Facility layout problems are an important class of operations research problems that has been studied for several decades. Most variants of facility layout are NP-hard, therefore global optimal solutions are difficult or impossible to compute in reasonable time. Mathematical optimization approaches that guarantee global optimality of solutions or tight bounds on the global optimal value have nevertheless been successfully applied to several variants of facility layout. In this talk, we review three classes of layout problems, namely row layout, unequal-areas layout, and multi-floor layout. and summarize the main contributions to the area made using mathematical optimization, mostly mixed integer linear optimization and conic optimization. We also briefly discuss directions that remain open for future research.
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