A Mathematical Optimization Approach Based on Linearized Mip Models for Solving Facility Layout Problems

Abstract

One of the strategies used to optimize production processes is to define the best layout. For this, the relative positioning of the various equipment, areas, or functional activities inside the company is studied. Proper arrangement of facilities will result in shorter process times and higher productivity. In general, the objective function of the facility layout problem (FLP) is to reduce the total material handling cost. Although over six decades have been passed since the first work on FLP modeling was published, research on many aspects of this problem is still in an early stage and needs to be further explored, which motivated this study. In this paper, the unequal area of rectangular blocks with fixed dimensions and input/output points are considered for FLPs. Four new mixed-integer programming (MIP) models based on previous research formulations are developed. Then, a mathematical optimization approach based on the linearization of the models is applied. An algorithm that solves the linearized MIP model by CPLEX setting a time limit for the solution obtained excellent results for different test problems when compared to those reported in the literature.