最小妒忌公平性区位模型及案例分析

• 作者： 孔云峰 ^1,2 翟石艳 ^1,2
• 作者单位：
  1.  河南大学黄河中下游数字地理技术教育部重点实验室
  2.  河南大学地理与环境学院
• 提交时间：2023-05-13

摘要: 区位模型广泛应用于公共健康、义务教育、应急管理和物流配送等领域。然而，主流区位问题多以服务效率为目标，注重设施成本、距离成本、覆盖客户数量等指标，未考虑服务公平性。部分区位模型考虑服务空间公平性，但存在公平指标多且选择使用缺乏共识、公平指标会严重扭曲效率指标、模型针对简单应用场景和缺乏通用性等局限。本文创新性地引入空间妒忌这一概念，构建公共服务最小嫉妒目标函数，并将其整合在容量约束P中值问题(Capacitated P-Median Problem, CPMP)模型目标函数中，形成最小妒忌公平性区位模型(CPMP-envy)。新模型克服了最小方差目标会扭曲效率指标的局限，实现公平指标与效率指标相兼容。本文考虑城市和农村地区人口空间分布特征，以及数据规模等因素，使用三个典型区域数据探索经典区位模型和公平性区位模型的基本特征。案例实验表明：最小妒忌目标能够显著地改进设施区位空间公平性指标，特别是设施数量较少时，公平性指标能够得到较大幅度改进。最小妒忌目标在公共服务设施布局规划中具有实用性，对于构建公平性区位模型具有理论价值。

Abstract: Location problems have been widely applied to service planning of public health, compulsory education, emergency management, and delivery logistics. However, the mainstream location models are usually to optimize the efficiency objectives such as travel cost, facility cost and the number of customs to be served, rather than the equality objectives. A few location models aim to optimize one of the equality measures, such as the variance of distances, the deviation of distances, the Gini coefficient between the travel distances, and the variance of spatial accessibility indexes. However, the facility locations, capacities and their service areas can be easily distorted by most equality-oriented objective functions. In this paper, a spatially envy objective function for service equality is proposed to overcome the shortcomings of commonly used equality functions. The envy value of customers at a location is determined by their travel distance that beyond a predefined distance. The envy function can be added to mainstream location models in a weighted manner. As a result, the capacitated p-median problem (CPMP) is enhanced as CPMP-envy. The original and improved models were tested on three large instances. Case experiments show that the equality measures, such as maximum travel distance, variance of distances, coefficient of variation, and Gini coefficient between travel distances, can be substantially improved by minimizing the weighted sum of spatial envy and travel cost. It is argued that the envy indicator has theoretical and practical potentials in facility planning towards spatial equality of public service.

• 来自： 孔云峰
• 分类： 地球科学 >> 地理学 数学 >> 控制和优化
• 投稿状态： 已投稿期刊
• 引用： ChinaXiv:202303.00200 (或此版本 ChinaXiv:202303.00200V2)
  DOI:10.12074/202303.00200V2
  CSTR:32003.36.ChinaXiv.202303.00200.V2
• 推荐引用方式： 孔云峰,翟石艳.(2023).最小妒忌公平性区位模型及案例分析.null.doi:10.12074/202303.00200V2 (点此复制)