A new mathematical-programming framework for facility-layout design

We present a new framework for efficiently finding competitive solutions for the facility-layout problem. This framework is based on the combination of two new mathematical-programming models. The first model is a relaxation of the layout problem and is intended to find good starting points for the iterative algorithm used to solve the second model. The second model is an exact formulation of the facility-layout problem as a nonconvex mathematical program with equilibrium constraints (MPEC). Aspect ratio constraints, which are frequently used in facility-layout methods to restrict the occurrence of overly long and narrow departments in the computed layouts, are easily incorporated into this new framework. Finally, we present computational results showing that the complete framework can be solved efficiently using widely available optimization software, and the resulting layouts improve on those obtained using previous approaches in the literature. Moreover, the framework can be used to find different competitive layouts with relatively little computational effort, which is advantageous for a user who wishes to consider several competitive layouts rather than simply using a mathematically optimal layout.