An Improved Formulation for the Ring Hierarchical Hub Network Design Problem

This work addresses the Ring Hierarchical Hub Network Design Problem, which combines hierarchical allocation decisions with a ring structure connecting central hubs. The problem is computationally challenging due to its combinatorial nature and the interaction between location, allocation, and routing decisions. Motivated by the limited number of formulations available in the literature, this study proposes improvements to an existing mixed-integer linear programming model. The approach introduces reformulations and valid inequalities that reduce structural redundancies and enhance computational performance. Computational experiments on instances from the USA423 dataset demonstrate consistent performance gains. In instances where both models reach optimality, the proposed formulation reduces total solution time by 18.59%, and is also able to find high-quality feasible solutions in cases where the original model fails. The results highlight the effectiveness of the proposed formulation, particularly for larger instances.