Optimal Prioritization Model for School Closure Decisions Considering Educational Accessibility in Shrinking Regions

Abstract

The consolidation and closure of small schools in rural areas has not only worsened the educational environment but also risked accelerating the socioeconomic decline of rural communities. This study examines how elementary school closures affect educational accessibility and seeks to optimize closure prioritization through a fairness-oriented approach. An optimal prioritization model, developed using the p-median algorithm, was applied to simulate and assess changes in commuting conditions and spatial equity. Using a case study of a South Korean county, we demonstrate the model’s ability to minimize disparities in urban and rural commuting environments while ensuring a balanced and fair decision-making process for school closures. This approach highlights a viable pathway to equitable educational infrastructure planning in regions facing demographic decline.

1. Introduction

The decreasing number of students following Korea’s low birth rates has accelerated the consolidation and closure of small schools, which, in turn, has rapidly worsened educational conditions in rural areas [1,2,3]. The lack of educational resources has not only deteriorated the educational environment and deprived families of educational opportunities but has also contributed to the wider accelerated collapse of rural communities [4,5,6,7]. In rural areas, where the educational environment has deteriorated due to the consolidation and closure of schools, residents have moved to other regions, searching for a better educational environment. The decline in the local population has further accelerated the collapse of demand and locational efficiency of educational facilities. This phenomenon has led to a vicious cycle that has further reduced schools and educational services [8,9,10]. The declining educational capacity has not only affected educational equity between urban and rural areas, but has also decreased the quality of life in rural areas, including the home-to-school distance and time spent commuting to school, students’ health problems such as sleep deprivation and obesity, classroom shortages and restricted educational activities, and limited access to school resources [11,12,13,14,15].

Various factors, such as limited student transportation options and regional conflicts, show that the policy of consolidation and closure of rural schools has reached its limit [16,17,18]. Given that social fairness is strongly recognized as an important factor for educational service infrastructure in Korea, educational facilities, which are inevitable public goods, should be fairly utilized and serviced. Since educational facilities have a strong public purpose, providing basic living services and quality of life, the social equity of facilities is an important factor that must be recognized with proper utility and distribution of resources. Importantly, in Korea, elementary school allocation is based on administrative district-based catchment areas designated by local education offices. This means students are assigned to schools based on their residential address, even if another school is geographically closer. As a result, students may be required to attend a more distant school if it falls within their designated district. This structural limitation of the current school allocation system motivated our exploration of catchment area fairness and inspired the research question of how to optimize school district assignment based on actual accessibility rather than administrative constraints.

The Korean Constitution stipulates that everyone has a right to be properly educated for six years and given free elementary education. Under this right, the government needs a more realistic and balanced consideration of student school access [19]. Ryu et al. [20] indicated that it is unreasonable to consolidate or close all small schools despite the shrinking population, arguing that the government should reconsider its perspective on small schools. Lee and Dong [21] also claimed that the entire education system needs to be restructured based on the declining school-age population. The educational offices of local governments need to find effective and feasible ways to save small schools, including enacting small school support ordinances. Various efforts to run small schools in rural areas through a special curriculum and an appointed principal system cannot reverse the tidal wave of the low fertility rate [22]. Thus, improving educational conditions in small schools or actively supporting and cooperating with local governments is necessary [23]. If the consolidation and closure of small rural schools cannot be avoided, the policy must reflect efficiency and fairness [24]. Despite these efforts, current school closure decisions are often determined by quantitative criteria such as enrollment size alone without considering the equity implications of accessibility. As a result, rural regions with sparse populations experience disproportionate educational burdens. There remains a significant policy gap in the lack of systematic, data-driven, and fairness-oriented methodologies to guide these decisions. Most research on educational fairness has focused on horizontal and vertical fairness in terms of education quality and financial distribution of educational resources [25,26,27,28,29], but relatively few studies have focused on access fairness by comparing the commuting distance to schools in urban and rural areas [24]. Talen [30] attempted to analyze accessibility by calculating road-network-based distances and commuting costs from residential areas to elementary schools in Virginia’s suburbs in the United States. In their study, accessibility to elementary schools was differentiated based on various socioeconomic factors such as urbanization, land prices, and owner-occupation rates. They concluded that spatial inequality in educational opportunities could lead to inequality in student outcomes. Lotfi et al. [31] suggested a multi-objective optimization model based on p-median algorithms to minimize the total distance between population blocks and their closest schools, maximize school capacity balance, and enhance coverage for population blocks. This model offers a holistic solution to school location/allocation challenges by incorporating demographic changes in the allocation process, enhancing the accuracy and effectiveness of school planning. Choi [11] also sought to measure social equity by analyzing the distribution and accessibility of public elementary schools to assess gaps in the educational environment by region. Choi’s study [11] revealed that the deterioration of commuting conditions in rural areas is more serious than in urban areas due to rural school closures. However, the accessibility results in their study may distort the outcome of accessibility by exploiting the Euclidian distance from students’ residents to schools rather than the actual road distance.

An appropriate commuting environment should be determined for elementary school services, which means that home-to-school commuting distance is an important factor in determining the distance to school. When determining the location of the school or school district, Liu et al. [32] stated that allocating the appropriate distance to the nearest school from the residential area is eco-friendly and economical. At the same time, their study addresses students’ health by comparing Euclidean straight and real road distances for commuting to school. Hanley [33] also estimated the cost changes considering consolidating schools into larger ones by analyzing the relationship between the size of the school district and bus transportation costs, suggesting that additional transportation and capital costs could increase by up to 10% and 7.7%, respectively.

The objective of this study is to quantitatively assess the impact of elementary school closures on educational accessibility and to develop an optimized model for prioritizing school closures based on spatial equity. This research uses advanced spatial optimization techniques to construct a demographic supply–demand model to systematically determine the sequence of school closures. The study involves a comparative analysis of existing school district boundaries and those generated by p-median optimization to identify spatial imbalances. Additionally, it evaluates the resultant changes in commuting patterns to provide a comprehensive understanding of the effects of school closure policies.

2. Optimal Prioritization Model for Closure Decisions

This study responds to this gap by proposing a spatial optimization model that reflects both efficiency and spatial fairness principles in school closure prioritization. Unlike previous approaches that rely on post hoc analysis or non-spatial thresholds (e.g., enrollment size), our model uses a spatial optimization framework (p-median) to derive actionable closure sequences based on equity-centered criteria. We applied the p-median problem to simulate the redistricting of educational boundaries for elementary schools to achieve academic fairness. The p-median problem introduced by Hakimi [34] is a method that efficiently uses limited resources [35,36]. The p-median problem determines the p-number of facilities that can meet the needs of all consumers at a minimum cost of transportation from the site of demand [37,38,39]. This method is often applied to public facilities such as police stations, fire stations, medical facilities, and environmental treatment facilities, as well as to the location of private facilities such as convenience stores, large discount chains, and bicycle parking lots [40,41,42].

The p-median algorithm is also suitable for reallocating elementary school districts to establish locations or boundaries to minimize students’ average commuting distance to school. Furthermore, we developed an enhanced model proposed by Whitaker [43] and Taillard [44] to construct a model for resetting school districts and suggesting the priority school(s) to consolidate based on the highest average commuting distance among all elementary schools. This algorithm has a process flow that first chooses a school with the largest average commuting distance and then sets up a school district that students can commute to with a minimum distance. We defined binary decision variables of the p-median problem using the algorithm in Equations (1) and (2).

$$X_j=\left\{\begin{array}{c}1, \mathrm{i}\mathrm{f} \mathrm{a} \mathrm{s}\mathrm{c}\mathrm{h}\mathrm{o}\mathrm{o}\mathrm{l} \mathrm{i}\mathrm{s} \mathrm{l}\mathrm{o}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{i}\mathrm{n} \mathrm{l}\mathrm{o}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} j\\ 0, \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}.\end{array}\right.$$

(1)

$$Y_{ij}=\left\{\begin{array}{c}1, \mathrm{i}\mathrm{f} \mathrm{a} \mathrm{v}\mathrm{i}\mathrm{l}\mathrm{l}\mathrm{a}\mathrm{g}\mathrm{e} i \mathrm{i}\mathrm{s} \mathrm{a}\mathrm{l}\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{n}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t} \mathrm{n}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{b}\mathrm{o}\mathrm{r} \mathrm{s}\mathrm{c}\mathrm{h}\mathrm{o}\mathrm{o}\mathrm{l} j\\ 0, \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}.\end{array}\right.$$

(2)

All demand nodes ($i$) and schools ($j$) consist of a set $\mathrm{N}$ ($\mathbf{\forall }\mathit{i}\mathbf{\in }\mathit{N}$) and a set P ($\forall j\in P$), respectively. The decision variable $X_j$ is a binary integer that determines where the school is located, defining 1 if a school is located in location $j,$ and 0 otherwise. The decision variable $Y_{ij}$ is also a binary integer, defining 1 if a village $i$ is allocated in the nearest neighbor school $j,$ and 0 otherwise. Given these decision variables, we can formulate the p-median problem as follows:

$$\mathrm{Z}=min{\sum }_{i\in N}{\sum }_{j\in P}{D}_{ij}{Y}_{ij}$$

(3)

Subject to

$${\sum }_{j\in P}{Y}_{ij}=1\hspace{1em}\hspace{1em}\hspace{1em}\forall i\in N$$

(4)

$${\sum }_{j\in P}{X}_j=p\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}$$

(5)

$$\hspace{1em}\hspace{1em} Y_{ij}-X_j\le 0\hspace{1em}\hspace{1em}\hspace{1em} \forall i\in N,j\in P$$

(6)

$$X_j=\{0,1\}\hspace{1em}\hspace{1em}\hspace{1em} \forall j\in P$$

(7)

$$\hspace{1em}\hspace{1em} Y_{ij}=\{0,1\}\hspace{1em}\hspace{1em}\hspace{1em} \forall i\in N,j\in P$$

(8)

The objective function ($\mathrm{Z}$) in Equation (3) seeks to maximize student access to schools by minimizing the commuting distance ($D_{ij}$) between demand node ($i$) and supply node ($j$). The commuting distance refers to the shortest real road distance from a village to the nearest school. This means that the shorter the total commuting distance, the shorter the student’s total travel distance or average distance, which can provide spatially balanced educational services. Constraint (4) ensures that a demand node ($i$) is allocated for some schools. Constraint (5) ensures that only p schools are near the closest school. Constraint (6) implies that demand node ($i$) can be allocated by school ($j$), which also ensures that total demand is assigned to a school.

The basic p-median algorithm can select the optimal locations of facilities using the shortest path data between supply and demand, but we applied the enhanced method concept with a priority facility based on a 1-median algorithm that first selects one facility and adds or excludes it in a heuristic manner [45]. Thus, the method can be used to select facilities to be closed one by one from several final candidates to be determined or from existing supply sites. The p-median algorithm for solving the problem of district setting and consolidation prioritization in elementary schools minimizing commuting distance is performed using the following procedure (Figure 1).

In Step 1, initialize $m=0$. $x_m$ defines an empty set as $n\left(x_m\right)=0$. $m$ indicates the number of all elementary schools that have operated, consolidated, and closed in the region. $x_m$ is the number of $m$ schools that should be open considering educational fairness. Next, in Step 2, increase $m$ by one as $m$ = m + 1. Calculate the number of nodes selected for operating a school among the candidates. Then, in Step 3, compute $\sum _{i=1}{D}_{ij}$ for each candidate node $j$ that is not included in the set of $x_{m-1}$. The set of $x_{m-1}$ is already established at node $j$ to m—1 schools. Then, calculate $m$ as $\sum _{i=1}{D}_{ij}$, which is the value of the p-median first-order objective function. In Step 4, find the node $j^{\mathrm{*}}\left(\mathrm{m}\right)$ that minimizes the first-order objective function $\sum _{i=1}{D}_{ij}$, namely $j^{\mathrm{*}}\left(\mathrm{m}\right)=\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{m}\mathrm{i}\mathrm{n}\left\{\sum _{i=1}{D}_{ij}\right\}$. This formula means that $m-1$ schools are first selected to operate, and then $j^{\mathrm{*}}\left(\mathrm{m}\right)$ is chosen as the optimal location for $m$-th schools. Here, set $x_m=x_{m-1}\cup j^{\mathrm{*}}\left(\mathrm{m}\right)$ in the form of adding nodes $j^{\mathrm{*}}\left(\mathrm{m}\right)$ to the set $x_{m-1}$ to obtain the set $x_m$. In Step 5, build a subset $S_m$ of school facilities $m$. In the subset $S_m$, the candidate schools $m-1$ should be equal to or less than the marginal number of schools $m^{\mathrm{*}}$. Here, the marginal number of schools $m^{\mathrm{*}}$ is determined by the number of schools that the researcher or policymaker should operate except for the total number of schools in the region to be closed. In Step 6, if there is a capacity of schools to operate in the region in a set of school candidates $x_m$ ($x_m-S_m\ne \mathrm{\varnothing }$), return to Step 2. If there is no capacity for local schools to operate ($x_m-S_m=\mathrm{\varnothing }$), stop. Finally, in Step 7, $C_m$ school is a comprehensive set for the universal set $U_m$, as a set of elements not belonging to set $x_m$. This satisfies the problem of minimizing the objective function $Z_j^m$ in terms of fairness and is subject to closure priorities except for the number of schools operating.

3. Empirical Applications in South Korea

3.1. Materials and Study Area

In South Korea, elementary school students are not assigned to the geographically nearest school but are instead designated a specific school according to predetermined school district boundaries defined by local education offices. These districts are typically aligned with administrative units such as eup, myeon, or dong. As a result, students residing close to a certain school may still be required to attend a farther school if their residence falls outside the school’s assigned district. This rigid allocation system often results in spatial inefficiencies and inequities in school access, especially in rural areas where an increasing number of small schools are being closed due to declining enrollment. These institutional constraints form the foundation for this study’s focus on spatial equity in school closure decisions.

The target area in this study is Chuncheon in Ganwon, South Korea (Figure 2). We selected this area considering the number of closed schools and changes in commuting distance. As many as 58 elementary schools have been open in this area, 38% of which are located in urban areas (22 schools) and 62% in rural areas (36 schools). Among the total elementary schools, 16 of the schools in rural areas were closed due to the decreasing school-age population. As of 2020, Chuncheon provides elementary education at 42 schools (41 national and 1 private). Since students who want to go to private schools can commute to school regardless of the school district, we conducted a spatial optimization analysis on only the 41 public schools designated by the local governments. Of the 41 public schools, 40 school districts are directly assigned to one school, and one school district is a joint school district where students can choose from two schools. Based on the schools’ locations, the urban area consists of 21 school districts and the rural area has 19 school districts.

Kim, Jeon, and Suh [24] found that 24.2% of the villages (22 out of 91) in Chuncheon had increased the commuting distance to schools due to the new school district designation even though some students were physically closer to their designated schools. In the worst case, students in one village (Daedong village) have a physical distance of 17.0 km to the nearest elementary school, but according to the district’s designation, students living in this village must actually travel to an elementary school 32.6 km farther away, making the commuting distance 49.6 km. The Chuncheon region has a city in the middle of the region and rural areas surrounding the city. The difference between the physical commuting distance and the school district designation is the largest in the country. Therefore, we set Chuncheon as our target site and determined that it is a meaningful region for simulating a model that reorganizes the school district more rationally through spatial optimization analysis.

3.2. Comparison of Current Status with Optimal Simulated Districts

Both urban and rural schools in Chuncheon have significant differences in school district areas as well as commuting distances based on the existing status and the p-median-based optimal simulated situation (see

Table 1. Comparison of coverage area and commuting distance in urban and rural areas under the reference situation and optimally simulated situation.

Location of School	Reference Situation		Optimally Simulated Situation
	Urban	Rural	Urban	Rural
Coverage area (unit: km2)
Average	3.63	52.00	4.14	51.25
Standard deviation	5.22	33.02	7.24	43.88
Maximum	21.65	119.69	28.78	181.20
Minimum	0.18	5.70	0.61	3.21
Commuting distance (unit: km)
Average	3.36	12.09	4.29	10.43
Standard deviation	2.95	13.94	4.46	11.31
Maximum	12.94	72.32	17.10	50.34
Minimum	$\le 0.1$	$\le 0.1$	$\le 0.1$	$\le 0.1$

). Based on the current situation, the catchment (coverage) area of urban school districts is about 14.3 times smaller than that of rural school districts. The urban school districts cover an average of 3.6 km². The smallest is 0.18 km², and the largest is about 21.6 km². In contrast, in rural areas, the coverage area of the school districts is, on average, 52.0 km², with the difference between the smallest and largest districts being 114 km² (ranging from 5.7 km² to 119.7 km²). In the existing school districts, the difference in commuting distance between urban and rural schools is about 3.6 times. Students in urban areas travel 3.4 km on average, while in rural areas, they travel 12.1 km to their allocated schools. However, in the optimal school district model based on the p-median, the average school district area in urban areas is 4.1 km², and in rural areas, it is about 12.5 times that, which is larger than the current 51.3 km². In addition, the average commuting distance in urban areas is 4.3 km and in rural areas is 10.4 km.

Although the gap between urban and rural educational environments is still large, the optimal conditions increase the coverage area and commuting distance for urban schools but reduce the district area and the commuting distance of rural schools. As for the coverage area controlled by one school, urban schools would expand slightly from an average of 3.6 km² to 4.1 km², which is a reduction compared to the average of 52.0 km² to 51.3 km² for rural schools. Based on the algorithm, commuting distance would increase by 900 m from 3.4 km to 4.3 km on average in urban areas, and decrease by 1.7 km from 12.1 km to 10.4 km in rural areas.

To evaluate how different the optimal school boundaries based on spatial optimization would be from the current situation, we used the p-median to reset the school districts with minimal commuting distance and compared them with the existing status (see

Table 2. Consistent and inconsistent coverage areas of schools based on current districts compared to optimal districts in urban and rural areas.

Area	Consistent Area	Inconsistent Area	Total
Urban	40.82 (53.58%)	35.36 (46.42%)	76.18 (100.0%)
Rural	774.65 (74.56%)	264.30 (25.44%)	1038.95 (100.0%)
Total	815.47 (73.13%)	299.66 (26.87%)	1115.13 (100.0%)

Unit: km².

and Figure 3). In the existing school district allocation, residents living in an area of 299.7 km² (about 26.9% of Chuncheon) have to commute to a farther school, not the nearest one. The consistent area with the existing and new optimal school districts is 815.5 km², 73.1% of the total area (1115 km²), but the inconsistent area is 299.7 km², accounting for 26.9%. After dividing this into urban and rural areas, 53.6% of the total area of 76.2 km² in urban areas were analyzed to be consistent with 40.8 km², and the discrepancy was 35.4%. In rural areas, 74.6% of the total area of 1039 km² was consistent, but 25.4% showed discrepancies.

3.3. Priority Comparison of Actual and Simulated School Closure

Local governments are consolidating small schools because of fewer students based on the market principle of supply and demand. In rural areas, residents are rapidly aging, and the school-age population is rapidly decreasing; thus, most schools have been subject to consolidation and closure. As most schools in rural areas continue to close, students’ commuting distance in rural areas continues to increase. Despite the government’s efforts to maintain schools, if some small schools need to consolidate and close, there needs to be a reasonable method to determine which schools will be closed. The simple decision has been based on the market principle of closing schools with the most decreasing number of students, but this is inconsistent with the purpose of public schools. To quantitatively assess how the educational environment has worsened due to the consolidation of rural areas, we explored the order (sequence) of rural area schools that have actually closed over the past 30 years. Furthermore, if closing schools is unavoidable, we need to analyze the order of closures using the p-median algorithm (Figure 4). The closure order using the p-median should be based on the school with the largest sum from all demand sites to the nearest school.

The closed schools in Chuncheon are mainly located on the outskirts of the city, and the order of closures (Figure 4a) are the same as the optimal closure prioritization, as shown in Figure 4b. The pattern of closures corresponds with the population decline trend toward the city center. However, the p-median analyzed the priority of closing schools in rural areas and analyzed the opposite scenario of the actual trend of closing schools (Figure 4b). School closures in Chuncheon mostly occurred in the outskirts of the city, but the p-median analysis showed that schools located in areas adjacent to urban areas were closed first. In particular, the southern part of the region was actually the ninth, fifteenth, and sixteenth closure within the area, until there were no more elementary schools in the area. However, the p-median-induced closure plot revealed that when a total of 16 schools were closed, the ninth closure in the region was the same, but both of the remaining schools were not subject to closure.

In fact, the analysis showed how the distance between urban and rural areas changed when 16 schools were closed in the region. We compared the change in commuting distance between urban and rural areas with optimal closure priorities using the p-median (Figure 5). After 16 schools in rural areas closed, the average commuting distance in urban areas became about 3.9 km, which is very small (Figure 5a for closures). However, the impact of the increase in commuting distance became greater as schools in rural areas closed. The average commuting distance in rural areas was 4.8 km when all of the schools were in operation, but after closing 16 schools, the commuting distance increased 2.2 times to 10.4 km, on average. The average distance to schools in rural areas remarkably increased the most when the 3rd, 4th, 13th, and 14th schools closed (see Figure 5b for closures).

When school closure priorities are based on the p-median algorithm, the average commuting distance between urban and rural areas is similar and the gap between urban and rural commuting environments narrows. According to the optimal scenario, the distance in the city increased by about 1.4 km from the initial 4.0 km distance to 5.4 km. In contrast, in the rural areas, the distance increased only by about 900 m, from 4.8 km to 5.7 km.

The school closure method based on the supply and demand market principle will create an educational environment that will further deepen the urban–rural gap. However, if they are prioritized using the p-median problem, the overall urban–rural commuting environment would be an effective way to make the closure of schools similar.

4. Discussion

In January 2021, the total fertility rate in South Korea marked a fresh record low of 0.84. For the first time in history, there was a population “dead cross”, (i.e., the natural decline when the number of people born is fewer than the number of deaths). The government also predicted that South Korea’s population will shrink faster as the death toll continues to rise, the birth rate declines, and the population ages. Given this situation, closing small schools in rural villages is inevitable as the school-age population continues to decline. As Choi [11] and Kim, Jeon, and Suh [24] argued, however, consolidation policies need to be both efficient and equitable, rather than simply using the existing trajectory method of determining consolidation based on a lack of the appropriate number of students per school.

Local governments need to reset their school districts, considering local educational resources and commuting conditions to provide an appropriate academic environment. For example, the joint school district located east of Chuncheon is a school boundary where students can go to two schools in this region (Chugok elementary school and Cheonjeon elementary school, marked in red in Figure 6). Of these two schools, however, the northern school (Chugok elementary school) is the closest school in a straight line, but there is no road to commute to it from the joint school district. Soyang lake is located between the joint school district and Chugok elementary school, but there are no roads and bridges that can be accessed immediately. Thus, students living in the joint school district need to travel west of the district across the city center and then go back to the northeast. It takes students more than an hour and a half by car, traveling more than 60 km. Alternatively, even though Gasan elementary school is geographically closer (marked in blue in Figure 6), if students commute to Cheonjeon elementary school located in the center of the urban area, it is a shorter commute, although it is still more than 40 km and takes about an hour. This may imply that current closure policies prioritize administrative or demographic criteria over spatial accessibility considerations. Such disparities suggest that existing school closure decisions—though aligned with population decline patterns—may inadvertently increase access burdens for rural students.

While the case study of Chuncheon provides valuable insights, we acknowledge limitations in the generalizability of the findings. Chuncheon’s unique combination of a compact urban core and wide-ranging rural periphery, along with Korea’s administrative catchment-based school assignment system, may not fully reflect the institutional and spatial dynamics present in other regions or countries. Differences in local governance, transportation systems, and population distributions can significantly influence both school access conditions and closure decision-making frameworks. To enhance external validity, future research should apply this model in diverse geographic contexts—such as densely populated metropolitan outskirts, depopulating island communities, or other countries with distinct school planning systems—to evaluate its broader applicability.

Some studies have found that commuting in rural areas is a much longer and more arduous journey than in urban areas [13,46,47], and we found that rural areas in Korea are in the same situation. As the result in Section 3.2 shows, if the 16 schools closed in Chuncheon had been selected through the p-median algorithm, there would not have been a situation in which the absence of the school unreasonably determined the school district. The two schools already located in the joint school district were closed in 1994 as part of the government’s policy of consolidating small schools, so this district has had poor commuting conditions for nearly 30 years. By simulating the closure priorities with the p-median algorithm, we found that one of the two schools should have been maintained.

Furthermore, comparable challenges related to educational accessibility and spatial equity have been observed in other depopulating regions. In rural China, Zhao and Barakat (2015) [48] demonstrated that nationwide school consolidation policies have led to a significant increase in commuting distances for students, particularly in mountainous and sparsely populated counties. Their quantitative analysis showed that the average distance to school in Xinfeng County increased by more than 13 km following school closures, disproportionately affecting rural villages without public transport options. Similarly, Hannum and Wang (2022) [49] found that school closures in minority-populated regions of China not only extended commuting distances but also reduced school enrollment rates and years of completed education for students from low-income households, exacerbating educational inequality. In the UK, Singleton et al. (2011) [29] demonstrated that rural students travel more than twice the distance of their urban peers, and that access inequities are embedded in catchment configurations. These examples reinforce the broader relevance of spatially informed closure strategies and suggest that our model may be applicable across diverse planning environments. These international studies align with our conclusions and underscore the broader relevance of the proposed optimization model. Future research can benefit from comparative case studies that adapt and validate the model in varied demographic and policy environments to improve spatial equity in educational infrastructure. This study has clear implications for both theory and practice in educational planning. Theoretically, it integrates spatial equity directly into the prioritization process for school closures, expanding on existing approaches that typically focus on efficiency or student population thresholds. By applying a spatial optimization framework, we demonstrate how facility planning can incorporate fairness metrics as core criteria, contributing to the literature on equity-based infrastructure allocation. Practically, the model offers a replicable and transparent tool for decision makers tasked with consolidating educational facilities amid demographic decline. Local governments can use the model to simulate various closure scenarios, assess equity impacts using commuting distance metrics, and derive justifiable closure sequences based on spatial fairness rather than political or enrollment-driven heuristics. This is particularly critical in rural areas, where traditional closure policies often widen existing disparities. The framework also has the potential to be extended for use in other public facility domains (e.g., clinics, libraries) where accessibility and fairness are central concerns.

Recent shifts in work and lifestyle patterns, such as increased remote work, flexible working hours, and digital learning environments, are also likely to influence the perception of school accessibility and the spatial distribution of educational demand. As highlighted in an emerging study [50], time geography and mobility behavior are evolving, particularly in response to demographic changes and technological advancement. While our current model focuses on minimizing physical commuting distance, future research could benefit from integrating time-use data or activity-based mobility patterns to reflect the actual spatiotemporal accessibility of school services more accurately. These changes may also mitigate the educational disadvantages faced by rural communities by reshaping the relationship between residential location and school usage.

5. Conclusions

We evaluated accessibility to educational facility resources in rural areas and an optimal facility location or closure model based on the p-median algorithm. The existing consolidation and closure system of small schools based on the government-led market principles of supply and demand may have increased efficiency by intensively using educational resources and infrastructure. Still, it has created a worse educational environment for rural students.

The school district of elementary schools has yet to be established by simply considering the commuting distance. Still, it should be determined on an appropriate scale of school boundaries by local governments by comprehensively reviewing the status of facilities and organizing classes for a proper curriculum. If consolidating and closing small schools is inevitable, we suggest that the method of reducing educational resources should be determined based on reasonable measures, considering the opportunity costs of commuting, and not just on the criterion of a declining number of students. In this study, we evaluated scenarios for school closures based solely on commuting distance using p-medians that emphasize the fairness of school accessibility. Compared to conventional methods that retrospectively evaluate school accessibility or use enrollment-based triggers for closures, our approach enables forward planning by simulating closure sequences that balance efficiency and fairness. It also enhances transparency by clearly quantifying accessibility trade-offs for each closure decision.

While this study offers promising results, it has several limitations. The model was tested in a single regional case—Chuncheon—which, although representative of urban–rural mixed areas in South Korea, may not capture spatial, demographic, or institutional variations found in other regions. In addition, the current framework relies primarily on commuting distance as a proxy for accessibility, without integrating qualitative factors such as school quality, socioeconomic vulnerability, or parental preferences.

In future studies, we expect to derive more reasonable measures to reset school districts or to prioritize schools that will be targeted to close by diagnosing the educational environment based on the various attributes of schools (i.e., number of teachers, facilities, school buses) and commuting distance and stakeholder feedback such as parental satisfaction and local economic impacts. Further, the model could be validated through applications in diverse spatial and governance contexts—such as metropolitan fringes, remote rural islands, or international cases—and expanded to incorporate machine learning and time-use data to reflect dynamic mobility behaviors and support equitable educational planning at scale.