Abstract Hub location models are one of the basic concepts to model design problems for communication and traffic networks. These networks are often exposed to threats such as attacks or natural disasters. However, the literature on extensions of hub location models capable of taking such threats into account is scarce. In this article, we investigate the so-called multiple allocation p-hub r-interdiction problem, where a locator has to choose p hubs, knowing in advance that r p of them will be interdicted. The objective is to minimize the total routing costs in the network after interdiction. This problem can also be interpreted as a minmax-robust p-hub location problem with an exponentially large uncertainty set containing the worst case for each choice of hubs. We present a new bi-level formulation for the problem and investigate its mathematical structure. Using these structural results, we propose the first exact solution procedure for the problem. We compute the optimal solutions for the well-known CAB-data set and compare them to heuristic results. Moreover, we investigate the complexity of the problem and show that already the interdiction problem for given hubs is NP-hard.

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关于 p-Hub 拦截问题

摘要 枢纽位置模型是对通信和交通网络设计问题进行建模的基本概念之一。这些网络经常面临攻击或自然灾害等威胁。然而，关于能够将此类威胁考虑在内的枢纽位置模型扩展的文献很少。在本文中，我们研究了所谓的多分配 p-hub r-interdiction 问题，其中定位器必须选择 p 个 hub，事先知道其中的 rp 将被拦截。目标是在拦截后最小化网络中的总路由成本。这个问题也可以解释为一个 minmax-robust p-hub 位置问题，它具有指数级大的不确定性集，其中包含每个集线器选择的最坏情况。我们为这个问题提出了一个新的双层公式并研究了它的数学结构。使用这些结构结果，我们提出了问题的第一个精确求解过程。我们为著名的 CAB 数据集计算最优解，并将它们与启发式结果进行比较。此外，我们调查了问题的复杂性，并表明给定集线器的拦截问题已经是 NP-hard 了。