Novel integer linear programming models for the facility layout problem with fixed-size rectangular departments

This paper considers the facility layout problem (FLP) that places a set of fixed-size rectangular departments on a given rectangular site in such a way that the total material flow between adjacent departments is maximized. We demonstrate that an existing integer linear programming (ILP) model for this problem is flawed. Then, two novel ILP models are developed by reformulating some constraints of the existing model from different perspectives. They both significantly reduce the quantity of decision variables. It is also shown that the proposed models can be simplified if all departments have the same size. Numerical experiments conducted on several benchmark instances show that the proposed models outperform the existing one with promising results. Our models can solve all tested instances to optimality within reasonable time, while the existing one cannot.