义务教育就近入学优化建模研究

doi:10.12082/dqxxkx.2021.200728

摘要/Abstract

摘要：

就近入学是国内外义务教育的基本共识,也是我国义务教育制度的重要组成部分。为满足就近入学需求,引入优化建模方法进行义务教育空间布局规划。首先,定义了4种就近入学场景：严格就近入学、学额限制的相对就近入学、学区连续的就近入学,以及学校布局调整下的就近入学,并构造了相关的优化模型,讨论了每个模型的优势与局限。其次,以河南省某县516个居民区和31所初级中学为例,尝试进行多个实验情景下的最优就近入学安排,并进行比较分析。案例研究发现：① 基于现有学校的布局,严格就近入学缺乏可行性;② 打破乡镇行政边界招生,能够显著地降低学生入学距离;③ 考虑学校学额限制后,学生入学距离比严格就近入学增加40.75%;④ 空间连续的学区划分方便义务教育管理,对学生入学距离影响不明显;⑤ 通过模拟少数学校扩建、新建或撤销,学校布局明显改善,学生入学距离比学区连续入学将下降31.32%。整体上,本文将空间指派、服务区划分、设施选址等优化模型用于义务教育就近入学分析,能够为基层义务教育管理提供规划决策建议,也能为其他公共服务设施规划提供参考。

关键词: 义务教育, 就近入学, 优化, 指派问题, 设施服务区问题, 区位问题, 整型线性规划, 案例研究

Abstract:

Nearby school enrollment is one of the fundamental principles of the compulsory education in China. In this paper, the spatial optimization methods have been applied to local education planning in order to comply with the educational policy on nearby school enrollment. Four planning scenarios are defined: the nearest school enrollment, the optimal nearby school enrollment constrained by the school quotas, the optimal nearby school enrollment constrained by the school quotas and contiguous service areas, and the optimal nearby school enrollment by adjusting school locations. The Mixed Integer Linear Programming (MILP) models for the four scenarios were formulated. The optimization models were tested on a real instance in a county of Henan Province, China. There are 516 residential areas and 31 junior middle schools in the study region. All the instance models were successfully solved by the IBM ILOG CPLEX Optimizer. The case study shows that: (1) It is not feasible to assign all the students to their nearest schools because some schools will be severely overloaded. (2) The total travel distance of students can be significantly reduced by assigning some students to the schools outside their township boundary. (3) Compared with the nearest school enrollment, the total travel distance of students will increase by 40.75% when the school quotas are considered. (4) The design of contiguous service areas of schools is convenient for managing school enrollment, which has no obvious influence on the total travel distance of students. (5) The school service will be significantly improved by adjusting locations of three schools and expanding quotas of two schools in the study area, which will reduce the total travel distance of students by 31.32%. The case study indicates that the nearby school enrollment of compulsory education could be spatially designed by solving the mathematical models such as the generalized assignment problem, the facility service area problem, and the capacitated facility location problem. Both the generalized assignment problem and the facility service area problem aim to minimize the travel distance of students to existing schools, while the capacitated facility location problem is capable of searching better school locations and thus reducing the travel distance of students.

Key words: compulsory education, nearby school enrollment, optimization, assignment problem, facility service area problem, location problem, mixed integer linear programming, case study

王玉璟, 孔云峰. 义务教育就近入学优化建模研究[J]. 地球信息科学学报, 2021, 23(9): 1608-1616.DOI:10.12082/dqxxkx.2021.200728

WANG Yujing, KONG Yunfeng. Optimization Modeling for Nearby School Enrollment of Compulsory Education[J]. Journal of Geo-information Science, 2021, 23(9): 1608-1616.DOI:10.12082/dqxxkx.2021.200728

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实验情景	应用区域	优化模型	主要特征
1A	乡镇域	模型1	严格就近入学
1B	县域	模型1	严格就近入学
2A	乡镇域	模型2	学额限制+就近入学
2B	县域	模型2	学额限制+就近入学
3A	乡镇域	模型3	学区连续+学额限制+就近入学
3B	县域	模型3	学区连续+学额限制+就近入学
4B	县域	模型4	调整布局+学区连续+学额限制+就近入学

应用区域	实验情景	优化模型	学生入学总距离/km	超额/人	学区连续	计算时间/s
乡镇域	1A	模型1	34 726.86	2339	否	0.07
	2A	模型2	34 730.91	2334	否	1.71
	3A	模型3	35 055.92	2044	是	1.92
县域	1B	模型1	31 561.06	2524	否	0.02
	2B	模型2	44 421.41	0	否	24.10
	3B	模型3	44 475.81	0	是	7201.89