Abstract The Coverage Location Problem (CLP) seeks the best locations for service to minimize the total number of facilities required to meet all demands. This paper studies a new variation of this problem, called the Coverage Location Problem with Overlap Control (CLPOC). This problem models real contexts related to overloaded attendance systems, which require coverage zones with overlaps. Thus, each demand must be covered by a certain number of additional facilities to ensure that demands will be met even when the designated facility is unable to due to some facility issue. This feature is important in public and emergency services. We observe that this number of additional facilities is excessive in some demand points because overlaps among coverage zones occur naturally in CLP. The goal of the CLPOC is to control overlaps to prioritize regions with a high density population or to minimize the number of coverage zones for each demand point. In this paper, we propose a new mathematical model for the CLPOC that controls the overlap between coverage zones. We used a commercial solver to find the optimal solutions for available instances in the literature. The computational tests show that the proposed mathematical model found appropriate solutions in terms of number of demand points with minimum coverage zones and sufficient coverage zones for high demand points.

中文翻译：

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具有重叠控制的覆盖位置问题的数学模型

摘要 覆盖位置问题 (CLP) 寻求服务的最佳位置，以最小化满足所有需求所需的设施总数。本文研究了该问题的一种新变体，称为具有重叠控制的覆盖位置问题 (CLPOC)。这个问题模拟了与过载考勤系统相关的真实环境，这些系统需要重叠的覆盖区域。因此，每个需求必须由一定数量的附加设施来满足，以确保即使在指定设施由于某些设施问题而无法满足需求时也能满足需求。此功能在公共和紧急服务中很重要。我们观察到，在某些需求点，额外设施的数量过多，因为覆盖区域之间的重叠在 CLP 中自然发生。CLPOC 的目标是控制重叠以优先考虑具有高密度人口的区域或最小化每个需求点的覆盖区域数量。在本文中，我们为 CLPOC 提出了一种新的数学模型，用于控制覆盖区域之间的重叠。我们使用商业求解器为文献中的可用实例找到最佳解决方案。计算测试表明，所提出的数学模型在具有最小覆盖区域的需求点数量和高需求点的足够覆盖区域方面找到了合适的解决方案。我们使用商业求解器为文献中的可用实例找到最佳解决方案。计算测试表明，所提出的数学模型在具有最小覆盖区域的需求点数量和高需求点的足够覆盖区域方面找到了合适的解决方案。我们使用商业求解器为文献中的可用实例找到最佳解决方案。计算测试表明，所提出的数学模型在具有最小覆盖区域的需求点数量和高需求点的足够覆盖区域方面找到了合适的解决方案。