This paper studies a two-stage decision-making framework for the profit-maximising hub location problem under uncertain transportation costs, wherein the first stage, the optimal location of hubs, is determined, and in the second stage, flow routeing decisions are made. We assume that while the true probability distribution of uncertain parameters might be unknown, the decision maker has access to a set of historical data from which a prior belief is formed about the underlying distribution. We propose to construct a set of probability distributions around this belief in the sense of Wasserstein distance. Then, we study a data-driven distributionally robust optimisation (DRO) approach to the studied problem to maximise the worst-case profit over the set of candidate probability distributions. We propose the Benders\\\\\\\\\\\\\\\' decomposition and L-shaped algorithms to solve the studied problem. Numerical results show that the L-shaped algorithm reaches optimal solutions with less computation effort when compared to the Benders\\\\\\\\\\\\\\\' decomposition algorithm and an off-the-shelf solver. Moreover, the Wasserstein DRO approach effectively enhances the out-of-sample performance compared to deterministic and stochastic programming approaches. Finally, the Wasserstein DRO approach leads to a more resilient network by establishing more hubs and links in the worst-case scenario compared to other approaches.

Keywords