Abstract This paper addresses a version of the single-facility Maximal Covering Location Problem on a network where the demand is: i) distributed along the edges and ii) uncertain with only a known interval estimation. To deal with this problem, we propose a minmax regret model where the service facility can be located anywhere along the network. This problem is called Minmax Regret Maximal Covering Location Problem with demand distributed along the edges. Furthermore, we present two polynomial algorithms for finding the location that minimises the maximal regret assuming that the demand realisation is an unknown constant or linear function on each edge. We also include two illustrative examples as well as a computational study for the unknown constant demand case to illustrate the potential and limits of the proposed methodology.

中文翻译：

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Minmax Regret 边缘需求的最大覆盖位置问题

摘要 本文解决了网络上单一设施最大覆盖位置问题的一个版本，其中需求是：i）沿边缘分布，ii）仅具有已知间隔估计的不确定性。为了解决这个问题，我们提出了一个最小最大遗憾模型，其中服务设施可以位于网络的任何地方。这个问题称为 Minmax Regret 最大覆盖位置问题，需求沿边缘分布。此外，假设需求实现是每个边上的未知常数或线性函数，我们提出了两种多项式算法，用于找到最小化最大遗憾的位置。我们还包括两个说明性示例以及未知恒定需求案例的计算研究，以说明所提出方法的潜力和局限性。