基于空间优化的连续型多设施选址方法研究

Location theory is concerned with the geographic location of socio-economic activities, including land use, industrial production, central places and spatial competition. Founded on such theory, location science has long been recognized as playing an important role in regional and urban planning, and other contexts, and it continues to be a very active research area involving people from diverse disciplines, including mathematics, operation research, management science, geography, urban planning, and industrial engineering among others. In fact, whenever a question about where to place things is posed, a location problem arises..Location problems usually concern determining one or more sites for facilities under certain constraints, sometimes involving demand allocation, to optimize certain objectives. Of interest in this resarch is a minimization model - the Weber problem and the multi-facility Weber problem, where demand is continuously distributed.? As one of the first formalized location problems ever posed, the classic context of the Weber problem is siting a factory in order to minimize the transportation costs to acquire raw materials and distribute products.An extension of interest here is siting several facilities simultaneously, which is called the continuous location-allocation problem or multi-Weber problem (MWP). This generalization is more complicated than the original problem in both model formulation and solving, because of the need to address both location and allocation decisions. Given the fact that underlying demand such as population is often better conceived to be continuously distributed over space, another concern in this study is addressing continuous demand representation in the Weber problem and multi-Weber problem..When facilities can be located anywhere and demand is continuously distributed, the model formulations as well as solution procedures become more complicated. Given that geographic space is a crucial element in location related decision-making, this problem nuance is important. Recent years have seen a proliferation in application of spatial optimization approaches involving geographic information system (GIS) in location science, mainly attributed to the advances in geographic information science and computer technologies. Usually, GIS is used to facilitate data input and result visualization, but it arguably more valuable and meaningful in assisting the modeling and analysis processes..The aim of this research is to employ spatial optimization approaches that combine GIS and operation research methods to solve the continuous Weber and continuous multi-Weber problems. It will contribute to theories and methods of location science in the sense that it investigates important extensions of a classic location problem from a spatial/geographic perspective as well as develops spatial optimization approaches to solve them.

设施选址问题(facility location problems)起源于地理学的经典的区位-土地利用模型问题。设施选址问题主要研究通过某种方法适当地布局一个或多个设施，以实现预定目标的最优化，如最小化交通成本，为客户提供均衡的服务，获得最大的市场份额等等。本研究将GIS 和优化模型相结合，在探索连续型需求的多类型、多尺度表达的基础上，借助韦伯问题这一多种空间优化问题的原型，从单个设施的选址问题入手，进而研究连续型多设施的选址问题的方法论，并进行连续型需求的韦伯问题和选址-分配问题的通用求解，改进算法计算效率。研究成果将其用于中国南京和美国菲尼克斯两大都市的实际案例研究，研究计划以两市人口作为连续型需求，利用连续型选址-分配问题求解多个新消防站点的最佳选址，借此评估现有消防站点布局的合理性，并对未来消防站点的布局规划提供决策支持。

空间优化(Spatial Optimization)是地理学空间分析的重要分支。设施选址问题是一种重要的空间优化应用，主要研究通过某种方法适当地布局一个或多个设施，以实现预定目标的最优化，如最小化交通成本，为客户提供均衡的服务，获得最大的市场份额等等。在理论方法层面，本研究将GIS和优化模型相结合，在探索连续型需求的多类型、多尺度表达的基础上，借助韦伯问题这一多种空间优化问题的原型，从单个设施的选址问题入手，进而研究连续型设施的选址问题的方法论，并进行连续型需求的韦伯问题和选址-分配问题的通用求解，改进算法计算效率。在实践应用层面，研究成果将其用于中国南京的实际案例研究，研究以人口作为连续型需求，利用连续型选址-分配问题求解多个消防站点的最佳选址，借此评估现有消防站点布局的合理性，并对未来消防站点的布局规划提供决策支持。研究还将空间优化的方法扩展用于土地利用面元的空间优化，以及水利观测站网的雨量站(不含拓扑关系)及水位站(含拓扑关系)的空间优化。本研究显示出较高的理论价值和应用前景，未来应加强在大数据时代的应用优化研究，提高算法的效率和进行实时空间建模。