RELAYOUT OF A MANUFACTURING FACILITY WITH SAFETY CONSIDERATIONS. Shamaya Morris

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1 RELAYOUT OF A MANUFACTURING FACILITY WITH SAFETY CONSIDERATIONS Shamaya Morris Problem Report submitted to the Benjamin M. Statler College of Engineering and Mineral Resources at West Virginia University in partial fulfillment of the requirements for the degree of Master of Science Industrial Engineering Alan McKendall, Ph.D., Chair Ashish Nimbarte, Ph.D. Don Stewart M.S., TMMWV Department of Industrial & Management Systems Engineering Morgantown, West Virginia 2016 Keywords: Facility Layout Planning, Unequal-Area Facilities, Mixed Integer Linear Programming Models, Copyright 2016 Shamaya Morris

2 ABSTRACT RELAYOUT OF A MANUFACTURING FACILTY WITH SAFETY CONSIDERATIONS Shamaya Morris This study investigates layout options for the machining department of the transmission production area of the Toyota Motor Manufacturing West Virginia (TMMWV) plant in Buffalo, WV. TMMWV is making modifications to one of its products. The current layout has a combination of 2 different types of machines used for machining of the existing model, model type A and model type B. For the production of the new model, the model A machines will be reused, which will require the removal of all model B machinery. This will require a re-layout of the machining area. As a result, the goal of this project is to provide TMMWV layout proposals, of which includes only the machinery for model type A. Of the provided proposals, an optimal or ideal layout as well as practical layouts will be pursued, with the objective of minimizing material handling cost while considering safety issues. This problem is defined as the unequal-area facility layout problem (FLP), which determines the positions of unequal-area facilities (e.g., departments, cells, machines) on the continuous plant floor. A mixed integer linear programming (MILP) model is presented for the FLP and is solved using the CPLEX solver. Layouts for each of the three departments within the machining area and two layout alternatives for the overall layout of the machining area were obtained for the TMMWV plant. Overall layout option 2 had a 61.8% improvement over the overall layout option 1 with respect to the objective of minimizing total distance parts travel.

3 DEDICATION I would like to dedicate this study to my entire family. Through every change, loss and heartbreak we ve emerged even closer than ever. Thank you for the encouragement, love and support. iii

4 ACKNOWLEDGEMENTS To Dr. McKendall, thank you so much for your consistent patience and encouragement. I couldn t have imagined going through this process without you. Your time spent helping me become a better student has is the greatest contribution possible. My deepest and most sincere Thank you. I wish to thank the entire IMSE for every year of my time here. Undergraduate was an unbelievable journey, and now I can say the same for my graduate studies. I appreciate the votes of confidence, every encouraging word and the many different ways they went above and beyond to assist me with whatever I needed. This has truly been the difference maker in my academic career. I would like to sincerely express my deepest gratitude to Don Stewart and everyone at Toyota Motor Manufacturing plant in Buffalo, WV. This project definitely wouldn t have been possible without you! Thank you so much for the wonderful opportunity of participating in the Co-Op program. The experience and lessons learned have helped me to become the engineering professional I ve always envisioned. Thank you! Lastly to my committee members: Dr. McKendall, Dr. Nimbarte and Don Stewart. Thank you so much for your patience with me during this process. My deepest expression of gratitude for your time and understanding. Thank you! iv

5 TABLE OF CONTENTS ABSTRACT... i DEDICATION... i ACKNOWLEDGEMENTS... ii LIST OF FIGURES... iv LIST OF TABLES... iv CHAPER 1: INTRODUCTION Introduction Problem Definition Research Objectives Organization... 5 CHAPTER 2: BRIEF LITERATURE REVIEW Literature Review... 6 CHAPTER 3: PROBLEM STATEMENT AND METHODOLOGY Problem Statement Methodology Data CHAPTER 4: COMPUTATIONAL RESULTS AND CONCLUSIONS Data and Discussion Safety Considerations Conclusive Remarks and Future Research References v

6 LIST OF FIGURES Figure 1.1a... 2 Figure 1.1b... 2 Figure Figure Figure Figure Figure Figure Figure Figure Figure LIST OF TABLES Table Table vi

7 CHAPER 1: INTRODUCTION 1.1 Introduction Facility re-layout is becoming more and more frequent as many industrial settings and manufacturing facilities are changing over time to include expanses in production systems and/or product modification. Changes in any layout are most often brought about due to fluctuations in the production flow (an increase or decrease in customer demand), changes in the design of the current product, products added or removed from the production schedule, and/or shortened product life cycles (McKendall et al., 2010). Planning is an essential component to ensuring a facility s continuing and effective production activity. One of the objectives of any existing facility modification is to decrease the number of days the facility has to halt production in order to achieve the desired changes (i.e. to reduce loss of production costs), which makes layout planning an imperative necessity for efficiency. Additional objectives, just as important, are the reduction of rearrangement costs (the cost incurred to relocate machine(s) from one location on the plant floor to another) as well as material handling costs. The facility layout problem (FLP) is determining the assignment of facilities (e.g. cells, machines, or departments) on the plant floor in such a way that minimize material handling costs. In some case, the objective may also be to maximize adjacency or closeness of pairs of facilities. The layout alternatives or designs generated from the FLP will be a direct derivative of the time spent planning. As stated above, it is especially crucial that considerable time is placed in the planning process at the beginning of the layout development to ensure high quality layout designs. The developed alternatives can take the form of a block layout which shows the relative locations and sizes of the planning facilities (or departments) and/or a detailed layout which shows the exact location of all equipment, work benches, and storage areas within each department. The representation of the layout will either be discrete, which is where the facility floor is divided into equally-sized grids representing the locations of the departments (Figure 1.1a) or a continuous layout representation where the facility floor is not divided equally but is represented as a continuous plane (Figure 1.1b). 1

8 a: Discrete representation b: Continuous representation Figure 1.1: Discrete and continuous representation of the plant floor. Realistically most facility areas are not equally-sized as it relates to an overall depiction of the facility, which makes the continuous representation a more flexible adaptation to use when modeling the layout problem. Because the departments are not located within equally-sized areas in this study the layout will be represented continuously. Input/Ouput (I/O) points indicate the entering and exiting locations for a machining cell. Ho and Moodie (1997) discusses the importance of I/O locations when automated material handling devices are in place to ensure and maintain efficiency of flow within the cell. I/O points can be located either at the center of the cell (the centroid of the cell) or along the cell s boundary due to the variance in the size and overall shape of the cell (Xiao et al., 2013). Xiao et al. (2013) also states, that when the I/O points of the cell are not located at the center but along the boundary of the cell the total travelling distance (TTD) is affected. Many studies present cases in which the fixed location of the I/O point is at the center of the cell. However, in this paper I/O points are considered and can be located anywhere within a department or along the boundary of a department. 2

9 The orientation of the department is a major component in the calculation of the distance a part travels as well as the effect the I/O point has on the cost calculation, as mentioned above. The orientation of a department can be either fixed or may be allowed to vary. A department is said to have vertical orientation if the longer side of the cell is along the y-axis and horizontal if the opposite is true. A department with fixed orientation is most commonly considered in situations where the plant floor may be restricted in size, or the location to which the cell will be assigned has other items that have already been placed or have existed in the space (i.e. large machinery that may be too costly to move or re-locate). This paper will consider variable orientation due to the amount of floor space available within each department. The FLP can be categorized as either static or dynamic. In the static FLP (SFLP) the material flows are assumed to be constant during the planning horizon. However, in the dynamic FLP (DFLP) there are multiple periods in the planning horizon, and the flow of materials changes from period to period. The objective then becomes to minimize the sum of the material handling cost for each period and the rearrangement costs. Rearrangement cost is the cost of rearranging the location of a department between consectutive periods. In this paper, the SFLP is considered. There are four basic types of FLPs (Tompkins et al., 2003) : 1) Product layout or otherwise known as a flowshop environment includes a combination of workstations performing operations on similar products or components (i.e. production/assembly line). 2) Process layout or a job shop environment consisting of a group of departments that perform similar processes on a large variety of products. The machines are group based on machine type based on the sequence of operations (i.e. metal cutting and gear cutting departments). 3) Product family or a group technology department which consists of a group of cells of the same or similar processes performing operations on a family of products. Group technology layouts are integrated with practices such as just in time (JIT), total quality management (TQM) and lean manufacturing concepts and techniques. Another aspect of this particular layout is known as cellular manufacturing (CM) where manufacturing cells can be formed in a variety of ways. The most popular grouping technique involves the grouping of machines to produce a family of parts. Once the groups are formed, 3

10 layout strategies will depend on the intra-cell layout which refers to the layout of the machines within the cells and the inter-cell layout which signifies the layout of the cells on the plant floor. 4) A fixed materials location layout is one where all of the work the product requires is located at the site of production. An example of this would include large items such as aircrafts and large sea vessels that are not easily moved (or moved at all) to manufacture. The main attributing characteristic for the proposed FLP relates to problem three (3) above, product family or group technology. This study focuses on the layout of three departments all of which are named and grouped according the to family of products in that particular area. Each cell performs a very similar set of processes on the part specifically moved through each cell. Instead of focusing on the intra-cell layout, this paper considers the inter-cell layout problem, which assigns the cells to locations on the plant floor. This study will investigate the re-layout (or relocation) of already identified machining cells within three departments, where the continuous representation is used to represent the plant floor. The objective of this problem is to find the most efficient layout that will make the most use of the made-available floor space while considering safety concerns for the walk-ways and travelling paths used by production team members as well as paths of flow for part conveyence. 1.2 Problem Definition Plant re-layout can be an expensive endeavor to explore. Modelling and solving the problem mathematically will provide good (and perhaps optimal) feasible solutions based on a given set of constraints that will allow the decision makers to view and analyze those solutions to see which is more adaptable to a specific plant and its needs. As a result, the goal of this project is to provide TMMWV layout proposals for the machining area, of which includes only the machinery for model type A. Of the provided proposals, an optimal or ideal layout as well as practical layouts will be pursued, with the objective of minimizing material handling cost while considering safety issues. A major component to the success and continually improving characteristic Toyota displays in its manufacturing practices is the attention and concerns for team members and their safety. 4

11 1.3 Research Objectives The objective of this study is to develop a mathematical model that will produce layout alternatives in regards to floor requirements, capacity constraints, material handling costs and team member safety. The anticipated results would serve as an ideal (optimal) layout as a basis for future work or plant expansions. Ideally the research methodology, which will be discussed in the sections to follow, will constitute an improved process for times to follow. 1.4 Organization The organization of this problem report is as follows: Chapter 2 comprises a brief literature review on the FLP and its problems, methodologies and a case study for layout designs for cellular manufacturing. Chapter 3 presents the problem statement in its entirety, which will include current plant diagrams, and the methodology used for solving the problem. Chapter 4 will conclude the report with a discussion of the achieved results from the problem, conclusive remarks and recommendations for future work. 5

12 CHAPTER 2: BRIEF LITERATURE REVIEW 2.1 Literature Review Bazargan-Lari (1997) presented the application of multi-objective inter- and intra-cell layout designs methodologies in a cellular manufacturing environment of a dynamic food manufacturing and a packaging facility located in Australia. The developed model, includes constraints that address machine orientation, overlapping, floor boundaries, closeness relationships, location preferences/restrictions, traveling cost (referred to as material handling costs) all of which renders a more-realistic model consistent with the needs and requirements of that particular space. The multi-objective approach includes a mathematical model, specifically a mixed integer linear programming (MILP) model in conjunction with a combination of goal programming and simulated annealing to generate efficient layout designs. McKendall and Hakobyan (2010) presented a MILP model to solve the unequal-area dynamic FLP (DFLP). There are three stages in determining the solution technique for the DFLP: the first is the selection procedure which is to use the flow to determine the order in which departments are to be selected for placement on the plant floor; the second is to use the placement procedure to place departments on the plant floor which yields a layout plan and its associated cost; and the third is the use of the tabu search to improve the layout plan obtained in the second stage. The results demonstrated the finding of solutions quickly using the construction technique (i.e. boundary search heuristic (BSH) which consisted of a selection and placement procedure) and the tabu search, an improvement heuristic, uses BSH to generate layout plans which performed well for solving large problems. Heragu and Kusiak (1988) examines the machine layout problem in flexible manufacturing systems (FMSs). The suggested method of solving the machine layout problem is the use of one of two construction algorithms with the second algorithm known as the Triangle Assignment Algorithm (TAA), known for its following advantages: low CPU time requirements compared to existing algorithms; no initial solution required; and the required CPU time is fairly equal for problems with equal and unequal machine sizes. Xiao et al. (2013) presented a MILP model and a two-step heuristic method to solve an unequal-area FLP with fix shapes, horizontal and vertical department orientations, and input/output points. However, the authors restrict the I/O points to specific locations on the boundaries of the department. 6

13 The survey presented by Drira et al., (2007) presents a frame-work to more effectively navigate the research of facility layout literature and presentations based on the given facility specifics such as workshop characteristics (i.e. product flow type, facility shapes and dimensions, product variety and volume, material handling systems, multi-floor layout, flow-line layouts such as backtracking and bypassing, and pick-up and drop-off location points), static/dynamic considerations, continuous/discrete representation, problem formulation and resolution approach. The conclusion of the paper offers several identified and discussed research directions congruent with the focus and aim of the performed research characteristics needed for the defined study. Other review papers available in the literature are Meller and Gau (1996) and Heragu and Kusiak (1987). 7

14 CHAPTER 3: PROBLEM STATEMENT AND METHODOLOGY 3.1 Problem Statement The area of interest (the machining area) has 3 departments. In Figure 3.1 the continuous representations of the department areas are depicted on the plant floor which shows the available area (e.g. existing location of machines) and the unavailable area. The current layout has a combination of 2 different machine types used for the machining of the existing models, the model type A and the model type B. For the newer model, only the A machines are needed and will be used thus requiring the removal of the model type B machinery. The problem consists of the re-layout of the machining cells within each department. The problem is defined as an unequal-area facility layout problem (FLP) which considers the continuous representation of the plant floor. Department 1 Department 2 Department 3 Figure 3.1: The 3 machining departments of the transmission plant which requires re-layout. The machining cells, part washers, inspection stations used for quality control and raw material areas will be relocated in their entirety on the plant floor in a manner that reduces total distance materials travel while considering worker safety such as safe traveling and walking paths or aisles, as well as part conveyance routes throughout the machining area. See figures 3.2, 3.3, and 3.4 for the current layout of departments 1, 2 and 3, respectively, after removing the type B machinery. 8

15 The assumptions for the FLP are as follows: 1. The layout within each cell (i.e. intra-cell layout) is given. It is important to note, team member safety was regarded when the machining cells were installed in their current location (during intra-cell layout design). It is standard that all machines are placed at a certain distance apart from one another to ensure ease of accessibility for tasks such as tool changes and machine maintenance. 2. In department 1, there were two identified machines that will be removed and replaced by one machine that will be common to both parts of the model being machined in this department. 3. All sections of the conveyors entering and leaving each cell will remain and be relocated with that cell in its entirety. 4. In department 1 (see figure 3.2), the raw material (RM) staging area (identified specifically in figure as cell 1) will be identified as its own cell feeding directly into department 1. Also, cells 7 and 8 are dummy cells (unavailable space) and are fixed to those locations on the plant floor. Figure 3.2: The layout of department 1. 9

16 5. In department 2 (see figure 3.3), the staging area (identified specifically in figure below as cell 9) will be identified as its own cell feeding directly into department Figure 3.3: The layout of department 2. 10

17 6. In department 3 (see figure 3.4), the staging area (identified specifically in figure below as cell 15) will be identified as its own cell feeding directly into department Figure 3.4: The layout of department 3. 11

18 3.2 Methodology An optimal layout for each of the three machining departments was first generated using a mixed integer linear programming (MILP) model. The model requires specific inputs (e.g. cell dimensions) that were taken from the layout provided by the plant. Each machining cell that received or dispersed part flow was given an identifying cell number (i.e. the part washer, inspection stations used for quality control, raw material cells, etc.) as depicted in the above Figures 3.2, 3.3 and 3.4 in Section 3.1. Next, the indices, parameters, and decision variables are defined for the MILP model. Indexes: i, j = 1,, N where N is the number of cells within the machining area. Parameters:, U W WU U B B Material flow quantity from cell i to cell j Lower (minimum) length of cell i allowed for orientation Upper (maximum) length of cell i allowed for orientation Lower (minimum) width of cell i allowed for orientation Upper (maximum) width of cell i allowed for orientation Lower (minimum) perimeter of cell i allowed for orientation Upper (maximum) perimeter of cell i allowed for orientation Length of layout area on plant floor Width of layout area on plant floor A large number Variables: (, ) The centroid of cell i ( ( 1 1 of lower left corner of (I 2, 2 ) Location of the upper right corner of cell i, I ) Location of the input point of cell i (, ) Location of the output point of cell i, Horizontal distance from the output point of cell i to the input point of cell j, Vertical distance from the output point of cell i to the input point of cell j 1 if cell is to the left of cell (, ) { 0 h 1 if cell is to the north of cell (, ) { 0 h 12

19 Next, a nonlinear mathematical programming formulation is presented below to solve the proposed FLP given the data set for each department. Minimize z = N N, ( + ) =1 =1,, (3.1) Subject to: ( 2 1 ) U i (3.2) W ( 2 1 ) WU i (3.3) 2( ) U i (3.4) 1 2 B i (3.5) 1 2 B i (3.6) = i (3.7) = i (3.8) (1, ) i and j, i j (3.9) (1, ) i and j, i j (3.10), +, +, +, 1 i and j, i < j (3.11), = I i and j, i j (3.12), = I i and j, i j (3.13),, 1, 2, 1, 2, I, I,, 0 i (3.14),,, 0 i and j, i j (3.15),,, = 0 1 i and j, i j (3.16) The objective function (3.1) is used to minimize the total traveling distance (TTD). Constraints (3.2) (3.4) ensure that each cell is within its the length, width and perimeter. Very similar to these, constraints (3.5) and (3.6) ensure that the lower left and upper right coordinates of each cell is within the boundary of the layout area on the plant floor considering horizontal and vertical orientation. Constraints (3.7) and (3.8) are equations to find the centroid location of each cell. Constraint sets (3.9) and (3.10) gives the relative locations between pairs of cells (e.g. cell 1 is to the left of cell 2). Constraint (3.11) makes certain that no two departments overlap. Constraints (3.12) and (3.13) gives the rectilinear distance from the output of cell i to the input of cell j. The final constraints, (3.14) (3.16), denote the restrictions on the variables. 13

20 CPLEX, an optimization software package, is a solver that has the ability to solve a linear mathematical programming model of a problem and return the optimal solution. A modeling language is used to generate the model for the CPLEX Solver. The model must be written into the modeling system, MPL (Mathematical Programming Language) with only linearized terms. To linearize the model, the standard method is used to linearize constraints (3.12) and (3.13). I = + i and j, i j (3.17),, I = + i and j, i j (3.18),, +,, +, 0 i (3.19),,,, Due to this change, the terms in the objective function (3.1) must be rewritten as well and be replaced with the following. N N + + (3.20) = =1 =1, (, +, +, +, ) As a result, the MILP model consist of objective function (3.20) subject to constraints (3.2) (3.11), (3.14), and (3.16) (3.19). 14

21 3.3 Data The data defined in Section 3.2, was collected using measurement tools within the AutoCad software from the provided detailed layout of the current design. Table 4.1 below is an overview of the data lifted from the AutoCad drawing and used for the MILP model discussed in Section 3.2. Table 3.1: Summary of data collected for problem. Width ft. Length ft. Perimeter ft. C1 Raw Material C2 Cell C3 Cell C4 Cell C5 Cell C6 Cell C7 FIXED C8 FIXED DEPARTMENT C9 Cell C10 Cell C11 Cell C12 Cell C13 Cell C14 FIXED DEPARTMENT C15 Cell C16 Cell C17 Cell C18 Cell C19 Cell C20 Cell C21 FIXED DEPARTMENT C22 Assembly FIXED

22 Production (part) flows (, ) are needed to calculate the objective function value (OFV) in the above model discussed in section 3.2 (objective function (3.20)). The production plan for the machining area was approximated at 600 parts per shift (3 shifts, 1800 parts/day) for all 3 departments. This amount was divided equally among the machining cells in its respective department and the flow was surveyed according to the process flow from cell to cell (e.g. in department 2, the machining cells are mirroring processes. The 600/shift part flow was divided equally among the 2 cells to represent an accurate flow route). Table 3.2 shows the exact flow from each cell in their respective departments. Table 3.2: Flow matrix for machining cells in departments 1, 2, and 3. 16

23 The collected data entries and the proposed MILP model were used to optimally layout the cells for all three departments as well as present layout alternatives to depict the machining area in its entirety (i.e. present inter-cell layouts)., the fixed departments are identified as well, in addition to assembly. Since the assembly area was not included in the layout area, this particular department was designated as a single point at the very top of the layout area. From the current plant layouts/designs provided, the production flow carries from the machining area and enters the assembly area for the assembly of the full part. In order to adequately define the product flows, and to evaluate the layout, an input/output point for the assembly area was defined and utilized to identify a thorough product flow. However, the layout of the machining area (departments 1, 2, and 3) and the assembly area should be considered simultaneously, since these two areas interact with each other (i.e. materials flow between them), and the layout of one affects the layout of the other. 17

24 CHAPTER 4: COMPUTATIONAL RESULTS AND CONCLUSIONS 4.1 Data and Discussion To graph everything in a relative location (relative to the plant floor), the I/O point of the assembly area was located above the top right corner of department 1, above the top center of department 2 and above the top left corner of department 3. Completing it this way would ensure that when the entire floor was evaluated for layout alternatives, that the other designs achieved would be as comparable as possible. Figures 4.1, 4.2 and 4.3 shown below are the optimal layouts for departments 1, 2 and 3 based on the MILP model and the given data inputs. Figure 4.1: Optimal layout generated by MPL/CPLEX for department 1. 18

25 Figure 4.2: Optimal layout generated by MPL/CPLEX for department 2. Figure 4.3: Optimal layout generated by MPL/CPLEX for department 3. 19

26 The overall cost of the solution was calculated to be 145, feet. The solution means that with this layout arrangement, the parts have to travel a total of 145,500 feet (TTD = 145,500). In Figure 4.4, you can see the entire floor layout for the machining area. Figure 4.4: Overall layout of the machining area. A second alternative overall layout was generated as well using MPL/CPLEX. The difference being the I/O points were allowed to vary. The layout, figure 4.5 below, had a solution of 55,500 feet, which is a 61.8% improvement over the layout obtained in Figure 4.4. Figure 4.5: Alternative overall layout of the machining area 20

27 4.2 Safety Considerations Safety is a major priority to the environment and culture of the plant. With employing over 1,300 team members in areas across the plant, safety and ergonomic studies have become an important factor with how the plant makes its decisions especially regarding facility changes. For simplicity purposes the safety outlook was summarized into two focal points regarding how to produce the best design alternatives possible for both production and the team members. The first being the traveling paths for team member safety. It is a company standard that any traveling path throughout the plant, especially in a heavy industrialized area, must maintain at lea st a 10-foot-wide identified pathway to ensure that team members are easily seen and can maneuver if necessary. This becomes essentially important when walking between the machining lines (or cells) and doing their daily required tasks. Notice the block layouts are given in figures 4.4 and 4.5 for the machining area. The next step would be to obtain a detailed layout, where aisle widths for team member travel would be obtained. In addition, consideration for the material handling path to the machines required by the part conveyance team in this area is particularly important as well. Just like the standard above for travelling paths, the plant requires a certain amount of space to and from each cell for part delivery for the safety of the workers in that area. This consideration is targeted directly for the raw material cells located in each department. Because of the automated feature of the cells (i.e. the material handling section for departments 2 and 3) it is important to ensure that the conveyance team has a certain amount of clearance and accessibility to deliver to the raw material cells since there is a level of interaction with these automated systems. In department 1, the raw material zone is actual a manual zone where team members use fork tuggers to deliver to the cell and to collect what they need during production. 4.3 Conclusive Remarks and Future Research The results obtained serves as an excellent starting point for further layout developments. As discussed above, the safety considerations are an important aspect to any industrial company who places employee safety at the top of the priority list. The most common practice used is to solve the problem in two steps; the first being to obtain a block layout showing the sizes and the relative locations of the cells; the second step is to obtain a layout design showing the specific details of the layout such as aisle widths, specific locations of machines within the cells, etc. (i.e. 21

28 detailed layout). This sort of problem takes a considerable amount of time to solve and evaluate. It is the suggestion of this study to pursue and set this option in place for future work. Another goal for future research is to consider the layout of the machining and the assembly area simultaneously because of the high interaction between the machining and assembly areas. 22

29 References Bazargan-Lari, Massoud. (1997). Case Study: Layout designs in cellular manufacturing. European Journal of Operational Research, 112, Drira, Amine., Pierreval, Henri., & Hajri-Gabouj, Sonia. (2007). Facility layout problems: A survey. Annual Reviews in Control, 31, Heragu, Sunderesh S., & Kusiak, Andrew. (1988). Machine Layout Problem in Flexible Manufacturing System. Operations Research in Manufacturing, Vol. 36, Ho, Ying-Chin., & Moodie, Colin L. (1997). Locating I/O Points of Flexible Manufacturing Cells with the Consideration of Within-Cell and Inter-Cell Flow Distance. Computers & Industrial Engineering, 33, Kim, Jae-Gon., Kim, Yeong-Dae.(2000). Layout planning for facilities with fixed shapes and input and output points. International Journal of Production Research, 38, Kusiak, A., & Heragu, Sunderesh S. (1987) The Facility Layout Problem. European Journal of Operational Research, 29, Meller, Russell D., & Gau, Kai-Yin. (1996). The Facility Layout Problem: Recent and Emerging Trends and Perspectives. Journal of Manufacturing Systems, 51, McKendall, Alan R., & Hakobyan, Artak. (2010), Heuristics for the dynamic facility Layout problem with unequal-area departments. European Journal of Research, 201, Tompkins, James A., John A. White, Bozer, Yavuz A. and Tanchoco, J. Facilities Planning. Hoboken: Wiley, Print. 23

30 Xiao, Yujie., Seo, Yoonho., & Seo, Minseok. (2013). A two-step algorithm for layout design of unequal-sized facilities with input/output points. International Journal of Production Research. 51,