Abstract: In order to identify the critical hubs in hub-and-spoke networks, a bilevel programming model is constructed considering the capacity limitation of hubs. Based on the dual problem of the lower level model, the bilevel programming model is transformed into single-level programming and linearized. The validity of the model is verified by a numerical example. The results show that the model has larger numbers of constraints and variables, longer solution time and different results of critical hub identification under the capacitated constraints. With the reductions of discount coefficients or the number of critical hubs or the increase of penalty cost, the calculation time generally increases. Penalty cost affects the results of critical hub identification. By comparing the critical hubs with different parameters, the relatively fixed critical hubs can be identified and fortification strengthened.

Key words: hub-and-spoke network, identification of critical hubs, bilevel programming model, capacity constraints