The hub location is a major problem in the systems with high dependence on the transportation of goods, information, and passengers between the constituent parts. The present study is aimed to introduce a multi-commodity multi-model hierarchical hub location problem with uncertain demand. Thus, it is estimated by intuitionistic fuzzy variables. The objective function in the present problem is to minimize the total transportation costs in the network to determine the optimal hub location, allocate non-hub nodes to the hubs and the ground hubs to the air hubs, and identify the type of vehicles required in each route. The model has a hierarchical structure consisting of a three-echelon network (i.e., central hubs, non-central hubs, and demand nodes) connected in the star-tour-star form. A four-index mathematical model was presented and solved by GAMS optimization software. The results indicated that the objective function (cost) has a descending trend with increasing the number of hubs which can be assigned to the decline in the transportation costs. The costs increased by a decrease in the maximum delivery time which could be due to the selection method of the transportation mode. In the multi-product case, the costs declined by increasing the number of hubs as these hubs decremented the network complexity. Regarding the NP-Hard nature of the hub problems, a genetic meta-heuristic algorithm was proposed in the MATLAB software to solve the large-scale problem. According to the results, this algorithm offered close-optimal solutions. Noteworthy, this study employed known AP datasets.
