农村学校撤并后规模约束对学校优化布局的影响——以北京延庆区为例

Optimizing school distribution with constraints of school size after school consolidation in rural China:A case study of Yanqing District, Beijing City

在城镇化和农村人口减少的背景下,中国农村地区大量学校撤并,如何优化学校布局成为研究的重点。2008年原建设部发布了农村学校的最小和最大学生规模标准,但该标准对学校布局的影响尚缺乏研究。本文在包含最大距离约束的P-中值模型中增加了学校规模约束,构建了学校布局优化模型,并以北京延庆区小学布局为例,采用分支界定算法进行了求解。结果表明:实施学校规模标准化对学校优化选址有显著的影响,在优化模型中加入学校规模约束后,有65.22%的学校位置发生了改变,呈更加分散型布局;但在乡镇尺度下考察,学校的空间格局则基本未发生变化;学校规模标准化带来的距离增长较小,平均每个学生上学距离仅增长了135 m。并根据结果进一步讨论了研究结果对学校布局优化的政策启示。

With urbanization and the decrease of rural population, a large number of rural schools in China has been merged. How to optimize the layout of schools has become a research hotspot. In 2008, China issued the standards of school size, but the impact of the standards on the layout of schools is yet to be researched. In this study, based on existing location allocation models, constraints of the size of schools were applied to build a model of school layout optimization, which also considered the constraint of maximum distance to school. We chose the primary schools in Yanqing District, Beijing for case study and used the branch and bound algorithm and global optimal solution method to solve the model. The data range from 1995 to 2010, which include 295 pri- mary schools distributed in nearly all villages at the start, and 46 primary schools after the large-scale school merging. The results show that after the school size constraints were applied in the optimization model, 65.22% of the rural schools need to be relocated, which reflects the significant impact of school size constraints. But school spatial distribution pattem remained essentially unchanged at the town and township scale, with the prox- imity index higher than 1, larger than before. After applying the size constraints, the distribution pattern of schools was still a discrete type. But the degree of dispersion has decreased. The optimal solution with school size constraints can satisfy the national standards. At the same time, the optimal solution results in an increase of schooling distance at 135 m per student, which is acceptable. Finally, this study examined the implications of the results for the school layout optimization policy.