Reliable single allocation hub location problem under hub breakdowns

The design of hub-and-spoke transport networks is a strategic planning problem, as the choice of hub locations has to remain unchanged for long time periods. However, strikes, disasters or traffic breakdown can lead to the unavailability of a hub for a short period of time. Therefore it is important to consider such events already in the planning phase, so that a proper reaction is possible; once a hub breaks down, an emergency plan has to be applied to handle the flows that were scheduled to be served by this hub. In this paper, we develop a two-stage formulation for the single allocation hub location problem which includes the reallocation of sources to a backup hub in case the hub breaks down. In contrast to related problem formulations from the literature, we keep the non-linear structure of the problem in our model. A branch-and-cut framework based on Benders decomposition is designed to solve large scale instances to proven optimality. Thanks to our decomposition strategy, we keep the structure of the resulting formulation similar to the classical single allocation hub location problem, which in turn allows to use classical linearization techniques from the literature. Our computational experiments show that this approach leads to a significant improvement in the performance when embedded into a standard mixed-integer programming solver. We report optimal solutions for instances much bigger than those solved so far in the literature.