宋正娜
, 颜庭干, 刘婷, 黄涛
南京信息工程大学,南京 210044
SONG Zhengna, YAN Tinggan, LIU Ting, HUANG Tao
版权声明: 2016 地理科学进展 《地理科学进展》杂志 版权所有
基金资助:
作者简介:
作者简介：宋正娜(1980-),女,山东潍坊人,博士,讲师,主要从事城市发展与区域规划研究,E-mail: songzhengna@163.com。
展开
摘要
区位—分配模型是实现公共服务设施最适配置的有效方法之一。传统的P中值模型以效率作为导向,采用“邻近分配”规则,不考虑设施容量(规模),难以适应城市综合医院供需之间相互作用规律下适度均衡、居民随机概率式选择和区位与规模同步求解的布局要求。本文尝试以P中值模型为基础框架,在对P中值模型来源及其适用性进行分析的基础上,构建出基于供需双方(居民—综合医院)空间相互作用的重力P中值模型。新模型通过纳入“邻近就医”最大出行成本因子,确保居民至少邻近1所综合医院(保障空间公平);通过追求总加权出行成本最小化,确保设施空间配置效率;通过纳入设施容量规模因子实现设施区位和规模同时求解;通过纳入最小规模因子,保障设施规模效率和服务质量公平。进一步通过无锡市区综合医院空间配置进行实证检验发现：采用新模型优化后,综合医院空间配置更加公平、居民邻近就医更加便捷,且能够实现与社区卫生设施协同布局,使整个医疗设施体系空间布局更加合理。本文构建的新重力P中值模型(模型的变量参数可作适当调整)可用于竞争型公共设施区位决策,为相关设施布局调整或者规划提供决策依据。
关键词：
Abstract
Location-allocation model is one of the best methods to find the optimal location of public service facilities. Traditional p-median model takes efficiency as a major criterion and applies the adjacency rule—that is, allocating the residents of every demand site to the closest facility, neglecting difference in facilities’ capacity (scale). Hence it is difficult to adapt such model to certain distribution requirements of urban comprehensive hospitals that are moderate equilibrium—residents select comprehensive hospital stochastically with certain probability and location and capacity calculation of the facilities should be solved synchronously due to the spatial interaction between supply and demand. In order to address this type of location-allocation problem, we take the P-median model as the basic framework and discuss the development and applicability of the model, then construct a gravity P-median model based on the spatial interaction between the residents (demand) and urban comprehensive hospitals (supply). The new model makes some improvements in a number of aspects. First, spatial equality, that is, all residents can conveniently reach at least one comprehensive hospital, can be ensured by incorporating the highest travel cost (from the demand site to the adjacent hospital) factor. Second, spatial allocation efficiency is guaranteed through the pursuit of minimizing total weighted travel cost. Third, facility location decision and scale configuration are solved simultaneously by incorporating a facilities’ capacity factor. Fourth, facility scale efficiency and fairness of service quality are ensured by incorporating the minimum scale factor. Furthermore, through the empirical test in Wuxi City comprehensive hospital spatial configuration, the new model is validated and considered effective and practical. After optimization using the new model, compared with the current distribution the new spatial allocation of urban comprehensive hospitals is more equitable and more convenient for residents in the service areas to access; the collaborative distribution of comprehensive hospitals and community health service institutions can be achieved, and therefore the spatial distribution of the health facilities is more reasonable. Instead of practical applications, this study focused on the theoretical approach of model building, so some parameters need to be adjusted based on the supply and demand change when such model is applied to practical planning. It should be noted that such new model gives a relative optimal distribution result, which can support certain decision making for future public facility distribution adjustments or new town construction, meanwhile enrich research on public facility location allocation both in China and abroad.
Keywords：
寻找最佳区位是公共服务设施规划布局的核心问题(王铮等, 2005),区位—分配模型(Location-Allocation Model,LA模型)是实现各类设施最适配置的有效方法之一(Drezner et al, 2002; 陈忠暖等, 2006; 叶嘉安等, 2006; 周小平, 2007),其基本原理是要使设施位于可达性最佳的区位(叶嘉安等, 2006)。自20世纪60年代泰兹公共设施区位理论诞生以来,平衡公平—效率的公共设施区位决策问题便持续引起运筹管理、地学与规划各领域学者的极大热情与关注。在此后的50多年中,各领域学者推动发展了多种情景下数量丰富的公共设施扩展选址问题。纵观其发展历程,区位分配模型的研究方兴未艾,但因绝大部分模型求解属于NP-hard或NP-complete问题(Owen et al, 1998),在较大程度上制约了模型的创新发展与应用推广。
经典的LA模型包括P中值模型、P中心模型、最大覆盖模型,通常用于解决确定性设施区位选址问题(Owen et al, 1998)。P中值模型致力于寻找消费者总出行成本最小化目标下的设施(相对)理想区位,适用于空间效率导向、对出行成本敏感度有限的非紧急型公共设施(如二、三级综合医院);P中心模型以实现至所有设施的最大出行成本最小化为目标,适用于空间公平导向、对出行成本较为敏感的非紧急型公共设施(如社区卫生服务中心);最大覆盖模型力图在合理出行成本下覆盖尽可能多的需求人口,适于完全或部分覆盖的紧急型公共设施(如急救、消防设施)。其中针对P中值模型的扩展、改进及应用相对更为活跃。
若以上述三类模型作为候选,对于综合医院而言,更适于选用P中值模型进行区位选址。一方面,“小病到社区、大病上医院”的分级诊疗模式决定了综合医院的兜底性质——主要解决“经过社区卫生服务机构初次过滤以后的重大疾病和疑难杂症”,这一职能分工赋予综合医院非紧急性。居民选择综合医院首要考虑因素是其技术实力,距离远近只是次要的参考因素;另一方面,综合医院的职能分工要求其具有较高的规模门槛(与技术实力相对应),并且对应较多的服务人口,同时政府公共财政又是有限的(综合医院的建造和营运成本相对较高),这共同决定了综合医院的数量较为有限。非紧急性、设置数量有限性与居民使用频率较低共同决定了综合医院的布局导向以空间效率为主,让所有居民从总体上更快捷地到达综合医院,这与P中值模型目标较为吻合。
通常情况下,居民在未确诊前,可能选择任一医院,选择意愿强度与医院服务能力(大部分居民难以准确获取医院的医疗技术及其服务水平相关信息,往往以卫技人员数、床位数等医院规模作为判断其服务能力的依据)呈正相关,与空间出行成本呈负相关。居民与综合医院之间的此类相互作用特点与随机概率式重力规则高度契合。因此,P中值模型的“邻近分配”规则难以准确表述综合医院的供需作用特点。同时,P中值模型以效率作为导向,无法兼顾综合医院作为社会性公共设施的公平性诉求,且该模型不考虑设施容量(规模),致使区位与规模求解须两步完成,而以“邻近分配”规则求算的规模相悖于现实中居民相对自由随机式的需求选择行为规律。有鉴于此,城市综合医院的区位决策,需针对P中值模型的局限性作出修改。
值得一提的是,有关设施选址的学术探讨中,针对P中值模型的改进与扩展从未停止。例如Khumawala(1973)于1973年提出了最大极限距离限制下的P中值模型;Carreras等(1999)于1999年提出了受最小服务规模限制的P中值模型;Drezner等(2001, 2006, 2007, 2011)自2001年以来将P中值模型与重力规则相融合构建出一系列复杂的重力P中值模型,并利用模拟数据进行了求解,其研究思路对本文具有较大启发。已有研究或侧重模型局部改进,或将模拟现实情景的空间相互作用引入以构建新模型框架,但在吸收上述思路的基础上形成一个完整框架的研究鲜有出现,且针对规模甄选与求解的文献亦亟需推进。
上述重力P中值模型正逐步引起运筹与管理学领域的浓厚兴趣,这类融入空间相互作用原理的系列模型便是以随机式规则将顾客(往往以居民点进行抽象表征)分配至备选设施。这是一类能够有效揭示现实消费行为规律的仿真模型,既充分纳入供需之间的空间相互作用关系,又继承并优化了传统的区位分配模型,可为综合医院区位决策与优化问题提供新的解决思路。已有部分学者进行了实验模拟或实证分析,其中Ammari等(2000)、Drezner等(2006, 2007, 2011)、Yasenovskiy等(2007)、万波(2012)分别对多等级医疗设施区位选址、重力P中值模型构建思路及基于模拟数据的算法、服务器区位决策、基于Huff重力模型与最大覆盖模型对小学的选址等问题展开探讨。综合来看,国外已有系列空间交互模型取得了较大进展,但研究范式及现实适用性仍待改进;而国内研究较为少见,尚处于发轫期。
本文尝试以P中值模型为基础框架,构建基于居民(需求方)与城市综合医院(供给方)之间的空间相互作用,兼顾设施空间配置公平—效率,包含设施容量规模因子和最小规模限制(保障规模效率和质量公平)的新重力P中值模型(不同于Drezner等构建的重力P 中值模型(Drezner et al, 2001, 2006, 2007, 2011),并将其应用于无锡市区综合医院区位选择,以检验模型合理性。相比已有研究,新构建的重力P中值模型实现了同时将设施容量计算、最小规模限制、邻近设施最大出行成本限制、概率分配规则(重力规则)统一纳入一个模型框架,能够更加准确、全面地模拟现实情景下居民对于综合医院特定条件下的需求选择规律,且能够实现空间效率为主导、兼顾公平的适度均衡配置目标。新模型致力于相对有效地解决有限财政框架内的供—需失衡矛盾,可为政府部门配置公共资源提供决策依据,其区位优化选择模式可为其他设施区位配置提供借鉴。
需要说明的是,多数区位模型属于NP-hard或NP-complete问题,其求解本身即是一个较大挑战。大多数考虑未来不确定性因素的区位问题往往都转化为静态的确定性问题(Owen et al, 1998),竞争型区位选址问题(重力P中值模型归属于竞争型随机问题,计算理想解具有相当难度)囿于其复杂性更着重探讨确定性问题(即使考虑随时间连续规律性变化的模型参数取值,纳入了“动态”理念,也仍然属于确定性问题范畴)。而国外绝大多数研究应用空间相互作用建模时也都设置在一个静态的或比较静态的框架内,且采用少量数据或模拟数据进行检验(Ammari et al, 2000; Drezner et al, 2011; Carling et al, 2015)。本文构建的模型亦为针对静态确定性选址问题,但新模型本身属于随机区位问题,又纳入了规模因子进行求解,并且运用无锡市区系列较大规模数据进行检验,这3个因素共同抬高了模型的复杂性与求解难度。
P中值问题(也译作P中位问题)是由Hakimi(1964)在1964年提出的,是指在已知需求点集合位置、需求数量和设施备选点集合位置的情况下,分别为P个设施找到合适的位置并指派每个需求点到一个特定的设施,使之达到连接需求点和设施点的总加权出行成本(距离、时间、费用等)最低(图1)。
用数学式表达所得P中值模型如下：
式中：Z表示目标函数;M表示m个需求点的集合,M={1, 2, …, m};N为n个设施备选点的集合,N={1, 2, …, n};i为需求点的编号,代表需求点的特定位置;j为设施备选点的编号,代表可能设施点的位置;P为设施配置的数量;Wi为需求点的需求量(通常采用人口数量);Dij为需求点i与设施j之间的出行成本(距离、时间、费用等);Xj为0/1决策变量,取1表示位置j有设施设置,取0表示位置j无设施设置;Yij为0/1决策变量,取1表示设施j为需求点i提供服务,取0表示设施j不为需求点i提供服务。
图1 P中值问题示意图,假设设施数为3
Fig.1 The diagrammatic sketch of P-median problem, assuming that the number of facilities is three
式(1)的目标在于使需求点与最近设施之间总的加权出行成本最小化;式(2)表示研究区域内需要配置P个设施;式(3)表示每个需求点只允许被分配到一个设施;式(4)约束需求点只允许被分配到有设施存在的位置;式(5)表示在j位置设置或不设设施;式(6)表示需求点i与设施可能位置点j之间只有被服务(取值为1)与未被服务(取值为0)两种关系。
Hakimi(1964)最早将P中值模型应用于通讯网络的交换中心布局问题,现今P中值及其改进模型主要用于解决网络型(设施备选点都在网络的节点上)、静态(参数不随时间变化)、确定性(需求被指定到确定的设施,不能自由随机选择)的区位—分配问题(static and deterministic location probelms)(Owen et al, 1998),在商业(Revelle, 1986; 宋广飞, 2008)、物流(Klose et al, 2005; 陈建国, 2005)、教育(Pizzolato et al, 1997)、医疗(Møller-Jensen et al, 2001)、避难(刘少丽, 2012)等各类设施选址决策中得到广泛应用。
P中值模型以效率作为导向,采用“邻近分配”规则,不考虑设施容量(规模)。P中值模型通过决定需求点与目标设施点之间的总出行成本来衡量设施布局有效性(Church et al, 1976),其目的在于追求总出行成本最小化,具有单一的效率导向。LA模型中最重要的部分是分配规则,即将需求分配给设施的方式(Ammari et al, 2000),P中值模型采用“邻近分配”规则,即每个需求点仅与最邻近的一个设施建立联系;“邻近分配”在一定情境下是符合需求选择逻辑的,即中央控制之下而非客户的自由选择,并且当设施具有同等吸引力时的需求分配(Drezner et al, 2006, 2011),这时设施之间不存在对于需求者的竞争,英、美、中等国通行的学区制(分片划区管理、指定就近入学)就是最典型的“邻近分配”。对于采用“邻近分配”规则的设施,可分两步确定设施容量规模：首先通过P中值模型确定设施位置,同时也就确定了相对应的需求点;然后再根据每一个设施服务的需求点规模总和计算相应设施容量规模。
P中值问题属于NP-Hard问题(Garey et al, 1979),P中值模型由于采用单一效率目标、“邻近分配”规则,但忽略了设施容量,因而模型数学表达式相对简单,一定程度上降低了模型的求解难度。但也限制了模型的应用,单一追求效率容易导致设施配置远离部分人口分散地区,使得模型不适用于具有一定公平性要求的设施配置问题;“邻近分配”规则假定需求者选择设施的标准仅凭出行成本而定,忽略不同设施带来的对于需求者的吸引力差异,也不能适应竞争环境下设施配置的要求(Drezner et al, 2007, 2011; Carling et al, 2015);基于设施区位决策和规模计算分两步,也使得模型无法解决非“邻近分配”设施的规模计算。
P中值模型采用“邻近分配”规则,然而实际情况是潜在需求者通常会在多所综合医院之间作出选择。综合医院作为区域性医疗中心,提供重症和疑难杂症的诊疗服务,根据已有研究,城市居民在选择综合医院时,“首要考虑因素依次是医疗技术、位置远近、服务态度、有无熟人、就医环境、价格因素”(张春瑜等, 2009),位置并非最主要的决定性因素(卫生部统计信息中心, 2009)。因此当一个城市的综合医院数量多于一所时,每一个潜在需求者在没有确诊的情况下,通常会根据自己每一次具体需求选择其中一所医院,一段时间下来,所有居民(需求方)与所有综合医院(供给方)之间建立如图2所示的联系。
图2 居民需求点与综合医院之间建立的联系,假设有3所综合医院
Fig.2 Connections between demand sites and urban comprehensive hospitals, assuming that the number of facilities is three
图3 潜在需求者与综合医院间的“服务流”
Fig.3 “Service flow” between demand sites and urban comprehensive hospitals
对于大部分潜在需求者,都存在或多或少的信息不对称,因此从大样本范围来看,使用规模大小(卫技人员数、床位数等)代表综合医院的医疗技术实力是完全可行的。那么有理由认为,潜在需求者主要是在规模和距离因素共同作用下选择综合医院,最终形成了如图3所示的“服务流”：某一区域范围内(通常是一个大中型城市)所有综合医院有可能向该区域内所有潜在需求者提供服务;潜在需求者优先关注医疗技术,通常倾向于选择规模更大的医院;同时距离因素也会影响潜在需求者的选择,通常随距离增加,居民选择概率变小。
综合来看,需求者身体不适但尚未确诊时可能选择综合医院中的任一家(一旦确诊,则会有目的的选取合适的医院),选择概率与综合医院规模Qj成正比,与交通出行成本Dij成反比,这与Huff模型所体现出来的空间相互作用原理一致。因此要想使P中值模型用于综合医院区位选择的结果更具有说服力,就必须纳入医疗技术因素,综合考虑需求者与设施之间的空间相互作用。
在考量综合医院布局要求与基础模型特点基础上,将从分配规则、规模计算、均衡目标分解、容量限制等方面入手进行新模型框架的搭建。
首先,针对P中值模型“邻近分配”规则的局限性,本文拟将空间相互作用嵌入P中值模型。具体做法为：①将需求点i与某一综合医院j建立联系的自由选择概率(Aij/Ai)作为系数嵌入目标函数Z,其中Aij表示需求点i经由综合医院j潜在可获取服务的资源量(宋正娜等, 2009; 宋正娜等, 2010),Ai是需求点i从研究区域内所有综合医院潜在可获取服务资源量的累计值;②将P中值模型目标函数Z当中的Yij参数改为Xj,使得每个需求点可与所有综合医院建立联系。
其次,针对P中值模型单一效率目标导致公共设施配置公平性缺失的问题,本文引入D0变量表示需求点与邻近医院之间的最大出行成本,要求针对每个需求点至少存在一所医院位于D0距离以内。
再次,针对P中值模型不包含设施容量参数,带来后期较难确定综合医院规模的问题,本文引入Qj表示综合医院j的服务能力,计算中采用床位数、卫技人员数等代替。
最后,为保证综合医院一定规模,给需求者提供差别可接受的医疗服务,达成服务质量公平,同时适当的规模也可有效保证设施运营效率,拟加入Q0约束单一医院最小规模。
修正后的重力P中值模型数学式表达如下：
式中：Ej表示设施备选点j的服务人口规模影响系数;K表示所有设施总规模;β为距离衰减系数,本研究中距离函数采用幂指数形式;其他变量、系数的意义或者与P中值模型一致,或者在前文已经提及。
式(8)的意义在于多设施、多需求者竞争环境下,使基于需求者自由选择设施概率的总的加权出行成本最小化;式(9)表示在研究区域内一共布设P个设施;式(10)表示该备选点j是否有设施,0是没有,1是有;式(11)表示每个设施的服务能力Qj,Qj是非负整数;式(12)约束所有设施总服务能力为K;式(13)约束有设施的备选点,设施规模必须大于Q0,1000000表示一个很大的数;式(13)约束没有设施的备选点,设施规模为0,1000000表示一个很大的数;式(15)-(18)用以限制每个需求点至少对应一个设施位于D0距离以内;式(15)表示需求点是否与某个设施建立联系,0是没有,1是有;式(16)约束需求点只被分配到有设施的点;式(17)表示需求点必须并且只能选择一个设施;式(18)表示需求点与设施的距离位于D0之内。
为检验模型科学性,本文选取无锡市区作为实证区域展开探讨,由于实证数据年代较早(2009年数据),虽已不能完全代表无锡市区当下状况,但可作模型检验之用。截至2009年末,全市辖七区、总面积1622.64 km2、常住人口约371.75万;其中老城三区(崇安区、南长区、北塘区)人口高度集聚,新城四区(惠山区、锡山区、新区、滨湖区)人口相对分散(图4),研究所需数据由无锡市发改委、交通局、卫生局等单位提供。
(1) 已有综合医院位置及其规模。截至2009年底,无锡市区共有二、三级综合医院10所(图4,下文统一简称为“综合医院”),主要分布于人口相对密集的老城三区,文中选取卫技人员数代表医院规模(表1),10所医院共计4931人,平均每千人拥有卫技人员数约为1.326人。
图4 无锡市区已有综合医院分布、研究单元划分与人口密度
Fig.4 Distribution, study units, and population density of existing comprehensive hospitals in Wuxi City
表1 无锡市区已有综合医院规模
Tab.1 The scales of existing comprehensive hospitals in Wuxi City
| 序号 | 医院名称 | 卫技人员/人 |
|---|---|---|
| H1 | 第二人民医院 | 957 |
| H2 | 崇安人民医院 | 233 |
| H3 | 锡山人民医院 | 482 |
| H4 | 人民医院 | 1633 |
| H5 | 南长人医院 | 200 |
| H6 | 北塘医院 | 222 |
| H7 | 第四人民医院 | 843 |
| H8 | 第六人民医院 | 83 |
| H9 | 新区凤凰医院 | 156 |
| H10 | 无锡虹桥医院 | 122 |
| 合计 | 4931 |
(2) 需求点位置及其人口规模的确定。基于研究区域大小以及设施的具体分布,本文经过试算,最终采用2.5 km×2.5 km网格划分无锡市区,并适当合并部分边缘区域面积较小网格,形成202个网格——研究单元(图4),并将这些网格的几何中心视作人口重心——需求点。借助ArcGIS软件按照社区(村)人口密度,将人口切分到网格,得到需求点人口(图4)。
(3) 综合医院备选点。本文综合选取前述网格几何中心(剔除部分边缘几何中心,以及与已有设施距离较近的几何中心)和已有综合医院位置,最终确定193个备选位置(图5)。
图5 无锡市区综合医院193个备选点
Fig.5 The 193 alternative sites for optimized allocation of comprehensive hospitals in Wuxi City
(4) 交通路网、出行方式以及设施(备选点)与需求点最短通达时间计算。无锡市区以平原为主,区内交通发达,综合医院就医主要采用公路交通。因此本文选取车行方式确定居民出行成本,文中使用500 m×500 m网格对主要道路网进行加密,各级道路行车速度依据2004年《公路工程技术标准》(JTG B01-2003)确定,由于网格线代表的是小区内或者胡同一级的道路,车行速度一般都较慢,于是赋值10 km/h(表2)。并采用矢量数据结构下交通网络最短路径算法,利用ArcView软件中Network分析模块及二次开发脚本程序,计算出各需求点至各设施(备选点)的最短通达时间(宋正娜等, 2009)。
表2 无锡市区各级道路行车速度
Tab.2 Speed limits of different grades of roads in Wuxi City
| 道路等级 | 速度/(km/h) |
|---|---|
| 高速公路 | 100 |
| 一级公路 | 80 |
| 二级公路 | 60 |
| 三级公路 | 40 |
| 四级公路 | 20 |
| 加密网格 | 10 |
3.2.1 确定约束条件
(1) 设施数量P。为便于比较优化配置前后的均衡性变化,本文假定综合医院数量不变,即P=10。
(2) 单一设施最小服务规模Q0。综合考虑无锡市区已有综合医院数量以及规模总和,并经过试验计算,选取350为单一设施最小服务规模。
(3) 需求点到达邻近设施的最大出行成本D0。依照无锡市区现有医院分布,所有需求点到达邻近综合医院的最大出行时间为49.87 min;假定10所综合医院数量不变,采用P中心模型(在已知需求点集合位置和设施备选点集合位置的情况下,分别为P个设施找到合适的位置,使到达所有设施的最大出行成本最小化(Owen et al, 1998))进行区位优化,理论上所有需求点到达邻近综合医院的最大出行成本可以下降至22.37 min。综合前述两个数据,本文实验性选取40 min作为需求点到达邻近设施的最大出行成本。
(4) 所有设施服务能力总量K。为便于前后对比,假定区位优化后的设施服务能力总和仍为卫技人员数4931个。
(5) 衰减系数β。由实际调查、试验对比综合判定β为2(宋正娜等, 2010),此取值更能揭示居民至医院可达性的真实差异。
3.2.2 设施区位和规模确定
根据上述约束条件,借助目前世界上最先进的、以优化为基础的语言开发环境AIMMS 3.13,使用Cplex 12.5求解器,选择分支定界算法,经过多次尝试,最终得到相对合理的运算结果(表3、图6)。
表3 重力P中值模型计算的区位与规模结果
Tab.3 Locations and scales of comprehensive hospitals in Wuxi City with gravity P-median model
| 备选点序号 | 卫技人员/人 | 对应研究单元与原医院名称 |
|---|---|---|
| 14 | 435 | 15 |
| 19 | 402 | 20 |
| 83 | 522 | 91 |
| 93 | 498 | 104 |
| 114 | 380 | 126 |
| 145 | 420 | 157 |
| 183 | 343 | 198 |
| 188 | 376 | 无锡市第六人民医院 |
| 189 | 827 | 无锡虹桥医院 |
| 193 | 745 | 无锡市第四人民医院 |
图6 重力P中值模型优化后无锡市区综合医院布局
Fig.6 Distribution of hospitals in Wuxi city after optimization with gravity P-median model
利用基于潜能模型的可达性分析结果(宋正娜等, 2009; 宋正娜等, 2010),对比评价两种情况下综合医院布局(即已有的设施布局和重力P中值模型优化布局)(图7-10、表4),优化后的布局方案特点为：
(1) 设施空间配置更加公平。从人均获取资源量来看,更多居民潜在可获取资源量接近无锡市区平均每千人拥有卫技人员数1.326(图9),居民潜在可获取服务资源量基尼系数下降到0.18。
(2) 居民邻近就医更加便捷。在空间距离上,更多居民至少有1所医院位于较近距离(需求点至邻近综合医院最大出行时间降至37 min,需求点至邻近综合医院平均出行时间降至15.32 min,邻近医院30 min 出行时间覆盖人口比率提升到98.95%),让居民面临真实需求时,能方便快捷地就近找到1所综合医院。
(3) 整个医疗设施体系空间布局更加合理。作为高等级医疗设施,综合医院理应与社区卫生服务(低等级)在空间上相区分。现有布局中,综合医院集中于中心城区,导致较多人口距离综合医院交通出行成本过低(图10),与社区卫生“10分钟服务圈”相重叠;基于综合医院更优的服务质量,居民多数会倾向选择综合医院,造成对综合医院资源的过度消费,且让远郊居民真实需求可能面临更长的就医等待时间(中心城区居民过度消费挤压远郊居民真实消费需求)。优化后的布局,居民至综合医院(基于随机概率)的平均出行时间延长到22.66 min,与“社区卫生服务圈”适当区分,有助于让不真实的需求回归社区卫生服务,从空间上促进整个医疗设施体系空间布局更加合理。
图7 现有布局中各需求点千人综合医院卫技人员数标准化值Kriging插值图
Fig.7 Kriging interpolation of the standard value of comprehensive hospital health care personnel per thousand residents of every demand site under the current distribution
图8 模型优化后各需求点千人综合医院卫技人员数标准化值Kriging插值图
Fig.8 Kriging interpolation of the standard value of comprehensive hospital health care personnel per thousand residents of every demand site under the optimized distribution with the new model
图9 居民人均潜在可获取资源量(按照千人计算)分布频次对比
Fig.9 Comparison of distribution frequency of potentially available resources per thousand residents ofevery demand site
图10 居民交通出行成本分布频次对比
Fig.10 Comparison of residents’ transportation cost distribution frequency under the current and optimized distribution
表4 综合医院优化配置方案与现有布局居民就医可达性对比分析
Tab.4 Comparison of accessibility of residents to comprehensive hospitals between the optimized and current distribution
| 指标 | 现有布局 | 优化布局 |
|---|---|---|
| 需求点至邻近综合医院最大出行时间/min | 49.87 | 37.00 |
| 需求点至邻近综合医院平均出行时间/min | 18.58 | 15.32 |
| 邻近医院30 min 出行时间覆盖人口比率/% | 94.68 | 98.95 |
| 需求点至综合医院的平均出行时间/min | 17.56 | 22.66 |
| 居民潜在可获取服务资源量基尼系数 | 0.54 | 0.18 |
在公共财政有限框架内实现设施相对公平—效率地均衡配置,是提升公共财政空间效应及居民服务效用的关键环节。而区位决策是影响公共设施规划布局乃至公共服务品质的决定性因素之一,依据供需之间的空间相互作用特点选取或构建适宜的区位—分配模型成为一种有效途径。作为典型而特殊的一类公共设施,综合医院与居民健康息息相关,具有一定的公益性,居民的公平性诉求需要被兼顾;而财政局限、规模门槛与居民使用频率不高又共同决定了空间效率应成为主导目标。且随着医改的深入,综合医院已逐步被推向市场参与吸引消费者的竞争,居民以随机概率式对其进行选择。因此,综合医院区位决策较为复杂,既需考虑空间公平—效率的均衡目标,又需与空间相互作用原理(重力规则)相融合,还需同时解决区位与规模同步计算、容量限制、服务质量公平与规模效率等问题。
为实现上述综合医院区位决策中的多重要求,本文整合已有相关研究的思路,构建出一种新的重力P中值模型,旨在探讨针对竞争型公共设施空间配置模型的构建范式。首先,本文甄选经典的P中值模型,在对模型来源、数学表达式进行详细阐述的基础上,指出P中值模型以效率作为导向导致模型不能应用于具有公平性要求的设施选址问题;采用“邻近分配”规则使得模型不适用于自由选择竞争选址问题;不考虑设施容量给设施规模计算带来不便。其次,本文通过对供需之间空间相互作用的分析指出,综合医院设施区位决策是竞争选址问题,居民与城市综合医院(多于1所的情况下)之间的“服务流”与Huff模型所体现的空间相互作用原理相一致。再次,本文针对综合医院区位选择要求,以P中值模型为框架,将自由选择概率因子纳入模型目标函数,并且针对综合医院的公平性要求增加了设施最大出行成本限制条件,针对P中值模型不包含设施容量参数增加了规模因子,针对综合医院对于设施服务能力的要求增加了设施最小规模限制条件,构建了基于空间相互作用的重力P中值模型。最后,为检验模型的有效性,选取无锡市区作为实证研究区域,通过AIMMS开发环境,求解无锡市综合医院适宜区位,经过与已有设施区位对比分析发现,修正以后的新重力P中值模型设施区位空间配置更加公平,居民邻近就医更加便捷,与社区卫生设施协同布局、整个医疗设施体系空间布局更加合理。
综合医院区位选择是一个复杂而棘手的问题,本文旨在提供一个解决思路,但仍存以下几点有待进一步深入：①构建的新重力P中值模型求解存在很大难度,本文借助AIMMS软件求解,如能通过其他方式求解,或许会有不同收获。②本文实证检验时,从居民居住地出发最终归结形成每一个需求点,实则不然,多数居民夜晚确实待在居住地,但是白天或者上班,或者求学,只有少数仍在家中。人口的流动形成了城市的商业区、居住区、工厂区等,如果仅以居住地作为需求出发点,用于实际规划操作时,是否科学,有待进一步考虑。③本文实证检验中,综合医院备选点简单选取需求点位置和已有综合医院区位,用于实际规划操作时,备选点需要结合土地利用规划,综合考虑是否已经存在其他设施、备选点能够容纳设施规模、已存设施拆迁成本等因素。④修正的重力P中值模型对于数据精度要求较高,本文实证检验所涉大量数据,难免有疏漏错误,如通行时间虽已通过交通模型构建来实现计算,但对于早晚高峰与红绿灯等待时间等因素尚未纳入,可能在一定程度上影响计算结果。⑤本文探讨的模型尽管计算难度较大,但从实际情况来看,居民需求可能不断变化,引入动态理念计算被模拟的具有规律性变化的部分参数,或通过一系列离散情景模拟未来可能需求,以进一步完善模型框架,但这需要匹配更加强有力的算法。⑥已有综合医院的研究,主要分为3个脉络：依据经济学成本效益原理计算分析,采用空间数据挖掘与计算几何等方法进行区位决策分析,采用运筹学模型求算相对理想区位,其中运筹学模型已经逐步成为主导性技术手段。随着社会情景日趋复杂,多目标、多层次、随机性等复杂区位—分配模型的构建与应用已不断引起研究者的关注;嵌入更全面的变量因子,动态与随机性问题的结合,更准确地模拟现实社会行为规律俨然已成为未来区位模型的发展方向,也是本文新构建模型可进一步推进的突破口。
致谢：模型构建阶段,南京信息工程大学丁健老师、南京工业职业技术学院冯桂珍老师提出了有益建议;模型求解阶段,南京航空航天大学邱树萍研究生基于AIMMS平台编写了求解程序并运行得到了相应结果,在此表示衷心感谢。
The authors have declared that no competing interests exist.
| [1] |
区位分析中的若干可计算模型研究 [D].A research of computable models on location analysis [D]. |
| [2] |
区位模型在公共设施布局中的应用 [J].https://doi.org/10.3969/j.issn.1000-8462.2006.01.007 URL [本文引用: 1] 摘要
古典区位论是现代区位论的理论 基石,运用于公共设施布局的分配.区位模型是在对古典区位论进行新的诠释以及对其中的假设限制加以修订的基础上发展起来的。顺应当今社会福利化的发展趋 势,分配.区位模型正在为福利政策的全方位实施提供有效的理论借鉴。从量化的角度看,区位模型在应用方面大致可以分为解决“重心指向”、“中心指向”和 “覆盖指向”等3类问题。建立应用模型首先要确定区位选择的评价标准,其次是划定设置设施的服务范围与确定设施的数目和等级;分析微区位设施布局限制条件 的改变对目标函数的影响可以采用“感度分析”等方法。多目标的设施区位规划、GIS空间分析方法的有效使用,以及寻求更快捷的量化求解方法是分配.区位模
Application of location models in the distribution of common facilities [J].https://doi.org/10.3969/j.issn.1000-8462.2006.01.007 URL [本文引用: 1] 摘要
古典区位论是现代区位论的理论 基石,运用于公共设施布局的分配.区位模型是在对古典区位论进行新的诠释以及对其中的假设限制加以修订的基础上发展起来的。顺应当今社会福利化的发展趋 势,分配.区位模型正在为福利政策的全方位实施提供有效的理论借鉴。从量化的角度看,区位模型在应用方面大致可以分为解决“重心指向”、“中心指向”和 “覆盖指向”等3类问题。建立应用模型首先要确定区位选择的评价标准,其次是划定设置设施的服务范围与确定设施的数目和等级;分析微区位设施布局限制条件 的改变对目标函数的影响可以采用“感度分析”等方法。多目标的设施区位规划、GIS空间分析方法的有效使用,以及寻求更快捷的量化求解方法是分配.区位模
|
| [3] |
城市应急避难场所区位选择与空间布局: 以南京市为例 [D]. |
| [4] |
GIS在购物中心选址中的应用研究 [D].The application research of shopping mall location based on GIS [D]. |
| [5] |
基于潜能模型的医疗设施空间可达性评价方法研究 [J].https://doi.org/10.11820/dlkxjz.2009.06.003 Magsci [本文引用: 3] Measuring spatial accessibility to health care facilities based on potential model [J].https://doi.org/10.11820/dlkxjz.2009.06.003 Magsci [本文引用: 3] |
| [6] |
公共服务设施空间可达性及其度量方法 [J].https://doi.org/10.11820/dlkxjz.2010.10.009 URL Magsci [本文引用: 3] 摘要
<p>空间可达性度量既可用于评价公共服务设施空间布局的合理性，也可用于比较规划方案的优劣。公共服务设施空间可达性度量需要针对不同设施特有的空间布局目标，选取与之相适应的可达性评价因子，并采用合适的度量方法展开，对此进行专题研究的文献并不多见。本文一方面在对公共服务设施按照时效性、接受性、数量、等级性进行分类的基础上，系统阐述如何针对不同设施进行空间布局目标设定和可达性评价因子选取；另一方面将主要的度量方法分为比例法、最近距离法、基于机会累积的方法、基于空间相互作用的方法，并对各类方法的应用领域及优缺点予以分析比较，同时以潜能模型、两步移动搜寻法为例探讨相关方法在公共服务设施空间可达性度量中的应用；最后在对上述研究总结评述的基础上，本文指出多等级设施空间可达性、从需求者的活动规律考虑空间可达性、针对各类设施的综合空间可达性以及相关度量方法与GIS的集成等主题值得投入更多关注。</p>
Spatial accessibility to public service facilities and its measurement approaches [J].https://doi.org/10.11820/dlkxjz.2010.10.009 URL Magsci [本文引用: 3] 摘要
<p>空间可达性度量既可用于评价公共服务设施空间布局的合理性，也可用于比较规划方案的优劣。公共服务设施空间可达性度量需要针对不同设施特有的空间布局目标，选取与之相适应的可达性评价因子，并采用合适的度量方法展开，对此进行专题研究的文献并不多见。本文一方面在对公共服务设施按照时效性、接受性、数量、等级性进行分类的基础上，系统阐述如何针对不同设施进行空间布局目标设定和可达性评价因子选取；另一方面将主要的度量方法分为比例法、最近距离法、基于机会累积的方法、基于空间相互作用的方法，并对各类方法的应用领域及优缺点予以分析比较，同时以潜能模型、两步移动搜寻法为例探讨相关方法在公共服务设施空间可达性度量中的应用；最后在对上述研究总结评述的基础上，本文指出多等级设施空间可达性、从需求者的活动规律考虑空间可达性、针对各类设施的综合空间可达性以及相关度量方法与GIS的集成等主题值得投入更多关注。</p>
|
| [7] |
公共服务设施选址问题研究 [D].
Study on the public service facility location problem [D].
|
| [8] |
设施区位: 一个重要的科学问题 [C]//Facility location: An important scientific problem [C]// |
| [9] |
|
| [10] |
|
| [11] |
大型综合性医院患者就医行为影响因素分析 [J].
患者是医疗服务的利用者,并最终决定着医疗服务市场的需求水平.大型综合性医院要提高市场占有率,充分满足患者的需求,就必须深入研究患者就医行为的规律.对此,笔者随机抽取某大型综合性医院(以下称W医院)住院和门诊患者1443人,通过问卷调查,了解影响患者就医行为的认知因素、相关群体因素和媒介因素,据此制定医院品牌建设和品牌推广策略.
Daxing zonghexing yiyuan huanzhe jiuyi xingwei yingxiang yinsu fenxi [J].
患者是医疗服务的利用者,并最终决定着医疗服务市场的需求水平.大型综合性医院要提高市场占有率,充分满足患者的需求,就必须深入研究患者就医行为的规律.对此,笔者随机抽取某大型综合性医院(以下称W医院)住院和门诊患者1443人,通过问卷调查,了解影响患者就医行为的认知因素、相关群体因素和媒介因素,据此制定医院品牌建设和品牌推广策略.
|
| [12] |
GIS支持下的城市医院空间布局优化研究 [D].Allocation study of the city hospital based on GIS [D]. |
| [13] |
Spatial interaction model in health-care facility location-allocation [J].https://doi.org/10.2208/journalip.17.219 URL [本文引用: 2] 摘要
This study aims at developing a formulation and a simple solution procedure for location-allocation of hierarchical health care facilities. We deal with hospital as an upper level and health center as a lower level. The model is based on the hypothesis that the location and allocation are controlled by different decision-makers. The results that we expected in our model show the performance of users' behavior based on spatial interaction effect in choosing a site of hospital or health center to minimize the total patients weighted distance in a simple real network.
|
| [14] |
Testing the gravity p-median model empirically [J].https://doi.org/10.1016/j.orp.2015.06.002 URL [本文引用: 2] 摘要
Regarding the location of a facility, the presumption in the widely used p-median model is that the customer opts for the shortest route to the nearest facility. However, this assumption is problematic on free markets since the customer is presumed to gravitate to a facility by the distance to and the attractiveness of it. The recently introduced gravity p-median model offers an extension to the p-median model that account for this. The model is therefore potentially interesting, although it has not yet been implemented and tested empirically. In this paper, we have implemented the model in an empirical problem of locating vehicle inspections, locksmiths, and retail stores of vehicle spare-parts for the purpose of investigating its superiority to the p-median model. We found, however, the gravity p-median model to be of limited use for the problem of locating facilities as it either gives solutions similar to the p-median model, or it gives unstable solutions due to a non-concave objective function.
|
| [15] |
On optimal location with threshold requirements [J].https://doi.org/10.1016/S0038-0121(98)00005-6 URL 摘要
The optimal location of services is one of the most important factors that affects service quality in terms of consumer access. On the other hand, services in general need to have a minimum catchment area so as to be efficient. In this paper, a model is presented that locates the maximum number of services that can coexist in a given region without having losses, taking into account that they need a minimum catchment area to exist. The objective is to minimize average distance to the population. The formulation presented belongs to the class of discrete P-median-like models. A tabu heuristic method is presented to solve the problem. Finally, the model is applied to the location of pharmacies in a rural region of Spain.
|
| [16] |
Theoretical and computational links between the p-median, location set-covering, and the maximal covering location problem [J].https://doi.org/10.1111/j.1538-4632.1976.tb00547.x URL [本文引用: 1] 摘要
Abstract Top of page Abstract LITERATURE CITED It has been shown that the p-median problem, the location set-covering and the maximal covering location problems are important facility location models. This paper gives a historical perspective of the development of these models and identifies the theoretical links between them. It is shown that the maximal covering location problem can be structured and solved as a p-median problem in addition to the several approaches already developed. Computational experience for several maximal covering location problems is given.
|
| [17] |
A note on applying the gravity rule to the airline hub problem [J].https://doi.org/10.1111/0022-4146.00207 URL [本文引用: 1] 摘要
In this note we propose a new model for the airline hub selection problem. Passengers use a hub on the way to their destination. We apply the objective of minimizing the total miles traveled by passengers. This formulation can be used as the basis for other objectives also.
|
| [18] |
Multiple facilities location in the plane using the gravity model [J].https://doi.org/10.1111/j.1538-4632.2006.00692.x URL [本文引用: 2] 摘要
Two problems are considered in this article. Both problems seek the location of p facilities. The first problem is the p median where the total distance traveled by customers is minimized. The second problem focuses on equalizing demand across facilities by minimizing the variance of total demand attracted to each facility. These models are unique in that the gravity rule is used for the allocation of demand among facilities rather than assuming that each customer selects the closest facility. In addition, we also consider a multiobjective approach, which combines the two objectives. We propose heuristic solution procedures for the problem in the plane. Extensive computational results are presented.
|
| [19] |
The gravity p-median model [J].https://doi.org/10.1016/j.ejor.2005.04.054 Magsci [本文引用: 1] 摘要
<p id="">In this paper we propose a new model for the <em>p</em>-median problem. In the standard <em>p</em>-median problem it is assumed that each demand point is served by the closest facility. In many situations (for example, when demand points are communities of customers and each customer makes his own selection of the facility) demand is divided among the facilities. Each customer selects a facility which is not necessarily the closest one. In the gravity <em>p</em>-median problem it is assumed that customers divide their patronage among the facilities with the probability that a customer patronizes a facility being proportional to the attractiveness of that facility and to a decreasing utility function of the distance to the facility.</p><p id="">The model is analyzed and heuristic solution procedures are proposed. Computational experiments using a set of test problems, provide excellent results.</p>
|
| [20] |
The gravity multiple server location problem [J].https://doi.org/10.1016/j.cor.2010.08.006 URL [本文引用: 3] 摘要
Models for locating facilities and service providers to serve a set of demand points are proposed. The number of facilities is unknown, however, there is a given number of servers to be distributed among the facilities. Each facility acts as an M/M/k queuing system. The objective function is the minimization of the combined travel time and the waiting time at the facility for all customers. The distribution of demand among the facilities is governed by the gravity rule. Two models are proposed: a stationary one and an interactive one. In the stationary model it is assumed that customers do not consider the waiting time at the facility in their facility selection decision. In the interactive model we assume that customers know the expected waiting time at the facility and consider it in their facility selection decision. The interactive model is more complicated because the allocation of the demand among the facilities depends on the demand itself. The models are analyzed and three heuristic solution algorithms are proposed. The algorithms were tested on a set of problems with up to 1000 demand points and 20 servers.
|
| [21] |
Facility location: Applications and theory [M]. |
| [22] |
Computers and intractability: A guide to the theory of NP-completeness [M]. |
| [23] |
Optimum locations of switching centers and the absolute centers and medians of a graph [J].https://doi.org/10.1287/opre.12.3.450 URL 摘要
The concepts of the 'center' and the 'median vertex' of a graph are generalized to the 'absolute center' and the 'absolute median' of a weighted graph (a graph with weights attached to its vertices as well as to its branches). These results are used to find the optimum location of a 'switching center' in a communication network and to locate the best place to build a 'police station' in a highway system. It is shown that the optimum location of a switching center is always at a vertex of the communication network while the best location for the police station is not necessarily at an intersection. Procedures for finding these locations are given.
|
| [24] |
An efficient algorithm for the p-median problem with maximum distance constraints [J].https://doi.org/10.1111/j.1538-4632.1973.tb00493.x URL 摘要
First page of article
|
| [25] |
Facility location models for distribution system design [J].https://doi.org/10.1016/j.ejor.2003.10.031 Magsci [本文引用: 1] 摘要
<p id="">The design of the distribution system is a strategic issue for almost every company. The problem of locating facilities and allocating customers covers the core topics of distribution system design. Model formulations and solution algorithms which address the issue vary widely in terms of fundamental assumptions, mathematical complexity and computational performance. This paper reviews some of the contributions to the current state-of-the-art. In particular, continuous location models, network location models, mixed-integer programming models, and applications are summarized.</p>
|
| [26] |
Exploiting available data sources: Location/allocation modeling for health service planning in rural Ghana [J].https://doi.org/10.1080/00167223.2001.10649457 URL [本文引用: 1] 摘要
The preconditions for applying GIS-based location-allocation analysis for health service planning in rural Ghana are examined in terms of data availability and quality. A population map is established from the latest available census using geo-coding methods and digital topographic sheets. A vector-based transport model of the region is established by merging data from several sources including GPS. It is suggested that a hybrid transport model is required. This model combines the possibilities for all-direction transportation inherent in the raster-based approach with the possibilities for road/path transportation inherent in the vector-based approach. All-direction movements are expected to take place close to the villages in order to reach a suitable linear transport corridor represented by a vector. Several scenarios for improving the accessibility aspects of the health service provision are examined in light of Ghana's current health service policy. Location-allocation modelling tools are used to select optimal locations and provide statistics on average distance to health centres and percentage of population covered.
|
| [27] |
Strategic facility location: A review [J].https://doi.org/10.1016/S0377-2217(98)00186-6 URL [本文引用: 5] 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.
|
| [28] |
The location of public schools: Evaluation of practical experiences [J].https://doi.org/10.1111/j.1475-3995.1997.tb00058.x URL [本文引用: 1] 摘要
This paper discusses practical experiences resulting from the use of Operations Research techniques for the location of elementary public schools in large urban settings. The experiences reported are based on two counties of the metropolitan area of Rio de Janeiro, Brazil. In these relatively poor areas walking is the most common means of traveling to school, and the ideal location is the one that minimizes the sum of the overall residence-to-school distances. The model used was the uncapacitated p-median, but current capacities of existing schools have been introduced in the interpretation of the results. In both counties, the study first evaluated the existing spatial distribution of schools and then proceeded to propose their ideal location. Both analyses lead to short and long-run managerial suggestions. A description of the practical status of the study is also included.
|
| [29] |
The maximum capture or “sphere of influence” location problem: Hotelling revisited on a network [J]. |
| [30] |
Hierarchical location-allocation with spatial choice interactionmodeling [J].
|
/
| 〈 |
|
〉 |
