A two-stage mathematical-programming method for the multi-floor facility layout problem

The purpose of this research paper is to present a three-stage method using mathematicalprogramming techniques that finds high-quality solutions to the multi-floor facility layout problem. The first stage is a linear mixed-integer program that assigns departments to floors such that the total of the departmental interaction costs between floors is globally minimized. Subsequent stages find a locally optimal layout for each floor. Two versions of the proposed approach are considered. The first solves the layout of each floor independently of the other floors, allowing up to one elevator location. The second solves the layout of all floors simultaneously, allowing for multiple elevator locations. Variations to the problem and to the basic method are also investigated. The two versions are tested and compared to each other through computational experiments and also to existing results in the literature. It is clear that the proposed method can provide several high-quality layouts for medium and large-scale problem instances. Not only does it achieve competitive results compared to previous methods, but it also overcomes some of their limitations.