Robust hub network design problem

•We develop a robust hub location formulation with demand uncertainty.•A conic integer programming formulation is provided.•A strong linear relaxation is provided.•Robust hub locations are different from the deterministic solutions.•Linear relaxation provides the optimal solution for all cases tested.

This paper presents a robust formulation for the uncapacitated single and multiple allocation hub location problem where demand is uncertain and its distribution is not fully specified. The proposed robust model is formulated as a mixed integer nonlinear program and then transformed into a mixed integer conic quadratic program. An efficient linear relaxation strategy is proposed which is found to deliver the optimal solutions for all the cases considered in this paper. Numerical experiments suggest location of more number of hubs when accounting for demand uncertainty using robust optimization compared to the deterministic setting.