Abstract: With construction allocation resource constraint taking into account, the R-allocation p-hub median problem is put forward. Then, two versions of mixed integer programming models are developed to describe the problem. Based on the models, analysis is done and result shows that, for some special cases, these two models are equivalent to the classic single and multiple allocation formulations. Well-known datasets are used to test the proposed method. It indicates that, by the proposed method, when the permissive allocation number is 60, the total network traffic cost is 15% less than that by UrApHMP. When the permissive allocation number is small, the increase of total allocation number results in significant cost saving. When this number is 45, the increase of this number can gain only a little cost saving. When the total allocation number reaches 60, the increase of this number has no effect on the traffic cost and hub location. The effectiveness and practicability of these models are demonstrated by numerical examples.

Key words: hub, p-hub median, single allocation, multiple allocation