农村中小学选址的空间运筹

Space operation of rural primary and secondary school location

农村中小学的选址问题是当前地理学区位理论应用的一个热点,学校作为一个设施对学生上学安全和便捷程度有很大影响。许多学者研究了学校的区位问题,然而对农村地区来说,采用模型不够适合。本文学校选址研究充分考虑P-重心模型和P-中心模型的优缺点,在P-重心模型的基础上对模型进行改进,增加学生上学最大距离不超过某一阈值的约束,这样改进后的模型同时具有P-中心和P-重心模型的优点,既保证农村偏远地区的学生上学相对方便,又保证加权距离和相对最小。为了方便应用,应用地理信息科学方法,使用改进的节点交换搜索算法求解,然后通过Visual Studio开发平台和ArcGIS Engine二次开发组件库开发了农村中小学最优选址的决策支持系统。最后以山东省某镇为例,用该系统解决该镇的小学选址,结果发现改进后同时具有P-重心和P-中心特性的模型比传统的P-重心模型更能适合农村小学选址,能够作为小学学校规划选址的辅助决策依据。

The location of the primary and secondary schools has a great significance on ensuring the safety and convenience when students attending and leaving schools. Many previous researches have proposed school location-allocation models, but the models are not suitable for rural schools. In this manuscript, we improve the P-median model by fully considering the advantages of P-center model and P-median model. A maximum distance constraint between students＇ home and school are coupled into the original P-median model. Thus, the improved P-median model owns the advantages of both P-center model and P-median model, i.e. ensuring the convenience for students from remote rural areas, and minimizing the sum of weighted distance. In order to facilitate the model application, an decision support system based on our newly derived vertex substitution search algorithm for allocating optimal location of rural elementary and secondary school were developed on the ArcGIS Engine development component library and Visual Studio development platform. Afterwards, a town of Shandong province is taken as a system test case. The school location selected by our system is better than the locations selected by traditional P-median model. The results prove that the improved P-center model can supply a reference for allocating the location of elementary and secondary school.