A hierarchical location model for cultural center location problem

A location problem with a hierarchy of cultural center is proposed and solved. This work describes a statistical model of a nested hierarchy with capacity constraint and utility function, motivated by results in mathematic deduction. Sub-utility function is adopted and a variety of location factors have been taken into account, such as distance, the level of service, etc. The constraints of the model include the whole coverage of demand, the maximum and the minimum capacity constraints of cultural center, the single-distribution of the demand and the utility priority distribution. The usefulness of the model is illustrated through a real-world application to Xi'an cultural center location.