Abstract In prior literature regarding facility location problems, there has been little explicit acknowledgement of problems arising from concave (non-convex) regions. This issue extends to computational geometry as a whole, as there is a distinct deficiency in existing center finding techniques amidst work on forbidden regions. In this paper, we present a novel method for finding representative regional center-points, referred to as “Concave Interior Centers”, to approximate inter-regional distances for solving optimal facility location problems. The validity of the proposal as a means for solving these placements is discussed on three “special cases”, and on a humanitarian focused real-world application. We compare the performance of the Concave Interior Center to the results from using Geometric Centers. We discuss the implications of using externally located representative centers in facility location problems. The context of the application involves maximizing the potential services available to homeless persons in Fairfield County, Connecticut under a given budget through the construction of limited capacity night-by-night shelters and optionally included food pantries. Our computational results show the efficiency of the proposed techniques in solving a critical societal problem.

中文翻译：

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在连续设施位置问题中导航凹面区域

摘要 在关于设施选址问题的先前文献中，几乎没有明确承认由凹（非凸）区域引起的问题。这个问题扩展到整个计算几何，因为在禁止区域的工作中，现有的中心查找技术存在明显的缺陷。在本文中，我们提出了一种寻找代表性区域中心点的新方法，称为“凹内中心”，以近似区域间距离以解决最佳设施位置问题。该提案作为解决这些安置的手段的有效性在三个“特殊情况”和以人道主义为重点的现实世界应用中进行了讨论。我们将凹形内部中心的性能与使用几何中心的结果进行比较。我们讨论了在设施选址问题中使用位于外部的代表中心的影响。该申请的背景涉及在给定预算下，通过建造容量有限的夜间庇护所和可选的食品储藏室，最大限度地为康涅狄格州费尔菲尔德县的无家可归者提供潜在服务。我们的计算结果显示了所提出的技术在解决关键社会问题方面的效率。