Analysis of Facility Location Using Ordered Rectilinear Distance in Regular Point Patterns
Analysis of Facility Location Using Ordered Rectilinear Distance in Regular Point Patterns
复制标题
DOI：
--
复制
发表时间：
2008-12
期刊：
影响因子：
--
通讯作者：
M. Miyagawa
中科院分区：
文献类型：
--
作者：
M. Miyagawa
本文讨论了正方形和菱形两种规则点模式的k次最近直线距离。本文从理论上导出了k = 1，2，.时第k最近直线距离的概率密度函数。. .，8.第k最近距离的上界和下界也被推导出来。作为k次最近距离的一个应用，我们考虑了一类设施封闭的设施选址问题。我们的目标是找到最佳的设施配置，最大限度地减少平均直线距离从居民到他们最近的开放式设施时，一些现有的设施被关闭。假设设施是封闭的独立和随机的，我们表明，钻石晶格是最好的，如果至少有73%的设施是开放的。
This paper deals with the kth nearest rectilinear distance of two regular point patterns: square and diamond lattices. The probability density functions of the kth nearest rectilinear distance are theoretically derived for k = 1, 2, . . . , 8. Upper and lower bounds of the kth nearest distance are also derived. As an application of the kth nearest distance, we consider a facility location problem with closing of facilities. The objective is to find the best configuration of facilities that minimizes the average rectilinear distance from residents to their nearest open facility when some existing facilities are closed. Assuming that facilities are closed independently and at random, we show that the diamond lattice is the best if at least 73% of facilities are open.