Fractional Polynomial Bounds for the Fixed Charge Problem

Abstract

In this paper we seek to enhance the understanding of the structure of the fixed charge transportation problem (FCTP) and to demonstrate the relationship between fixed charge problems and fractional polynomial functions. We provide a new approach for approximating and solving the FCTP by developing novel fractional polynomial approximations for the objective function to obtain lower and upper bounds for the optimal solution. In addition, the lower bound proposed in the paper can be used to obtain superior initial or starting conditions for any established branch-and-bound or iterative algorithm to accelerate convergence to the optimal FCTP solution.