地理科学进展  2015 , 34 (12): 1609-1616 https://doi.org/10.18306/dlkxjz.2015.12.009

Orginal Article

基于公平最大化目标的2020年北京市养老设施布局优化

陶卓霖12, 程杨1**, 戴特奇1, 李雪1

1. 北京师范大学地理学与遥感科学学院,北京 100875
2. 北京大学城市与环境学院,北京 100871

Spatial optimization of residential care facility locations in 2020 in Beijing: maximum equity in accessibility

TAO Zhuolin12, CHENG Yang1*, DAI Teqi1, LI Xue1

1. School of Geography, Beijing Normal University, Beijing 100875, China
2. College of Urban and Environmental Sciences, Peking University, Beijing 100871, China

通讯作者:  程杨(1982-),女,四川自贡人,副教授,主要从事健康地理学研究,E-mail: chengyang@bnu.edu.cn

版权声明:  2015 地理科学进展 《地理科学进展》杂志 版权所有

基金资助:  国家自然科学基金项目(41301164)

作者简介:

作者简介:陶卓霖(1990-),男,江西万载人,博士研究生,研究方向为区域与城市发展,E-mail: taozhuolin@pku.edu.cn

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摘要

北京市正快速步入老龄化社会,机构养老作为一种重要的养老模式,对其布局公平性和合理性的研究具有重要的科学和现实意义。本文首先预测了自然增长状态下2020年北京市老龄人口的空间分布,然后建立设施布局优化模型,该模型以各需求点到养老设施的可达性差异最小化为目标;并采用粒子群优化算法求解,对北京市养老设施进行以公平最大化为目标的布局优化。研究结果表明,在公平最大化的目标下,首都功能核心区和城市功能拓展区(即中心城区)所提供的机构养老资源不能完全满足本地需求。城市发展新区在满足当地的机构养老需求之外,还将为中心城区提供大量机构养老服务,生态涵养发展区在满足本地需求的基础上还可为其他地区提供少量机构养老服务。该布局导向与《北京市养老设施专项规划》提出的布局建议相一致,且符合中心城区用地紧张、郊区自然环境较舒适的现实情况。研究结果能为养老政策的制定提供科学建议,所采用的方法也能为其他类型公共服务设施的布局优化提供借鉴。

关键词: 空间优化 ; 公平最大化 ; 人口预测 ; 粒子群优化算法 ; 养老设施 ; 北京

Abstract

Beijing is facing rapid population aging. Residential care plays an increasingly important role in the care for the elderly people. It is of great importance to optimize the layout of residential care facilities to ensure equal and reasonable access, which has scientific and practical implications. This study first forecasted the spatial distribution of the elderly population under natural growth in 2020 in Beijing. Second, a spatial optimization model was established to maximize equity in access to residential care facilities. The Particle Swarm Optimization algorithm was used to solve the optimization model. As the results show, the elderly population aged 60 or older will reach 4.37 million in 2020 in Beijing, among which 7.9%, 50.2%, 30.1%, and 11.8% of the total elderly population will be located in the Capital Core Functional Area, Urban Functional Extension Area, Urban New Developing Area, and Ecological Protection Area, respectively. By contrast, 2.7%, 32.7%, 48.5%, and 16.1% of the total residential care facility (RCF) beds will be located in the Capital Core Functional Area, Urban Functional Extension Area, Urban New Developing Area, and Ecological Protection Area, respectively when optimized . The optimized RCF layouts improve spatially equal access to residential care resources with very low accessibility standard variation (0.0026), while the accessibility standard variation of actual layouts is 8 times (0.0207) that of the optimized results. In the layouts with maximum equity in access, only a portion of the demands for residential care in the Capital Core Functional Area and Urban Functional Extension Area will be met locally. The residential care resources in the Urban New Developing Area will meet both the local demands and the demands from the two functional areas in the central city. The Ecological Protection Area, however, mainly provides residential care services for the local elderly population. The optimized results of this study correspond to the “Special Plan for the Development of Residential Care Facilities in Beijing,” which also conforms to the reality that the land resources are in shortage in the central city and the physical environment in the suburb is more pleasant for the elderly people. The results of this study will support knowledge-based policy-making and planning of residential care facilities. The methods introduced in this study can also be applied to the spatial optimization of other types of public service facilities.

Keywords: spatial optimization ; maximum equity ; population forecast ; particle swarm optimization (PSO) ; residential care facilities ; Beijing

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陶卓霖, 程杨, 戴特奇, 李雪. 基于公平最大化目标的2020年北京市养老设施布局优化[J]. , 2015, 34(12): 1609-1616 https://doi.org/10.18306/dlkxjz.2015.12.009

TAO Zhuolin, CHENG Yang, DAI Teqi, LI Xue. Spatial optimization of residential care facility locations in 2020 in Beijing: maximum equity in accessibility[J]. 地理科学进展, 2015, 34(12): 1609-1616 https://doi.org/10.18306/dlkxjz.2015.12.009

1 引言

中国正快速步入老龄化社会,养老形势十分紧迫。2000年北京市60岁以上老年人口为170万,占总人口的12.5%,到2013年时已高达279.3万,占总人口的21.2%(北京市老龄工作委员会办公室, 2014)。在中国当前养老服务体系中,机构养老是一种重要的辅助养老模式(国务院办公厅, 2011)。北京市政府制定的2020年“9064”养老发展目标规划,到2020年将为4%的老年人提供14~16万张床位,以满足其机构养老需求(北京市规划委员会等, 2010)。2013年,北京市养老机构总床位数为6.93万张,与14~16万张的政策目标之间还存在较大差距。要达到这个目标,在2013-2020年间北京市平均每年约需新增1万张养老床位。公平性是公共服务设施合理布局的重要内容之一,其含义是为各区域居民提供均等的获取公共服务资源的机会。而养老设施供给的巨大缺口对加强其合理布局提出了更高要求。从空间分布现状上看,北京市养老设施的可达性存在较大空间差异(Cheng, Wang et al, 2012; 陶卓霖等, 2014),说明其布局并不合理,亟待进行调整和优化。

现有关于机构养老服务的研究主要集中于养老服务建设(Zhan et al, 2005, 2006, 2008)、养老设施的空间分布特征(Smith et al, 1998; Andrews et al, 2002; 席晶等, 2015)、选择机构养老方式的老年人口特征(Gu et al, 2007; Cheng et al, 2011)、养老设施偏好(高晓路, 2013),及其使用养老设施的可达性(Cheng, Rosenberg et al, 2012; Cheng, Wang et al, 2012; 陶卓霖等, 2014)等方面,缺少关于养老设施优化布局的研究。一些研究探讨了医疗和其他类型设施的布局优化(Owen et al, 1998; Church, 1999; Gu et al, 2010; Wang, 2012),但这些经典的设施区位—分配模型主要关注设施布局的效率,并非以公平性作为目标。Wang等(2013)提出了以公平最大化为目标的设施布局优化模型,具体方法是使需求点到设施的可达性差异最小化,较好地解决了设施布局的公平性问题。

Tao等(2014)基于老年人口空间分布现状,采用公平最大化为目标的模型对北京市养老设施布局进行了优化。但由于北京市正处于快速老龄化阶段,不仅老年人口总量迅速增加,而且老年人口的空间分布也在发生变化。养老设施的规划建设往往需要一个过程,因此要求规划具备一定前瞻性,基于老年人口分布现状的养老设施布局优化往往难以满足这一要求。目前《北京市养老设施专项规划》的规划期限为2020年,若基于老年人口的分布现状进行优化布局,可能导致规划的设施布局与未来老年人口分布的不匹配,造成规划的不合理。

因此,本文将首先预测自然增长状态下2020年北京市老龄人口空间分布,然后建立以各需求点到养老设施可达性差异最小化作为优化目标的设施布局优化模型,采用粒子群优化算法求解,对北京市养老设施布局进行优化,以期为北京市养老设施规划提供科学依据。

2 数据与方法

2.1 数据来源

本文所使用的数据包括2000年和2010年北京市乡镇和街道级老年人口和区县级人口死亡率数据,2010年北京市道路网络数据,以及2013年北京市养老机构及床位数。本文对老年人口的年龄界定为60岁及以上。2000年和2010年北京市分年龄段老年人数据及死亡率数据分别来自第五次和第六次人口普查数据。根据这些数据预测得到人口自然增长状态下2020年北京市乡镇与街道空间尺度下的老年人口,作为2020年养老设施需求规模及分布的依据。采用乡镇与街道一级居民点作为养老设施候选点,与《北京市养老设施专项规划》的布局建议相一致。乡镇与街道一级行政单元根据2010年第六次人口普查时北京市行政区划获得,共有324个乡镇与街道。养老机构数据来自北京市民政信息(http://www.bjmzj.gov.cn),截至2013年6月17日,采集到383所养老机构统计信息,空间数字化后建立北京市养老机构数据库。

路网数据采用北京市2010年的道路网络,参考已有研究中北京市实际道路速度(邓羽等, 2012),将4级道路的速度依次设置为50、40、30、20 km/h。采用乡镇与街道面图层的几何质心作为人口分布的质心。在ArcGIS平台上采用时间权重的网络分析工具计算每个需求点到每个候选设施点的最短出行时间,作为两者间出行成本。

本文使用中心城区、近郊区、远郊区的概念,其中,中心城区定义为东城、西城、朝阳、海淀、丰台和石景山区等六城区;近郊区为昌平、顺义、通州、大兴和房山区靠近中心城区的部分区域;远郊区为延庆、密云、怀柔、平谷、门头沟及房山区离中心城区较远的部分区域。

2.2 老年人口预测方法

老年人口的空间分布主要受自然增长和机械迁移的影响(易成栋等, 2014)。易成栋等(2014)的研究表明,2010年北京市迁入的老年常住人口仅占老年人口总数的7%,即外来老年人口所占比例很小;因此,自然增长是北京市老年人口变动的主要因素。根据各地区人口年龄结构和死亡率现状可预测自然增长状态下的老年人口。

从人口普查中得到的人口死亡率数据为按5岁分年龄段,而本文预测的时间跨度为10年。对于某一年龄段的人口而言,从基期到预测期要经过两个年龄段,因此将本年龄段和后一年龄段的人口死亡率平均值作为该年龄段在基期和预测期之间的人口死亡率预测值,称为移动平均死亡率。例如,对于2010年60~64岁年龄段的人口,在2020年之前依次经历60~64岁和65~69岁两个年龄段,将这两个年龄段人口死亡率的平均值作为60~64岁年龄段在2010-2020年间的人口死亡率预测值。为得到预测期60岁及以上的老年人口,需要从基期50岁及以上的年龄段开始预测。

由于2020年老年人口死亡率未知,本文将根据2000年和2010年的死亡率变化趋势推测2020年死亡率。考虑到随着社会经济的发展和生活水平的提升,人口死亡率呈现出下降趋势,但北京市的人口发展阶段已进入低出生率低死亡率阶段,人口死亡率下降的趋势应有所放缓。因此假定2010-2020年间人口死亡率下降程度为2000-2010年间的一半,从而预测得到2020年人口死亡率。

对2010-2020年间各年龄段人口死亡率的处理分为两步:第一步,先对2010年和预测的2020年各年龄段的死亡率平均得到2010-2020年间各年龄段的平均死亡率;第二步,对第一步得到的平均死亡率进行前后两个年龄段的移动平均,可表示为:

ai=(bi+bi+1)2,i<nbi,i=n(1)

式中: ai为第i个年龄段的移动平均死亡率,即为预测采用的死亡率; bibi+1分别为第ii+1个年龄段在2010-2020年间的平均死亡率;n为年龄段的个数,值为8。根据各年龄段预测死亡率,结合基期人口数据计算预测期的分年龄段人口数。计算公式为:

Pit=Pi0×(1-ai)m(2)

式中: Pit为第i个年龄段预测人口数; Pi0为第i个年龄段基期人口数; ai为第i个年龄段预测死亡率;m为预测期长度,在本文中为10年。将分年龄段预测值相加就得到各乡镇与街道的预测老年人口。

首先用2000-2010年的人口数据检验方法的有效性。根据2000年老年人口数据以及2000年和2010年死亡率数据,预测得到2010年北京市老年人口为238.3万人,而实际老年人口为246.0万人,预测误差仅为-3.13%,表明该方法是有效的。预测结果表明,在自然增长状态下,2020年北京市老年人口总数为437万人,其中首都功能核心区、城市功能拓展区、城市发展新区和生态涵养发展区分别占老年人口总数的7.9%、50.2%、30.1%和11.8%。在乡镇与街道尺度下,老年人口空间分布呈现中心城区较高、东南多于西北地区的趋势(图1)。2010年北京市老年人口分布则呈现出明显的中心往外递减的趋势,近郊区老年人口密度整体较小,且东南与西北地区差异不大等特点(陶卓霖等, 2014)。对比2010年和2020年的人口分布特点可知,在自然增长状态下,10年间近郊区老年人口增长较快,东南地区的增长明显快于西北地区。

图1   2020年北京市乡镇与街道老年人口空间分布

Fig.1   Spatial distribution of elderly population at subdistrict level in Beijing in 2020

2.3 公平最大化优化模型

设施空间可达性评价是公平最大化模型的基础。有关它的评价方法较多,其中两步移动搜寻法和重力模型法最为常用。Wang(2012)将多种设施空间可达性评价方法综合为统一形式,从而可以同时结合两步移动搜寻法和重力模型法的优点,模型可表达为:

Ai=j=1nSjfdijk=1mDkfdkj(3)

式中: Ai是需求点i的可达性得分; Sj是设施点j的设施规模; Dk是需求点k(i=1, 2,…,n)的需求规模,本文中为老年人口;f是一般化的距离衰减函数; dij( dkj)i(k)和j(k=1, 2,…,m)之间的出行时间。本文中 Ai也可表示需求点i的平均每名老人可获得的养老床位数。

距离衰减函数f包括离散型或连续型。其中,两步移动搜寻法采用离散型距离衰减函数,即认为在某一阈值距离之内可达性均一化,而在阈值之外则不可达。重力模型法则采用指数形式的连续型距离衰减函数。已有研究采用两步移动搜寻法评价了北京市养老设施空间可达性(Cheng, Wang et al, 2012)。研究表明,养老设施和家庭住址之间的距离是老年人口选择养老设施时的一个重要考虑因素(Cheng, Rosenberg et al, 2012; 高晓路, 2013)。但原始形式的两步移动搜寻法忽略了搜寻半径以内的可达性差异,而在其搜寻半径之内加入重力模型的距离衰减函数可以提高可达性评价的准确性。因此,本文所采用的距离衰减函数f可写为:

fdij=dij-β,dijd00,dij>d0(4)

式中: dij是需求点ij之间的出行时间; d0是出行时间阈值,即搜寻半径;β是距离衰减参数。

已有研究中β的取值大多位于0.9~2.29之间(Peeters et al, 2000)。如陶卓霖等(2014)在评价北京市养老设施可达性时将β设为1;Tao等(2014)在养老设施布局优化时对β取值进行了敏感性分析,并对β取值为1时的结果进行了深入讨论。本文也对β取值进行敏感性分析。此外,已有研究指出,北京的老年人及其家庭成员接受的有效服务半径为1~1.5 h(Cheng, 2010),本文采用调查结果中老年人可接受半径的下限1 h作为养老设施的搜寻半径。

经典的区位配置模型关注设施布局的效率。其优化目标包括覆盖人口数最大化(最大覆盖模型)、设施数量最少化(位置集合模型)和需求点到设施的出行成本最小化(p-中位模型)等(Wang, 2012)。很少有研究将公平性作为设施布局优化的目标,其中一个重要原因是难以对设施布局的公平性进行建模(Wang et al, 2013)。Wang等(2013)提出了以需求点到设施的可达性差异最小化为目标的设施布局优化模型,从而实现了设施布局的公平最大化问题,该模型可表达为:

mini=1mAi-a2(5)

a=i=1mDiDAi=SD(6)

式中: Ai是根据式(3)、(4)计算得到的可达性得分;a是可达性的加权平均值;S是总供给规模; Di为为需求点i的需求规模;D是总需求规模。该模型是非线性的二次规划问题,而传统的设施布局优化模型大多是线性的。

2.4 粒子群优化算法

本文采用粒子群优化算法求解公平最大化模型。粒子群优化算法最初由Kenned等(1996)提出,并得到了广泛的应用,可用来求解公平最大化目标的优化模型(Tao et al, 2014)。采用Malab中的粒子群优化工具箱运行粒子群优化算法。算法的参数采用工具箱的默认设定,并把最大迭代次数提增至3000以提升算法的优化效果(表1)。设施候选点为第六次人口普查中的324个乡镇与街道单元,为确保各粒子群所代表的总供给等于给定的总供给规模,将粒子群的维度设为323({ P1,P2,,P323}),则 P324=S-P1-P2-,,-P323。优化后得到最优的 P1,P2,,P324值,即为324个乡镇与街道单元的最优养老设施床位供给数量。

表1   粒子群优化算法参数设置

Tab.1   Parameters in the particle swarm optimization (PSO) solution

参数取值
粒子群个数36
最大迭代次数3000
加速常数c1,c22, 2
X取值范围[0, 2500]
最大速度0.2×X取值范围(2500)
粒子群维度323

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3 养老设施布局优化结果

根据《北京市养老设施专项规划》的政策目标,到2020年满足4%的老年人口选择机构养老方式的需求,本文将2020年北京市养老设施的总供给设定为2020年老年人口的4%,即17.5万张床位。

首先对距离衰减参数β取值进行敏感性分析,比较β不同取值时结果的差异。将β的取值区间设为0.4~1.4,以0.2为间隔设定了6个情景。计算了每个情景下现状和优化后养老设施可达性的标准差,现状标准差与优化后标准差的比例可反映优化效率,比例越大优化效率越高。由表2可知,β取值越大,设施现状布局下的可达性标准差越大,这是因为β越大时,距离衰减效应越强,人们对设施的距离越敏感。最优可达性标准差随着β增大先减小后增大,说明优化结果对β取值的敏感性较强且较复杂,设定β取值时应更为谨慎。现状可达性标准差和最优可达性标准差的比值则先增大后减小。最优可达性标准差在β=1时达到最小值,且现状可达性标准差与最优可达性标准差的比值在β=1时最大,说明在β=1时,优化后的养老设施布局下可达性差异最小,即公平性最大化目标得到最好的体现,而且与现状布局相比优化效率最高。因此,后文中将对β=1时的优化结果作进一步分析和讨论。

表2   现状和最优布局下北京市养老设施可达性标准差

Tab.2   Actual and optimized standard variation of accessibility to residential care facilities (RCFs) in Beijing

β现状可达性标准差最优可达性标准差两者比例
0.40.01400.00453.1110
0.60.01530.00354.3088
0.80.01750.00257.0896
1.00.02070.00248.5163
1.20.02430.00308.2141
1.40.02800.00456.1728

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优化结果中,布局在首都功能核心区、城市功能拓展区、城市发展新区和生态涵养发展区的养老床位数分别占总量的2.7%、32.7%、48.5%和16.1%,接近一半的养老床位布局在城市发展新区(图2)。相比之下,老年人口的分布呈现由中心向外围递减的趋势。首都功能核心区和城市功能拓展区老年人口所占比例分别为7.9%和50.2%,提供的养老床位数比例却仅为2.7%和32.7%;而城市发展新区和生态涵养发展区老年人口比例为30.1%和11.8%,但养老床位数比例却达48.5%和16.1%,尤其是城市发展新区,养老床位数比例相较于老年人口比例高出了18.4%。

图2   2020年北京市养老设施床位优化结果

Fig.2   Spatial distribution of the optimized residential care facility (RCF) beds in Beijing in 2020

上述结果表明,在公平性最大化的目标下,中心城区所提供的机构养老资源不能完全满足本地需求;城市发展新区在满足当地的机构养老需求之外,还可为中心城区提供大量机构养老服务;生态涵养发展区也在满足本地需求的基础上还可为其他地区提供少量机构养老服务。其原因在于,根据北京市老年人口愿意接受的到养老设施的距离,本文将养老设施服务半径设定为1 h。虽然老年人口在核心区以及近郊区尤其是东南地区分布较为集中,但布局在近郊区的养老设施仍能服务在1 h范围内核心区、近郊区以及靠近近郊的远郊老年人口。在公平最大化目标下,养老设施资源倾向于配置在服务范围最广的近郊区,因此核心区的很大一部分需求也由近郊区的养老设施满足。而远郊区的乡镇由于面积较大,大部分地区与近郊区之间的距离较远,因此主要由本地的养老设施提供服务。该布局导向与《北京市养老设施专项规划》提出的布局建议相一致,且符合中心城区用地紧张、郊区自然环境较好的现实情况。

从区县尺度来看(表3),朝阳区和通州区提供的养老床位超过2万张,两者均位于东部地区。提供养老床位数最多的8个区县均位于城市功能拓展区和城市发展新区。首都功能核心区的东城区与西城区优化后可提供的养老床位最少,分别为每百人1.57和1.11张,远远低于每百人4个床位的政策目标。生态涵养发展区的5个区县优化后本地养老床位供给水平均高于每百人7.01张,高于政策目标,但规模较小。在乡镇尺度,平均每个乡镇与街道可提供的养老床位数为539张,且养老床位数呈现近郊区多、中心城区和远郊区少的分布特点,而近郊区内部又呈现东南地区多于西北地区的趋势。

表3   北京市各区县养老床位数的优化结果

Tab.3   Optimized residential care facility (RCF) bed numbers at the district level in Beijing

区县优化后养老床位数/张优化后人均养老床位数/张现状养老床位数/张
朝阳区213294.929444
通州区2019413.913962
大兴区1987615.364910
海淀区178764.818655
昌平区1664510.8812369
房山区1574812.195386
丰台区128454.774610
顺义区1228611.602172
门头沟区835518.222067
密云县52377.552957
石景山区51376.192220
延庆县510410.933061
怀柔区477910.181671
平谷区46327.013093
东城区24091.57298
西城区23431.111377
总计174795-69314

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优化后各乡镇与街道到养老设施的可达性与加权平均值的标准差仅为0.0026,可达性差异达到非常低的水平。相比之下,现状可达性的标准差为0.0207,是优化后的8倍,可见优化效果显著。图3显示了优化之后各乡镇与街道到养老设施可达性与加权平均值0.04的比值,在大多数乡镇与街道该比值为0.95~1.05之间,而小于0.95或大于1.05的乡镇与街道均离散地分布在各区域,进一步验证了优化结果的有效性和可靠性。

图3   北京市养老设施可达性优化结果与优化目标比值分布

Fig.3   Spatial distribution of the ratio of optimized results and optimized objective in Beijing in 2020

图4为各乡镇与街道现状养老床位数与优化后养老床位数之间的差值,正值表示在现状的基础上还需要新增养老床位,负值则表示养老床位数应适当减少。由于北京市老年人口的快速增长,到2020年时将由2010年的235万人增至437万人,因此大部分乡镇与街道还需要新增养老床位。需要新增养老床位较多的乡镇与街道主要位于近郊区,其中东南部的通州区和大兴区最多。中心城区和北部远郊区新增养老床位较少,并有少量乡镇与街道的养老床位过剩,即现状的养老床位数已多于优化后2020年的供给水平。这些养老床位过剩的乡镇与街道大多数属于现状养老设施布局的热点区域,例如位于昌平区的十三陵镇和小汤山镇分别需减少1000张以上床位。这是因为上述养老机构分布的热点区域大多位于自然环境较舒适的地区,现状布局受自然环境和私营养老机构集聚效应的双重影响。在规划布局时,不能简单判断这些热点区域的过剩供给是否合理,需要对其养老设施的实际入住情况作进一步的调查和分析。

图4   北京市现状养老设施与优化结果差值

Fig.4   Gaps between the optimal and actual numbers of residential care facility (RCF) beds in Beijing

4 结论与讨论

4.1 结论

本文基于预测的2020年北京市老年人口分布,按照“到2020年将为4%的老年人提供机构养老服务”的政策目标,将公平最大化模型应用于养老设施布局优化研究。主要得到以下几条结论:

(1) 公平最大化模型的优化效果显著,优化后可达性的标准差仅为0.0026,远低于现状可达性标准差0.0207。

(2) 最优布局中城市发展新区是养老设施建设的重点区域,在满足当地机构养老需求外,还将为中心城区(首都功能核心区和城市功能拓展区)提供大量机构养老服务;生态涵养发展区在满足本地需求基础上还可为其他地区提供少量机构养老服务。

(3) 最优布局与《北京市养老设施专项规划》提出的布局建议相一致,且符合中心城区用地紧张、郊区自然环境较舒适的现实情况。

(4) 与基于老年人口分布现状的最优布局相比,养老设施资源向北京市东南部近郊区的集聚更为明显,说明基于预测老年人口分布进行优化的必要性。

4.2 讨论

本文的主要创新之处在于建立了基于2020年预测老年人口分布的公平最大化模型,既能将设施布局的公平性目标模型化,又能与2020年规划期限相一致,为中国包括养老设施在内的公共服务设施布局提供了重要的研究方法和模型工具,具有重要的理论和现实意义。此外,本文在以下几方面均具有一定创新性:采用粒子群优化算法作为求解算法,为公平最大化优化模型求解提供了新的方法;针对距离衰减参数取值进行敏感性分析,为模型关键参数的设置提供了更科学的依据;将2020年最优与现状布局作比较分析,为在现状布局基础上调整和优化养老设施布局提供了更直观的结果。

本文也存在一些局限与不足。一是未考虑社会经济及养老设施与医疗资源等因素对老年人口选择养老设施的综合影响。二是在人口预测中只考虑了老年人口的自然增长。虽然对2000-2010年间的老年人口数据检验显示预测误差仅为-3.13%,但老年人口在北京市内迁移的情况仍然需要进一步研究。在未来研究中,将考虑老年人口的市内迁移,以提升对其预测的准确性。此外,还将考虑不同优化目标下(如效率和公平目标)设施布局的差异。以期使研究结果能为养老政策的制定提供科学依据,所采用的方法也能为其他类型公共服务设施的布局优化提供借鉴。

The authors have declared that no competing interests exist.


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发展养老服务是当前中国社会建设中的重要部分.近年来,北京市养 老设施发展迅速,但是由于快速的人口老龄化,北京市养老设施的供给仍难以满足老年人口对养老设施的需求.对北京市养老设施空间可达性进行科学评价是进行合 理空间配置的基础,具有重要的现实意义.本文基于GIS技术,应用改进的两步移动搜索法,对北京市养老设施的空间可达性进行了测算,并重点对1小时单一有 效服务半径和按养老设施规模划分的三级有效服务半径这两种情形进行了比较分析.结果表明,后者对北京市养老设施的空间可达性评价更具合理性.本文对空间可 达性的测算结果识别出了北京市各区域养老设施的稀缺程度,为养老设施的空间布局提出了政策性建议.

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Measuring spatial accessibility to residential care facilities in Beijing

[J]. Progress in Geography, 33(5): 616-624.]

https://doi.org/10.11820/dlkxjz.2014.05.003      URL      Magsci      [本文引用: 5]      摘要

发展养老服务是当前中国社会建设中的重要部分.近年来,北京市养 老设施发展迅速,但是由于快速的人口老龄化,北京市养老设施的供给仍难以满足老年人口对养老设施的需求.对北京市养老设施空间可达性进行科学评价是进行合 理空间配置的基础,具有重要的现实意义.本文基于GIS技术,应用改进的两步移动搜索法,对北京市养老设施的空间可达性进行了测算,并重点对1小时单一有 效服务半径和按养老设施规模划分的三级有效服务半径这两种情形进行了比较分析.结果表明,后者对北京市养老设施的空间可达性评价更具合理性.本文对空间可 达性的测算结果识别出了北京市各区域养老设施的稀缺程度,为养老设施的空间布局提出了政策性建议.
[7] 席晶, 程杨. 2015.

北京市养老机构布局的时空演变及政策影响

[J]. 地理科学进展, 34(9): 1187-1194.

https://doi.org/10.18306/dlkxjz.2015.09.011      URL      [本文引用: 1]      摘要

近年来,随着老年人口的迅速增 长和家庭照料资源的减少,机构养老服务在北京市得到快速发展。本文采用文献分析和空间分析的方法,研究了北京市机构养老服务发展的历程,探析了养老机构布 局的时空演变过程及其政策影响因素。研究表明:1北京市养老机构的发展分为萌芽期(1953-1959年)、停滞期(1960-1977年)、增长期 (1978-1995年)和繁荣期(1996-2012年)4个阶段,各阶段具有不同的空间分布特征;2在区县尺度,机构养老服务的发展阶段和布局现状存 在空间差异。延庆县、怀柔区、顺义区、密云县、平谷区、门头沟区养老机构的发展主要处于增长期,呈现出增长期的布局特征;而昌平区、房山区、大兴区和通州 区养老机构的增长主要处于繁荣期,并呈现出这一时期的布局特征;3老年政策不仅影响了养老机构的总体规模,并且对各类所有制养老机构的发展历程与空间布局 产生了不同影响。

[Xi J, Cheng Y.2015.

Spatiotemporal evolution of residential care facilities in Beijing and policy impacts

[J]. Progress in Geography, 34(9): 1187-1194.]

https://doi.org/10.18306/dlkxjz.2015.09.011      URL      [本文引用: 1]      摘要

近年来,随着老年人口的迅速增 长和家庭照料资源的减少,机构养老服务在北京市得到快速发展。本文采用文献分析和空间分析的方法,研究了北京市机构养老服务发展的历程,探析了养老机构布 局的时空演变过程及其政策影响因素。研究表明:1北京市养老机构的发展分为萌芽期(1953-1959年)、停滞期(1960-1977年)、增长期 (1978-1995年)和繁荣期(1996-2012年)4个阶段,各阶段具有不同的空间分布特征;2在区县尺度,机构养老服务的发展阶段和布局现状存 在空间差异。延庆县、怀柔区、顺义区、密云县、平谷区、门头沟区养老机构的发展主要处于增长期,呈现出增长期的布局特征;而昌平区、房山区、大兴区和通州 区养老机构的增长主要处于繁荣期,并呈现出这一时期的布局特征;3老年政策不仅影响了养老机构的总体规模,并且对各类所有制养老机构的发展历程与空间布局 产生了不同影响。
[8] 易成栋, 张纯, 吴淑萍, . 2014.

2000-2010年北京市老年人口空间分布及其变动研究

[J]. 城市发展研究, 21(2): 66-71.

https://doi.org/10.3969/j.issn.1006-3862.2014.02.011      URL      [本文引用: 1]      摘要

中国已成为老龄化国家,且有加速趋势.北京的老龄化程度和速度超过了全国平均水平.根据第 五、六次人口普查资料以三种空间单元分析了北京老年人口的空间分布特征及发展趋势.研究表明,老年人口数量在城区呈圈层式集中分布,在郊区呈点状分布;高 老龄化率地区集中在城市中心区和生态涵养区西部和北部山区,其他地方较低;高老龄化率地区出现了空间扩散趋势;老年人口的居住隔离程度较低,且有所上升. 老年人口空间分布变动的直接原因是本地老年人口的增长和迁移;老龄化率的空间分布变动的直接原因是非老年人口和老年人口的增长和迁移.影响它们的因素有城 市规划、建设与管理政策、社会保障和老年福利政策、市场等因素.最后提出了相应的政策建议.

[Yi C D, Zhang C, Wu S P, et al.2014.

Spatial restructuring of senior population in Beijing from 2000-2010

[J]. Urban Development Studies, 21(2): 66-71.]

https://doi.org/10.3969/j.issn.1006-3862.2014.02.011      URL      [本文引用: 1]      摘要

中国已成为老龄化国家,且有加速趋势.北京的老龄化程度和速度超过了全国平均水平.根据第 五、六次人口普查资料以三种空间单元分析了北京老年人口的空间分布特征及发展趋势.研究表明,老年人口数量在城区呈圈层式集中分布,在郊区呈点状分布;高 老龄化率地区集中在城市中心区和生态涵养区西部和北部山区,其他地方较低;高老龄化率地区出现了空间扩散趋势;老年人口的居住隔离程度较低,且有所上升. 老年人口空间分布变动的直接原因是本地老年人口的增长和迁移;老龄化率的空间分布变动的直接原因是非老年人口和老年人口的增长和迁移.影响它们的因素有城 市规划、建设与管理政策、社会保障和老年福利政策、市场等因素.最后提出了相应的政策建议.
[9] Andrews G J, Phillips D R.2002.

Changing local geographies of private residential care for older people 1983-1999: lessons for social policy in England and Wales

[J]. Social Science & Medicine, 55(1): 63-78.

https://doi.org/10.1016/S0277-9536(01)00207-6      URL      PMID: 12137189      [本文引用: 1]      摘要

The population structures of many developed countries are changing and shifts towards much older age distributions are common. One way of meeting the resulting increasing demand for long-term care is through small business private sector provision allocated through market systems. However, the private residential care sector in England and Wales demonstrates some of the potential problems of leaving long-term care to the market. During the 1980s, the private residential sector for older persons enjoyed substantial state financed support. Since the 1990 National Health Service and Care in the Community Act introduced markets in social care in 1993, homes have had to compete amongst each other for a much smaller number of clients funded by limited local authority budgets. This impacted on their business and caring operations. Based on a three-stage quasi-longitudinal survey of over 100 residential care homes in one county, this paper considers changes in the overall size and structure of a local sector, discusses the specific management strategies that have been adopted by proprietors and the development of a purchasing and providing market culture. The paper also highlights the importance of interdisciplinary perspectives on the topic by illustrating how changes in social policy can influence local and national geographies of long-term care provision and how, in turn, an understanding of these geographies can inform the sensitive implementation of future social policy initiatives.
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[11] Cheng Y, Rosenberg M W, Wang W Y, et al.2011.

Aging, health and place in residential care facilities in Beijing, China

[J]. Social Science & Medicine, 72(3): 365-372.

https://doi.org/10.1016/j.socscimed.2010.10.008      URL      PMID: 21109338      [本文引用: 1]      摘要

In recent years, residential care has become an alternative option for elder care in Beijing, China. Little is known, however, about the well-being of elderly residents and the relationship between their health and living in residential care facilities (RCFs). Hence this research aims to understand the well-being of elderly residents in RCFs and how the environment of RCFs affects elderly people's everyday activities and health. The concepts of therapeutic landscapes, active aging, and well-being contribute to understanding the relationships among aging, health, and environment within RCF settings. Qualitative data from 46 in-depth semi-structured interviews with RCF managers, elderly residents, and family members in Beijing were transcribed and analysed using the constant comparative method. The results show that most of the elderly residents are satisfied with their lives in RCFs, but a few of them feel isolated and depressed after their relocation. Each RCF, as a place with its unique physical and social environment, has a significant influence on the elderly residents' physical and psychological well-being. Individual factors such as characteristics of elderly residents, their attitudes on aging and residential care, and family support also play important roles in their adaptation and well-being after relocation from home to RCFs. Although this study focuses on residential care at the local level, it sheds light on future research on geographical and socio-cultural meanings of elder care at local, regional, and national levels in China.
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Access to residential care in Beijing, China: making the decision to relocate to a residential care facility

[J]. Ageing and Society, 32(8): 1277-1299.

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Spatial access to residential care resources in Beijing, China

[J]. International Journal of Health Geographics, 11(1): 32.

https://doi.org/10.1186/1476-072X-11-32      URL      PMID: 22877360      [本文引用: 3]      摘要

Background: As the population is ageing rapidly in Beijing, the residential care sector is in a fast expansion process with the support of the municipal government. Understanding spatial accessibility to residential care resources by older people supports the need for rational allocation of care resources in future planning. Methods: Based on population data and data on residential care resources, this study uses two Geographic Information System (GIS) based methods--shortest path analysis and a two-step floating catchment area (2SFCA) method to analyse spatial accessibility to residential care resources. Results: Spatial accessibility varies as the methods and considered factors change. When only time distance is considered, residential care resources are more accessible in the central city than in suburban and exurban areas. If care resources are considered in addition to time distance, spatial accessibility is relatively poor in the central city compared to the northeast to southeast side of the suburban and exurban areas. The resources in the northwest to southwest side of the city are the least accessible, even though several hotspots of residential care resources are located in these areas. Conclusions: For policy making, it may require combining various methods for a comprehensive analysis. The methods used in this study provide tools for identifying underserved areas in order to improve equity in access to and efficiency in allocation of residential care resources in future planning.
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Optimization of preventive health care facility locations

[J]. International Journal of Health Geographics, 9(1): 17.

https://doi.org/10.1186/1476-072X-9-17      URL      PMID: 20298608      [本文引用: 1]      摘要

BACKGROUND: Preventive health care programs can save lives and contribute to a better quality of life by diagnosing serious medical conditions early. The Preventive Health Care Facility Location (PHCFL) problem is to identify optimal locations for preventive health care facilities so as to maximize participation. When identifying locations for preventive health care facilities, we need to consider the characteristics of the preventive health care services. First, people should have more flexibility to select service locations. Second, each preventive health care facility needs to have a minimum number of clients in order to retain accreditation. RESULTS: This paper presents a new methodology for solving the PHCFL problem. In order to capture the characteristics of preventive health care services, we define a new accessibility measurement that combines the two-step floating catchment area method, distance factor, and the Huff-based competitive model. We assume that the accessibility of preventive health care services is a major determinant for participation in the service. Based on the new accessibility measurement, the PHCFL problem is formalized as a bi-objective model based on efficiency and coverage. The bi-objective model is solved using the Interchange algorithm. In order to accelerate the solving process, we implement the Interchange algorithm by building two new data structures, which captures the spatial structure of the PHCFL problem. In addition, in order to measure the spatial barrier between clients and preventive health care facilities accurately and dynamically, this paper estimates travelling distance and travelling time by calling the Google Maps Application Programming Interface (API). CONCLUSIONS: Experiments based on a real application for the Alberta breast cancer screening program show that our work can increase the accessibility of breast cancer screening services in the province.
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https://doi.org/10.1016/S0377-2217(98)00186-6      URL      [本文引用: 1]      摘要

Facility location decisions are a critical element in strategic planning for a wide range of private and public firms. The ramifications of siting facilities are broadly based and long-lasting, impacting numerous operational and logistical decisions. High costs associated with property acquisition and facility construction make facility location or relocation projects long-term investments. To make such undertakings profitable, firms plan for new facilities to remain in place and in operation for an extended time period. Thus, decision makers must select sites that will not simply perform well according to the current system state, but that will continue to be profitable for the facility's lifetime, even as environmental factors change, populations shift, and market trends evolve. Finding robust facility locations is thus a difficult task, demanding that decision makers account for uncertain future events. The complexity of this problem has limited much of the facility location literature to simplified static and deterministic models. Although a few researchers initiated the study of stochastic and dynamic aspects of facility location many years ago, most of the research dedicated to these issues has been published in recent years. In this review, we report on literature which explicitly addresses the strategic nature of facility location problems by considering either stochastic or dynamic problem characteristics. Dynamic formulations focus on the difficult timing issues involved in locating a facility (or facilities) over an extended horizon. Stochastic formulations attempt to capture the uncertainty in problem input parameters such as forecast demand or distance values. The stochastic literature is divided into two classes: that which explicitly considers the probability distribution of uncertain parameters, and that which captures uncertainty through scenario planning. A wide range of model formulations and solution approaches are discussed, with applications ranging across numerous industries.
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Distance predicting functions and applied location-allocation models

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https://doi.org/10.1007/PL00011453      URL      Magsci      [本文引用: 1]      摘要

Distances between demand points and potential sites for implementing facilities are essential inputs to location-allocation models. Computing actual road distances for a given problem can be quite burdensome since it involves digitalizing a network, while approximating these distances by l p -norms, using for instance a geographical information system, is much easier. We may then wonder how sensitive the solutions of a location-allocation model are to the choice of a particular metric. In this paper, simulations are performed on a lattice of 225 points using the k -median problem. Systematic changes in p and in the orientation of the orthogonal reference axes are used. Results suggest that the solutions of the k -median are rather insensitive to the specification of the l p -norm.
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Geographical change in residential care provision for the elderly in England, 1988-93

[J]. Health & Place, 4(1): 15-31.

https://doi.org/10.1016/S1353-8292(97)00029-4      URL      PMID: 10671008      [本文引用: 1]      摘要

This paper offers an investigation of the spatial consequences of changes in the structural organization of residential care in England between 1988 and 1993. Data from various government publications were analysed using descriptive and spatial statistical methods. While the study period witnessed an overall levelling of residential care growth, the independent (i.e. private and voluntary) sector's share of all elderly residents in England increased from 56% to 73%. At both national and intra-regional scales, the structural changes resulted in an increasing geographical concentration of public sector residents and a moderate trend towards a more uniform spatial distribution of private residents.
[21] Tao Z L, Cheng Y, Dai T Q, et al.2014.

Spatial optimization of residential care facility locations in Beijing, China: maximum equity in accessibility

[J]. International Journal of Health Geographics, 13(1): 33.

https://doi.org/10.1186/1476-072X-13-33      URL      PMID: 25178475      摘要

Background The residential care system is rapidly developing and plays an increasingly important role in care for the elderly in Beijing. A noticeable disparity in the accessibility to
[22] Wang F H.2012.

Measurement, optimization, and impact of the health care accessibility: a methodological review

[J]. Annals of the Association of American Geographers, 102(5): 1104-1112.

https://doi.org/10.1080/00045608.2012.657146      URL      PMID: 23335813      [本文引用: 2]      摘要

Despite spending more than any other nation on medical care per person, the United States ranks behind other industrialized nations in key health performance measures. A main cause is the deep disparities in access to care and health outcomes. Federal programs such as the designations of Medically Underserved Areas/Populations and Health Professional Shortage Areas are designed to boost the number of health professionals serving these areas and to help alleviate the access problem. Their effectiveness relies first and foremost on an accurate measure of accessibility so that resources can be allocated to truly needy areas. Various measures of accessibility need to be integrated into one framework for comparison and evaluation. Optimization methods can be used to improve the distribution and supply of health care providers to maximize service coverage, minimize travel needs of patients, limit the number of facilities, and maximize health or access equality. Inequality in health care access comes at a personal and societal price, evidenced in disparities in health outcomes, including late-stage cancer diagnosis. This review surveys recent literature on the three named issues with emphasis on methodological advancements and implications for public policy.
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Planning toward equal accessibility to services: a quadratic programming approach

[J]. Environment and Planning B: Planning and Design, 40(2): 195-212.

https://doi.org/10.1068/b37096      URL      [本文引用: 1]      摘要

In the literature various accessibility indices have been developed to assess the relative ease by which the locations of services (supply) can be reached from a residential (demand) location. In this paper we address the planning problem: how the resources can be redistributed to achieve the highest equality of accessibility to the service providers. In particular, a quadratic programming approach is used to minimize the variance of accessibility scores across demand locations by readjusting the amounts of service supplies. Two case studies—job access in Columbus, OH and primary healthcare access in Chicago, IL—are used to illustrate the method. The result suggests that in order to achieve better equality of accessibility, peripheral areas, in general, need additional supplies to compensate for their less-central locations, and some central city areas also need to add supplies to accommodate high demands by the high population density there. Keywords: accessibility index, equal accessibility, quadratic programming, job access, health-care access
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Placing elderly parents in institutions in urban China: a reinterpretation of filial piety

[J]. Research on Aging, 30(5): 543-571.

https://doi.org/10.1177/0164027508319471      URL      摘要

The authors examined changing attitudes about filial piety, or xiao , using data from intensive interviews with 20 elderly residents, 14 family members, and 9 staff members in Nanjing, China. The findings reveal that respondents interpreted the notion of xiao in terms of their own social worlds and on the basis of their own social locations and contexts. The increasing unavailability of adult children, various benefits of institutional care, and children鈥檚 financial assistance for older parents are major explanations for xiao behaviors, even when elders are placed in institutions. The high cost of professional care in institutions is contributing to a shift in attitudes about institutional elder care from stigma to privilege. The authors argue that China can expect an increasing need and demand for elder care institutions as a large number of Chinese baby boomers retire.
[25] Zhan H J, Liu G Y, Bai H G.2005.

Recent development in Chinese elder homes: a reconciliation of traditional culture

[J]. Ageing International, 30(2): 167-187.

https://doi.org/10.1007/s12126-005-1010-2      URL      Magsci      [本文引用: 1]      摘要

This paper examines recent developments in elder care homes and changing attitudes toward institutional care in the Tianjin area of China. Based on research conducted at 12 sites, this study compares
[26] Zhan H J, Liu G Y, Guan X P.2006.

Willingness and availability: explaining new attitudes toward institutional elder care among Chinese elderly parents and their adult children

[J]. Journal of Aging Studies, 20(3): 279-290.

https://doi.org/10.1016/j.jaging.2005.09.006      URL      [本文引用: 1]      摘要

This paper studies the attitudes of Chinese elderly parents and their family members toward institutional elder care. Based on a sample survey of 265 elderly residents in 67 elder home institutions and 114 family members, this study finds that elders and family members generally had high evaluations of institutions' quality in terms of facility, medical, and direct care conditions. Elders who reported improved health and emotional well-being after entering institutions gave higher ratings to those institutions' quality. Among adult children, those who had more siblings tended to rate institutions higher than those who had fewer siblings. Factors that influenced elders' willingness to stay in an institution included marital status and financial ability. Widowed elders were more willing to stay in institutions compared with married counterparts. Elders who rated service charge very high preferred to stay at home due to the high cost of institutional care. In the family relatives' sample, gender was found to be related to willingness to place elderly parents in an institution; female children were less willing to place elderly parents in the institution.

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