by considering the stage of urban development and spatial functional characteristics. The shortcomings in cultural, medical, and recreational facility coverage rates in new first-tier cities indicate the need to enhance the balance of resource distribution, especially in improving facility coverage levels outside core areas. It is recommended to formulate differentiated resource allocation policies based on urban functional zoning, introduce social capital through diversified financing models to reduce construction costs, and improve operational efficiency. These measures aim to close the gaps with first-tier cities in terms of coverage and balance, fostering comprehensive facility coverage and coordinated development.

At the same time, addressing the spatial imbalance in public service facility supply–demand matching requires a coordinated approach from both supply–demand relationships and urban functional positioning. Core areas should focus on enhancing supply capacity to alleviate shortages, while peripheral areas need improved infrastructure to guide moderate population decentralization, thereby improving the stability of supply–demand matching across regions. Additionally, a dynamic monitoring and intelligent regulation mechanism should be established to adjust the layout and supply strategies of public service facilities in real-time based on urbanization progress and population changes. This would create a virtuous cycle of facility coverage and supply–demand balance, ultimately improving the overall quality of urban development.

Future research and practice should focus on the multi-scale and multi-dimensional optimization of public service facility layouts and dynamic regulation. On one hand, it is necessary to explore the coupling relationship between facility coverage rates and supply–demand matching, developing comprehensive analysis models based on big data and artificial intelligence to quantify facility allocation efficiency and spatial equity. This would enhance the scientific and practical basis of optimization strategies. On the other hand, efforts should be made to conduct classification studies on urban development stages and functional characteristics, constructing regionalized and diversified public service facility supply models to provide tailored solutions for different cities. Furthermore, future work should emphasize the establishment of real-time monitoring and feedback mechanisms, leveraging intelligent technologies to dynamically adjust facility layouts. This will ensure the spatial and temporal coordination of public service facilities, better meeting the diverse needs of urban residents.

5.4. Innovations and Significance

This study adopts the perspective of urban diagnostics, selecting 14 megacities in China as the study area to conduct a comprehensive diagnostic analysis of supply–demand matching patterns, spatial heterogeneity, and stability of public service facilities in these megacities. Compared with similar studies at this stage, this research has the following innovations: (1) A cross-scale evaluation framework for spatial heterogeneity and supply–demand patterns of urban public service facilities: Through horizontal and macro-level comparisons among 14 megacities from different urban agglomerations and regions in China, as well as vertical and micro-level analyses at the intra-urban parcel scale, this study reveals the scale-dependent patterns of public service facility allocation in multiple dimensions. (2) A diagnostic indicator system for public service facility allocation that balances coverage and equity: Under the cross-scale framework, this study integrates indicators such as coverage, equity, supply–demand matching, and their variations. Methods like radar chart analysis and supply–demand matching efficiency are employed to quantitatively evaluate multi-source data, objectively and comprehensively reflecting disparities in public service levels both between and within megacities, thereby facilitating scientific decision-making. (3) Revealing the relationship between public service facility allocation and urbanization levels: Given the varying urbanization levels of the 14 megacities, this study employs cross-scale, multi-dimensional spatial heterogeneity analysis to uncover the relationship and evolutionary patterns between public service facility allocation and urbanization processes. This provides theoretical support for future planning of public service facilities in megacities, offering insights into regulatory trends and developmental patterns [60,61,62].

6. Conclusions

To assess the coverage and supply–demand matching efficiency of urban public service facilities, this study integrates road network data with population data and divides the built-up areas of municipal districts into irregular parcels. By coupling the coverage range of different public service facilities with parcel areas, the study comprehensively calculates the number of times each main indicator and sub-indicator are covered within each parcel and further evaluates the coverage and supply–demand matching efficiency of each city.

The following conclusions are drawn:

(1)

The spatial distribution of facility coverage in mega-cities follows urban structure, with public service facilities concentrated in the core areas of built-up zones. As one moves from the core area to the peripheral area, the coverage range gradually decreases, with relatively fewer facilities covered in the peripheral areas.

(2)

The coverage rates of all six types of public service facilities in the 14 mega-cities are generally high, exceeding 50%. There are differences in coverage rates among different types of facilities, with transportation and education facilities having higher coverage rates, medical facilities having generally lower coverage rates, and leisure facilities having lower coverage rates in some cities.

(3)

Beijing, Shenzhen, and Guangzhou rank in the top three in terms of the comprehensive evaluation value of facility coverage. These cities have large coverage ranges of public service facilities and relatively balanced coverage of different types of facilities.

(4)

There is spatial heterogeneity in the degree of supply–demand matching of various types of public service facilities, with the supply–demand matching index of most mega-cities concentrated within a relatively tight range, indicating that these cities are generally similar in terms of supply–demand matching of public service facilities.