The Single Row Facility Layout Problem (SRFLP) is the NP-hard problem of arranging facilities on a line, while minimizing a weighted sum of the distances between facility pairs. In this paper, a detailed polyhedral study of the SRFLP is performed, and several huge classes of valid and facet-inducing inequalities are derived. Some separation heuristics are presented, along with a primal heuristic based on multidimensional scaling. Finally, a branch-and-cut algorithm is described and some encouraging computational results are given.
This was eventually published as: A.R.S. Amaral & A.N. Letchford (2013) A polyhedral approach to the single-row facility layout problem. Math. Program., 141(1-2), 453-477.