A linear programming embedded probabilistic tabu search for the unequal-area facility layout problem with flexible bays

In this paper, a probabilistic tabu search (PTS) approach is proposed to solve the facility layout problem (FLP) with unequal area departments. For the representation, the flexible bay structure (FBS), which is a very common layout in many manufacturing and retail facilities, is used. In this paper, the FBS is relaxed by allowing empty spaces within bays, which results in more flexibility in assigning departments into bays. In addition, departments are allowed to be located more freely within the bays, and they can have different side lengths as long as they are within the bay boundaries and do not overlap. To achieve these goals, department shapes and their locations within bays are determined LP. A PTS approach is developed to search an overall layout structure that describes relative positions of departments for the relaxed-FBS (RFBS). The proposed LP embedded PTS–RFBS approach is used to solve thirteen FLP instances from the literature with varying sizes. The comparative results show that this approach is very promising and able to find new best solutions for several test problems.