Reformulation-linearization method for global optimization of mixed integer linear fractional programming problems with application on sustainable batch scheduling

In this work, we propose a novel approach to the effective global optimization of mixed integer linear fractional programming (MILFP) problems: reformulation-linearization method. The proposed reformulation-linearization method is based on the integration of Charnes-Cooper transformation and Glover's linearization scheme. This method can provide the exact mixed integer linear programming (MILP) reformulation of a general MILFP problem, thus allowing the global optimization of MILFP problems by solving the equivalent MILP problems with the powerful MILP methods, only once. Reformulation and analysis are presented, along with a side-by-side comparison with the other MILFP solution methods. To illustrate its application, we address in this work a case study on sustainable batch scheduling modelled as MILFP problems. The results show that orders of magnitude reduction in CPU times can be achieved when using the proposed approach, compared to solving the problems with the general-purpose MINLP solvers. The proposed method is also shown to have comparable computational performance as the parametric algorithm.