Global optimization of large-scale mixed-integer linear fractional programming problems: A reformulation-linearization method and process scheduling applications

Mixed-integer linear fractional program (MILFP) is a class of mixed-integer nonlinear programs (MINLP) where the objective function is the ratio of two linear functions and all constraints are linear. Global optimization of large-scale MILFPs can be computationally intractable due to the presence of discrete variables and the pseudoconvex/pseudoconcave objective function. We propose a novel and efficient reformulation-linearization method, which integrates Charnes-Cooper transformation and 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. Extensive computational studies are performed to demonstrate the efficiency of this method. To illustrate its applications, we consider two batch scheduling problems, which are modeled as MILFPs based on the continuous-time formulations. Computational results show that the proposed approach requires significantly shorter CPU times than various general-purpose MINLP methods and shows similar performance than the tailored parametric algorithm for solving large-scale MILFP problems. Specifically, it performs with respect to the CPU time roughly a half of the parametric algorithm for the scheduling applications.