Abstract Uncertainty and error are inevitable when continuously varying geographic phenomena are approximated. Describing geography and spatial relationships is, therefore, challenging using analytics for planning and management. A critical aspect of spatial description has to do with allocation, a process of determining who is best served by which facility. Allocation is useful in reflecting customer behavior, efficient assignment, districting, etc. Even though spatial and temporal heterogeneity is part of assignment processes formalized in allocation problems, previous studies often assume a pre-specified network. The assumption is understandable since many service vehicles currently travel over road networks. However, there are some other vehicles, such as planes, unmanned aircraft vehicles, boats, ships, etc. Their access is not restricted to a network. How to structure and solve an allocation process is particularly challenging when heterogeneity must be taken into account across continuous space and through time. In this paper, a method is developed to construct service areas in order to minimize assignment cost in a continuous region where accessibility is spatially and temporally heterogeneous. Application findings are reported for planning problems involving emergency drone delivery since it is impacted by heterogeneity in the local environment. The travel accessibility of drones changes due to time-varying wind and airspace restrictions. Results show that the optimal allocation and service area of drone-based stations vary over time. The response time (or system costs) can be saved by taking into account wind and travel obstacles. Further, feasibility, practicality, and importance are demonstrated for incorporating spatial and temporal heterogeneity in continuous space allocation processes.

中文翻译：

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支持服务区响应的时空异构分配

摘要 对连续变化的地理现象进行近似处理时，不确定性和误差是不可避免的。因此，使用分析进行规划和管理很难描述地理和空间关系。空间描述的一个关键方面与分配有关，这是一个确定哪个设施最好为谁服务的过程。分配在反映客户行为、有效分配、分区等方面很有用。尽管空间和时间异质性是分配问题中形式化的分配过程的一部分，但以前的研究通常假设一个预先指定的网络。该假设是可以理解的，因为目前许多服务车辆都在道路网络上行驶。但是，还有一些其他的交通工具，例如飞机、无人驾驶飞机、船只、轮船等。他们的访问不限于网络。当必须考虑跨连续空间和跨时间的异质性时，如何构建和解决分配过程尤其具有挑战性。在本文中，开发了一种构建服务区的方法，以便在可访问性在空间和时间上具有异质性的连续区域中最小化分配成本。报告了涉及紧急无人机交付的规划问题的应用结果，因为它受到当地环境异质性的影响。由于时变的风和空域限制，无人机的旅行可达性发生了变化。结果表明，基于无人机的站点的最佳分配和服务区域随时间变化。考虑到风和行驶障碍，可以节省响应时间（或系统成本）。更多，