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