The one–dimensional facility layout problem is concerned with arranging n departments of given lengths on a line, while minimizing the weighted sum of the distances between all pairs of departments. The problem is NP–hard because it is a generalization of the minimum linear arrangement problem. In this paper, a 0–1 quadratic programming model consisting of only O(n2) 0–1 variables is proposed for the problem. Subsequently, this model is cast as an equivalent mixed–integer program and then reduced by preprocessing. Next, additional redundant constraints are introduced and linearized in a higher space to achieve an equivalent mixed 0–1 linear program, whose continuous relaxation provides an approximation of the convex hull of solutions to the quadratic program. It is shown that the resulting mixed 0–1 linear program is more efficient than previously published mixed–integer formulations. In the computational results, several problem instances taken from the literature were efficiently solved to optimality. Moreover, it is now possible to efficiently solve problems of a larger size.
