摘要：
空间优化正从地理学的一个研究方向成为学科分支,但公平导向的公共服务空间分配优化研究还较薄弱.学区配置是这方面的一个典型问题,受到社会的广泛关注.针对“多校划片”的随机入学方式,以各居住小区所获得的教育质量期望值的方差来定义入学指标空间分配的公平程度,构建了以该方差最小化为目标、包含最大上学距离约束的二次规划模型,探求各小区对所获得指标进行随机抽签的情景下,各校入学指标在各小区的公平最大化分配,并以北京市石景山区为案例进行了应用研究.结果表明,在维持学校布局和师资配置现状的前提下,与“就近入学”相比,公平最大化的“多校划片”能以有限的上学距离代价,显著降低教育分配的空间差异.在最大上学距离为5km的约束下,各小区教育质量期望值的方差降幅高达99％,教育质量期望值有所提升的小区或学生比例高达约2/3;付出的上学距离代价较显著但可接受,平均上学距离增加到3.99倍,达到3.20 km,仍低于案例区实际平均上学距离.当模型的最大上学距离参数从5km逐步增至8km时,教育公平的改善呈指数增长,平均上学距离呈算数增长;当距离为7km时,各小区教育质量期望值的方差趋近于0,可基本实现上学机会的空间均等化.本文进一步讨论了优化结果对入学政策的启示.%Spatial optimization is an important research area in geography.Most research on spatial optimization of education resource in this field is concerned with spatial efficiency,while the public is more concerned with spatial equity.In recent years,random allocation has heen tested in some places,but the optimization models on the random allocation of schools have not been well formulated and developed.In China,to improve the spatial equity of education,a newly proposed reform tries to use lottery for school admission,namely "allocating several schools to one school district".However,there is little literature on how to implement the new school allocation,its impacts on school distance and educational equity.This paper constructs a quadratic programming model to minimize the variance of all students'expected values on educational quality under constraints of the maximum distance and schools' capacities.Then,Shijingshan District in Beijing is taken as a case area.The result indicates that the new allocation model can significantly improve the spatial equity of educational resources compared with the way of allocating students to the nearby school.The variance of the former decreases by 99％.Over 2/3 of the communities benefit from our model of maximum spatial equality,whose expected values of educational quality will increase.The ratio of benefit students is also about 2/3.On the other hand,the distance cost of school commuting is also significant.The average school distance increases by 3.99 times.However,it is still less than 5 lkm,which is commonly set as maximum distance to school.Moreover,it is also less than the survey school distance in the study area.When the parameter of the maximum distance in the model increases from 5 krn to 8 km,the improvement of the variance of expected value of educational quality obeys the law of exponential growth,and the average distance increase obeys the law of arithmetic growth.When it is set at 7 km,the variance of expected value of educational quality approaches zero.It can be regarded as a state of absolute equal opportunity for every student which is usually thought to be hard or impossible to realize.Based on the results,the policy implication for China's school admission system is discussed.
