Distributionally Robust Chance-Constrained p -Hub Center Problem

The p -hub center problem is a fundamental model for the strategic design of hub location. It aims at constructing p fully interconnected hubs and links from nodes to hubs so that the longest path between any two nodes is minimized. Existing literature on the p -hub center problem under uncertainty often assumes a joint distribution of travel times, which is difficult (if not impossible) to elicit precisely. In this paper, we bridge the gap by investigating two distributionally robust chance-constrained models that cover, respectively, an existing stochastic one under independent normal distribution and one that is based on the sample average approximation approach as a special case. We derive deterministic reformulations as a mixed-integer program wherein a large number of constraints can be dynamically added via a constraint-generation approach to accelerate computation. Counterparts of our models in the emerging robust satisficing framework are also discussed. Extensive numerical experiments demonstrate the encouraging out-of-sample performance of our proposed models as well as the effectiveness of the constraint-generation approach.