中文摘要：

考虑到我国中小学选址问题的特性,本文引入分段效用函数,综合考虑距离、服务质量等多种选址因素,提出基于效用函数的分级的带容量限制的中位模型。模型约束条件包括需求的全覆盖、设施的最小容量约束、需求点就近分配给设施点、需求点单一分配给设施点及开放与关闭设施数目限制等。本文使用拉格朗日松弛算法,以武汉市经济技术开发区为例,就目前学校选址及分配的合理性问题、学校最小容量的合理设置问题和需求波动后的重新选址及分配问题进行了分析。

英文摘要：

Considering the characteristics of elementary and secondary school location in China,sub-utility function is adopted and a variety of location factors such as distance,service quality,etc have been taken into account to set up hierarchical median model with capacity constraints and utility function.The constraints of the model include the whole coverage of demand,the minimum capacity constraint of facilities,closest-assignment,single-assignment,and the limited number of opened and closed facilities.As a real-world case,the lagrangian relaxation algorithm has been used to solve the school location-allocation problem of Wuhan Economic and Technological Development Zone,in which three scenarios are discussed：location-allocation rationality at the present,reasonable minimum capacity constrains,and re-location and allocation after fluctuations in demand.