In this article, we propose Simulated Annealing (SA) heuristic to solve Unequal Area Dynamic Facility Layout Problem (FBS) with Flexible Bay Structure (UA-DFLPs with FBS). The UA-DFLP with FBS is the problem of determining the facilities dimension and their location coordinates with flexible bays formation in the layout for various periods of the planning horizon. The UA-DFLP with FBS is more constrained than general UA-DFLP and it is an NP-complete problem. The proposed SA is tested with the available UA-DFLPs instances in the literature. The proposed SA heuristic has given new best solution or the same solution for FBS based problems as compared with the best-known reported in the UA-DFLPs with FBS literature. The proposed SA heuristic is also tested on standard UA-DFLPs used in non-FBS approaches. The SA heuristic solution is not significantly different from the best solution reported in the literature for non-FBS approaches. Equal area DFLP instances are also solved with the proposed SA and the results obtained are promising with the solutions reported in the literature. Hence the results obtained indicate that the proposed SA for UA-DFLP with FBS is effective and versatile for both equal and unequal area dynamic facility layout problems. The computational efficiency of the proposed SA heuristic is very much competitive as compared to other meta-heuristics computational timings reported in the literature.

Purpose The purpose of this paper is to develop a mathematical model for the design of robust layout for unequal area-dynamic facility layout problem with flexible bay structure (UA-DFLP with FBS) and test the suitability of generated robust layout in a dynamic environment. Design/methodology/approach This research adopts formulation of a mathematical model for generating a single layout for unequal area facility layout problems with flexible bay structure under dynamic environment. The formulated model for the robust layout formation is solved by developing a simulated annealing algorithm. The proposed robust approach model for UA-DFLP with FBS is validated by conducting numerical experiments on standard UA-DFLPs reported in the literature. The suitability of the generated robust layout in a dynamic environment is tested with total penalty cost criteria. Findings The proposed model has given a better solution for some UA-DFLPs with FBS in comparison with the adaptive approach’s solution reported in the literature. The total penalty cost is within the specified limit given in the literature, for most of the layouts generated for UA-DFLPs with FBS. In the proposed model, there is no rearrangement of facilities in various periods of planning horizon and thus no disruptions in operations. Research limitations/implications The present work has limitations that when the area and aspect ratio of the facilities are required to change from one period to another, then it is not possible to make application of the robust approach-based formulation to the dynamic environment facility layout problems. Practical implications Rearrangement of facilities in adaptive approach disrupts the operations whereas in the proposed approach no disruption of production. The FBS approach is more suitable for layout planning where proper aisle structure is required. The solution of the proposed approach helps to create a proper aisle structure in the detailed layout plan. Thus, easy interaction of the material handling equipment, men and materials is possible. Originality/value This paper proposes a mathematical formulation for the design of robust layout for UA-FLPs with FBS in a dynamic environment and an efficient simulated annealing algorithm as its solution procedure. The proposed robust approach generates a single layout for the entire planning horizon. This approach is more useful for facilities which are difficult/sensitive to relocate in various periods of the planning horizon.

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Purpose The purpose of this paper is to review, evaluate and classify the academic research that has been published in facility layout problems (FLPs) and to analyse how researches and practices on FLPs are. Design/methodology/approach The review is based on 166 papers published from 1953 to 2021 in international peer-reviewed journals. The literature review on FLPs is presented under broader headings of discrete space and continuous space FLPs. The important formulations of FLPs under static and dynamic environments represented in the discrete and continuous space are presented. The articles reported in the literature on various representations of facilities for the continuous space Unequal Area Facility Layout Problems (UA-FLPs) are summarized. Discussed and commented on adaptive and robust approaches for dynamic environment FLPs. Highlighted the application of meta-heuristic solution methods for FLPs of a larger size. Findings It is found that most of the earlier research adopted the discrete space for the formulation of FLPs. This type of space representation for FLPs mostly assumes an equal area for all facilities. UA-FLPs represented in discrete space yield irregular shape facilities. It is also observed that the recent works consider the UA-FLPs in continuous space. The solution of continuous space UA-FLPs is more accurate and realistic. Some of the recent works on UA-FLPs consider the flexible bay structure (FBS) due to its advantages over the other representations. FBS helps the proper design of aisle structure in the detailed layout plan. Further, the recent articles reported in the literature consider the dynamic environment for both equal and unequal area FLPs to cope with the changing market environment. It is also found that FLPs are Non-deterministic Polynomial-complete problems, and hence, they set the challenges to researchers to develop efficient meta-heuristic methods to solve the bigger size FLPs in a reasonable time. Research limitations/implications Due to the extremely large number of papers on FLPs, a few papers may have inadvertently been missed. The facility layout design research domain is extremely vast which covers other areas such as cellular layouts, pick and drop points and aisle structure design. This research review on FLPs did not consider the papers published on cellular layouts, pick and drop points and aisle structure design. Despite the possibility of not being all-inclusive, the authors firmly believe that most of the papers published on FLPs are covered and the general picture presented on various approaches and parameters of FLPs in this paper are precise and trustworthy. Originality/value To the best of the authors’ knowledge, this paper reviews and classifies the literature on FLPs for the first time under the broader headings of discrete space and continuous space representations. Many important formulations of FLPs under static and dynamic environments represented in the discrete and continuous space are presented. This paper also provides the observations from the literature review and identifies the prospective future directions.