Distributionally Robust Chance-Constrained p-Hub Center Problem

Abstract

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. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This work is partially supported by the National Natural Science Foundation of China [Grants 72101187 and 72021002] and Early Career Scheme from the Hong Kong Research Grants Council General Research Fund [Grant 9043424] and NSFC/RGC Joint Research Scheme N_CityU105/21. Y. Zhao is supported by the Ministry of Education, Singapore, under its 2019 Academic Research Fund Tier 3 grant call [Grant MOE-2019-T3-1-010]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0113 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0113 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .