the capacitated hierarchical p-hub median problem considering delivery time

in this paper, a hierarchical p-hub median problem is considered that all the nodes and arcs on the network have limited capacities. proposed model has three-level where the complete network at the top level consists of the central hubs. the second and third levels consist of hub and demand nodes respectively, which are connected through star networks. also, delivery time restriction is taken into account. the problem is to decide on the locations of a predetermined number of hubs and central hubs among the available nodes in order to minimize the total costs. numerical experiments demonstrate the efficiency and applicability of the proposed model for actual decision-making problems.