Strong mixed-integer formulations for the floor layout problem

TL;DR

This paper develops a unified systematic approach to creating mixed-integer programming formulations for the floor layout problem, leading to new formulations that improve computational efficiency and solve previously unsolvable instances.

Contribution

It introduces a systematic formulation construction method that unifies existing models and generates new, more effective formulations for the FLP, with potential applications to other problems.

Findings

New formulations significantly reduce solution times.

Some previously unsolvable instances are now solved.

The approach unifies all known formulations for the FLP.

Abstract

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.