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.

ABSTRACT In this work we propose a heuristic algorithm for the layout optimization for disks installed in a rotating circular container. This is a unequal circle packing problem with additional balance constraints. It proved to be an NP-hard problem, which justifies heuristics methods for its resolution in larger instances. The main feature of our heuristic is based on the selection of the next circle to be placed inside the container according to the position of the system's center of mass. Our approach has been tested on a series of instances up to 55 circles and compared with the literature. Computational results show good performance in terms of solution quality and computational time for the proposed algorithm.