Considering different kinds of vehicles in a hierarchical hub location model

In this study a hierarchical hub location problem with two layers is considered. the first layer includes small hubs and the second one includes a star-shaped network central hub. the considered case is a cargo delivery network where there is hierarchy between hubs. all the hubs and links are capacitated and there are three kinds of commodities for each of which there is a special kind of vehicle. the purpose is to determine the optimal cost by locating small hubs (city hubs) and the central hub, allocation of links to the hubs, and finding the optimal number of vehicles for each hub. the model is a mixed integer nonlinear programming. a case study for this model is performed in a cargo delivery network by using published data in iranian statistics organization website, and it is solved by appropriate software.