  The floor layout problem (FLP) tasks a designer with positioning a collection
of rectangular boxes on a fixed floor in such a way that minimizes total
communication costs between the components. While several mixed integer
programming (MIP) formulations for this problem have been developed, it remains
extremely challenging from a computational perspective. This work takes a
systematic approach to constructing MIP formulations and valid inequalities for
the FLP that unifies and recovers all known formulations for it. In addition,
the approach yields new formulations that can provide a significant
computational advantage and can solve previously unsolved instances. While the
construction approach focuses on the FLP, it also exemplifies generic
formulation techniques that should prove useful for broader classes of
problems.
