Spatial allocation is a fundamentally important process reflecting customer behavior, efficient service assignment, districting, etc., and is at the heart of many spatial analytical methods and processes. The Voronoi diagram has proven to be an important mathematical and geometric construct and has been widely applied in various fields because it is intuitive and efficient in the allocation and/or partitioning of space. However, existing Voronoi diagram approaches rely on the assumption that the attribute(s) of continuous space (non-generator points) is homogenous, which often is not the case for many application contexts. This paper introduces the concept of spatial heterogeneity in allocation. A new Voronoi diagram is defined—the heterogeneous Voronoi diagram. A geographic information system-based method is developed to derive the heterogeneous Voronoi diagram using discretized spatial allocation properties. Application of the heterogeneous Voronoi diagram is reported for a planning problem involving emergency drone delivery. Results show that response potential is over- and underestimated when heterogeneity and travel obstacles are disregarded. Further, feasibility, usefulness, and significance are demonstrated for incorporating geographic heterogeneity in the allocation process.

中文翻译：

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使用异构空间Voronoi图进行分配

空间分配是反映客户行为，有效服务分配，分区等的根本重要过程，并且是许多空间分析方法和过程的核心。Voronoi图已被证明是重要的数学和几何构造，并且由于它在空间的分配和/​​或分区方面直观且有效，因此已广泛应用于各个领域。但是，现有的Voronoi图方法依赖于以下假设：连续空间（非生成器点）的属性是同质的，在许多应用程序上下文中通常并非如此。本文介绍了分配中空间异质性的概念。定义了一个新的Voronoi图-异构Voronoi图。开发了一种基于地理信息系统的方法，以使用离散的空间分配属性来导出异构Voronoi图。对于涉及紧急无人机交付的计划问题，报告了异构Voronoi图的应用。结果表明，当忽略异质性和旅行障碍时，反应潜力被高估和低估。此外，展示了将地理异质性纳入分配过程的可行性，有用性和重要性。