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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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

The purpose of this article is to develop a bi-directional relaxed flexible bay structure (BRFBS) in the layout for the unequal area facility layout problems (UA-FLPs) and test the suitability of the proposed approach using literature data.

This research adopts a two-stage solution approach for UA-FLPs to form BRFBS in the layout. The solution to UA-FLPs is carried out in discrete space. The proposed heuristic method optimises the layout plan for minimising the material handling cost (MHC), and also, it indirectly optimises the space utilisation by reducing the empty space in the layout. The first stage of layout design assumes that all facilities are equal in size and uses quadratic assignment problem (QAP) model. QAP is solved with a simulated annealing heuristic method. In the second stage, a heuristic method is proposed to find the optimum width for each bay and the dimension for facilities. The proposed heuristic method is tested with numerical data available in the literature. Results are compared with the results obtained by layout planning software, and with the simulated annealing algorithm for flexible bay structure (SA-FBS) heuristic procedure for continuous space UA-FLPs.

The proposed two-stage solution approach gives the BRFBS for the UA-FLPs. BRFBS helps to create proper aisle structure in the layout plan. The layout configuration and solution of the proposed method is better than the layout planning software solution and SA-FBS solution. The application of the proposed heuristic method to case data gave lesser MHC, better space utilisation and better aisle formation than the existing layout.

The proposed approach has the limitation that it can be applied only to UA-FLPs solved in discrete space. When the UA-FLPs are solved in continuous space, then it is not possible to make application of this approach to form bi-directional relaxed flexible bays in the layout plan.

Most of the modern industries are automated, and they use material handling equipment (MHE) like automated guided vehicles (AGVs). Design of layout plans that help to create proper aisle structure for AGV’s in the layout plan is a challenging to the researchers. The BRFBS configuration is more suitable in the flexible manufacturing system where AGVs are used for material transportation.

This paper proposes a novel two-stage heuristic method for solving the UA-FLPs in discrete space. The proposed approach generates a BRFBS in the layout plan. The BRFBS helps to create a proper aisle structure suitable for better material handling operations. Hence, this type of layout helps in easy interaction of the MHE (e.g. AGVs) with the boundaries of the facilities touching the aisle.

As far as the authors know, no research has already been carried out on the multi-floor dynamic facility layout problem (MF-DFLP) in the continuous form regarding the flexible bay structure, the number and the variable location of the elevator. Therefore, the present paper models the given problem and attempts to find a sub-optimal solution for it using a meta-heuristic simulated annealing (SA) algorithm.

The efficient use of resources has always been a prominent matter for decision-makers. Many reasons including land use, construction considerations and proximity of departments have led to the design of multi-floor facilities. On the other hand, their fast-evolving environment calls for dynamic planning. Therefore, in this paper, a model and the SA algorithm for MF-DFLP are presented.

After presenting a mathematical model, the problem was solved precisely in a small size using the GAMS software. Also, a near-optimal solution method using a SA meta-heuristic algorithm is suggested and the proposed algorithm was run in the MATLAB software. To evaluate the presented model and the proposed solution, some test cases were considered in two aspects. The first aspect was the test cases that are newly generated in small, medium and large sizes to compare the exact optimal solution with the results of the meta-heuristic algorithm. Eight test cases with small sizes were solved using the GAMS software, the optimum solutions were obtained in a reasonable time, and the cost of their solutions was equal to that of the SA algorithm. Eight test cases with medium sizes were run in the GAMS software with the time limit of 80,000 s, and the SA algorithm had performed better for these test cases. Two test cases were also considered in large size that GAMS could not solve them, whereas the SA algorithm successfully found a proper solution for each. The second aspect included the test cases from the literature. The result showed that suggested algorithm is more capable of finding best solutions than compared algorithms.

In this paper, an unequal area MF-DFLP was studied in a continuous layout form in which the location and number of the elevators were considered to be variable, and the layouts were considered with flexible bay structure. These conditions were investigated for the first time.

This paper develops a platform that can be used to determine how to effectively and efficiently deal with a large number of temporary facilities under a constrained site condition(s). The ultimate goal is to reduce the material handling costs between transformation phases of construction works occurring during the project's development period.

Empirical and deductive research is first adopted to mathematical model dynamic site layout planning using the branch and bond algorithm (B&B). Second, a real-life construction project is examined to illustrate how dynamic site layout planning (using the aforementioned B&B algorithm and a computer software program called LINGO) can reduce the material handling costs. The application of the proposed methodology is then showcased against a case study that utilizes a comparative analysis between the “dynamic” and “statistic” site planning approaches.

By dividing the construction period into different phases, the developed model is shown to be capable of optimizing the material handling costs between the phases of transformation during construction works. Optimal costs are also considered using the site boundary and unit cost for moving construction materials between two facilities. The comparative analysis results illustrate that the B&B algorithm reduces material handling costs by 33%.

The proposed model offers an effective planning algorithm for the site layout and location of temporary facilities. More specifically, it can make a substantial improvement in reducing the travel time and material handling cost between the temporary facilities in the construction sites.

The primary knowledge contribution of this study to the site layout is successfully deal with the unequal area problem of temporary site facilities and incorporates the concept of dynamics site planning into the algorithm.

Real flight is cognitively demanding; accordingly, both indicators and display panel layout should be user-friendly to improve pilot-aircraft interaction. Poor pilot-interface interactions in aircrafts could result in accidents. Although a general reason of accidents is improper displays, relatively few studies were conducted on interfaces. This study aims to present an optimization model to create intuitively integrated user-friendly cockpit interfaces.

Subjectivity within most usability evaluation techniques could bring about interface design problems. A priori information about indicator’s possible locations may be available or unavailable. Thus different analytical approaches must be applied for modifications and new interface designs. Relative layout design (RLD) model was developed and used in new interface designs to optimize locations of indicators. This model was based on layout optimization and constructed in accordance with design requirements, ergonomic considerations with the pilot preferences. RLD model optimizes interface design by deploying indicators to the best locations to improve usability of display panel, pilot-aircraft interaction and flight safety.

Optimum interfaces for two problem instances were gathered by RLD model in 15.77 CPU(s) with 10 indicators and 542.51 CPU(s) with 19 indicators. A comparison between relative and existing cockpit interfaces reveals that locations of six navigation and four mechanical system indicators are different. The differences may stem from pilots’ preferences and relativity constraints. Both interfaces are more similar for the central part of the display panel. The objective function value of relative interface design (Opt: 527938) is far better than existing interface (737100). The RLD model improved usability of existing interface (28.61 per cent considering decrease in the objective function values from 737100 to 527938.

Future cockpit and new helicopter interface designs may involve RLD model as an alternative interface design tool. Furthermore, other layout optimization problems, e.g. circuit boards, microchips and engines, etc. could be handled in a more realistic manner by RLD model.

Originality and impact of this study related to development and employment of a new optimization model (RLD) on cockpit interface design for the first time. Engineering requirements, human factors, ergonomics and pilots’ preferences are simultaneously considered in the RLD model. The subjectivity within usability evaluation techniques could be diminished in this way. The contributions of RLD model to classical facility layout models are relativity constraints with the physical constrictions and ergonomic objective function weights. Novelty of this paper is the development and employment of a new optimization model (RLD) to locate indicators.

This paper presents a new approach for combining the quantitative and qualitative objectives to resolve the facility layout problem. In previous studies, there are various approaches to generate solutions for the facility layout problem. Suboptimal solutions need to be considered for large layout problems since optimal algorithms are computationally infeasible. Therefore, it is important to set criteria to measure the quality of various solutions. In this paper, a new measure of solution quality, the probability of superiority, is offered for the determination of the probability that one layout is better than the others. An example is presented to illustrate our proposed approach.

Some of the main features of the major existing approaches designed to solve the multi‐goal layout problem are highlighted. Most of these heuristic approaches are of the improvement type which take account of constraints within areas of departments. Two heuristic approaches of the construction type are outlined. MFLAP (Multi‐goal Facility Layout Planning) is a construction type algorithm based on cell formation technique. MFLAPSA (Multi‐goal Facility Layout Planning under the constraints on Shapes and Areas of Facilities), like MFLAP, is also a construction type heuristic based on cell formation technique but it incorporates additional constraints such as shape, location flexibility and exposure for a department. The procedure and capabilities of MFLAP and MFLAPSA are outlined.

The concrete building products manufacturing industry supplies 2,000‐4,000 precast concrete building products to the construction industry. Owing to seasonal demand, the industry builds up stock in winter to meet the high demand in summer. As concrete products are heavy and vary in shape and size, proper stocking in terms of layout and methods of stocking of products on the yard is essential. Industrial practice suggests that stockyard space management gets less attention during strategic and budget planning as it is left to the stockyard manager. The industry experiences space congestion for both the storage and dispatch of products. During dispatch process, greater retrieval time is required, long queues of lorries (shipping vehicles) are formed and desired level of service cannot be maintained. Presents a review of stockyard operations, analysis of parameters affecting loading and dispatch process on the yard and strategies to optimise the stockyard layout. It is expected that proper layout planning will reduce the cost of delivery of products by 5‐10 per cent in the industry where profit is less than 5‐8 per cent.

Facility layout is a classical industrial/production engineering problem. Good layout will help any company to improve its business performance. Presents a general overview of the facility layout problem and includes information about approaches to the solution of the problem. Discusses the role of the computer; and the contribution of facility layout to an organization’s competitive advantage. Describes experiences of organizations with facility layout.