An efficient multiple-stage mathematical programming method for advanced single and multi-floor facility layout problems

•A multiple stage mathematical programming method is presented for FLPs.•Both single and multi-floor problems can be handled.•A wide variety of high quality layouts at competitive cost can be obtained.•A short amount of time is consumed to approach the real-life problems.•Flexibility of the method to cover various real-life limitations has enhanced it. Single floor facility layout problem (FLP) is related to finding the arrangement of a given number of departments within a facility; while in multi-floor FLP, the departments should be imbedded in some floors inside the facility. The significant influence of layout design on the effectiveness of any organization has turned FLP into an important issue. This paper presents a three- (two-) stage mathematical programming method to find competitive solutions for multi- (single-) floor problems. At the first stage, the departments are assigned to the floors through a mixed integer programming model (the single floor version does not require this stage). At the second stage, a nonlinear programming model is used to specify the relative position of the departments on each floor; and at the third stage, the final layouts within the floors are determined, through another nonlinear programming model. The multi-floor version is studied in the states in which the locations of the elevators are either formerly specified or not. Computational results show that this framework can find a wide variety of high quality layouts at competitive cost (up to 43% reduction) within a short amount of time for small and especially large size problems, compared to the existing methods in the literature. Also, the proposed method is flexible enough to accommodate the complicated and real-world problems, because of using mathematical programming model and solving it directly.