On the p-hub interdiction problem

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.