A mathematical programming approach for bi-levels tree hub location network

We design an optimal tree hub location network containing bi-levels, hub nodes and non hub nodes. Often, the cost of connection link between two places is very high. Due to take over problem, some nodes play role of hub. Hub nodes act switching, transshipment, and distribution of people or commodity. A route between all nodes should be existed in the network. So, transportation network must be graph with minimum number of arcs while spans all nodes. There is no cycle in this network. Here, we propose a mathematical programming model for a network considering optimal location of hub facilities where all connection links in the network are in the form of tree. Our aim is cost minimization using minimum spanning tree (MST) method in the whole network.