The tree-of-hubs location problem with interhub stopovers

The tree-of-hubs location problem (THLP) is a variant of the classical hub location problem, in which the set of hubs must be connected in a tree topology. The key decision variables involve the selection of hub locations, the allocation of spokes to hubs, and the design of a tree-structured interhub network. In this paper, we introduce a new extension of the THLP that incorporates stopover nodes—intermediate locations situated along the paths between hubs. The inclusion of stopovers helps reduce transportation costs by minimizing unnecessary back-and-forth trips and limiting transshipments at hubs. However, this benefit comes at the expense of potential detours in the interhub connections. We propose a mixed-integer linear programming (MILP) formulation to model this problem, with an objective function that minimizes the total cost of transporting commodities between multiple origins and destinations. Computational experiments are conducted using adapted instances from the AP-200 dataset. We also perform a sensitivity analysis on the discount factors associated with the use of stopovers. The results show that stopovers can lead to logistics cost savings of up to 15%. In addition, we provide managerial insights and quantify the impact of stopovers on network design costs by comparing solutions with and without their inclusion. Finally, we discuss the conditions under which stopovers can be effectively leveraged in practice.