Parameterized integer programming models for multifactors representatives apportionment

This paper develops parameterized integer programming models for the problem of multifactors representatives apportionment. In the light of the idea of the optimal uniform approximation theory, we formulate such apportionment problem as three mathematical models. In all of the models, the total number of representatives is regarded as an adaptable parameter, the unfair degree of apportionment is evaluated using the norm-∞ of the vector, and the social characteristics of the different “units” are described by introducing the concept of the factor level matrix. In addition, we also attempt to describe some natural properties of each member in our models.