A reformulation-linearization method for the global optimization of large-scale mixed-integer linear fractional programming problems and cyclic scheduling application

Abstract

Global optimization of large-scale mixed-integer linear fractional programs (MILFPs) could be computationally intractable due to the presence of discrete variables and the pseudoconvex/pseudoconcave objective function. In this paper, we propose a novel and efficient reformulation-linearization method, which integrates the Charnes-Cooper transformation and the Glover's linearization scheme, to transform general MILFPs into their equivalent mixed-integer linear programs (MILP), allowing MILFPs to be globally optimized effectively with MILP methods. A case study on the cyclic scheduling of multipurpose batch plant is demonstrated to illustrate the efficiency of this method. Computational results show that the proposed approach requires significantly shorter CPU times than various general-purpose MINLP methods and is comparable with the tailored Dinkelbach's algorithm for solving large-scale MILFP problems.