Modeling fixed-charge problems with polynomials

In this paper we formulate fixed-charge problems with polynomials. Using polynomial formulations we show structural similarity between different kinds of linear and fixed charge formulations. We also show the benefits of applying polynomial formulation for finding an approximate solution for problems where no algorithms exist and in some cases for developing a method to provide direct solutions to those problems. The main benefit of this paper is better understanding of the fixed-charge function structure and better explanation of the local and global minima phenomena. We present a numerical example to illustrate applications of the proposed method.