Abstract An important class of facility location problems deals with service coverage. While there are many types of coverage models, among the most widely applied is the location set covering problem. A common instance is to find the minimum number of facilities that provide service to a region. It has been applied to a broad range of infrastructural services, including transportation, telecommunication, safety management, and emergency services. Among the variants, this paper is particularly concerned with optimal deployment of outdoor warning sirens. Given a region, we seek the minimum number of sirens needed to alert everyone across the region of an emergency situation. In contrast to previous work, we propose an approach to take into account acoustic properties. This approach requires formulation of superposition associated with multiple sounds as this interaction impacts audibility. Similar to the originally defined location set covering problem as an integer program, the developed approach is shown to reduce to an integer linear programming problem. Superposed sound pressure level is required to be equal or greater than an audible threshold across the region. To obtain an optimal solution, a bounding-based method is adopted. Starting with an initial disaggregation of a region, we iteratively seek optimal solutions of two layers until the gap of the upper and lower bounds converge. Empirical results are presented for a study involving an emergency warning siren system in a coastal community. The findings highlight the significance of acoustic properties, and the need to explicitly account for siren interaction in the evaluation and modeling of service coverage.

中文翻译：

---

紧急警报警报器覆盖规划中的声学特性

摘要 一类重要的设施定位问题涉及服务覆盖。覆盖模型有很多种，其中应用最广泛的是位置集覆盖问题。一个常见的例子是找到为一个区域提供服务的最小数量的设施。它已应用于广泛的基础设施服务，包括运输、电信、安全管理和应急服务。在这些变体中，本文特别关注室外警报器的优化部署。给定一个地区，我们寻求在紧急情况下向该地区的每个人发出警报所需的最少数量的警报器。与之前的工作相比，我们提出了一种考虑声学特性的方法。这种方法需要制定与多种声音相关的叠加，因为这种相互作用会影响可听度。类似于最初定义的位置集覆盖问题作为整数规划，所开发的方法被证明可以简化为整数线性规划问题。要求叠加声压级等于或大于整个区域的可听阈值。为了获得最优解，采用了基于边界的方法。从一个区域的初始分解开始，我们迭代地寻找两层的最优解，直到上下界的差距收敛。提供了一项涉及沿海社区紧急警报系统的研究的实证结果。研究结果突出了声学特性的重要性，