Efficient models for the facility layout problem

In this paper, two new models of the facility layout problem are presented: linear continuous with absolute values in the objective function and constraints, and linear mixed integer. The linear mixed integer models have lesser number of integer variables than any other existing formulation for the facility layout problem. While most other linear mixed-integer models available in the literature have been obtained through a linearization of the quadratic assignment problem, the ones presented in this paper are not. The continuous models have an even more compact form. An advantage of the formulations presented in this paper is that the location of sites need not be known a priori. More importantly, two of the formulations model the layout problem with facilities of unequal area. Solving the models presented with an unconstrained optimization algorithm yields good quality suboptimal solutions in a relatively low computation time. The continuous models appear to be more useful for solving the facility layout problem than other models published in the literature.