Layout Design of a Furniture Prodtction Line Using Formal Method

Journal of Industrial and Systems Engineering
Vol. 1, No.1, pp81-96
Spring 2007
Layout Design of a Furniture Production Line Using Formal Methods
Pinto Wilsten J, Shayan E. *

Faculty of Engineering, Swinbume University of Technology, Hawthom, Victoria, Australia

ABSTRACT
This paper experiments application of different heuristic approaches to a real facility layout problem at a furniture
manufacturing company. All the models are compared using AHP, where a number of parameters of interest are
employed. The experiment shows that formal layout modelling approaches can be effectively used real problems
faced in industry, leading to significant improvements.
Keywords: Facilities layout design, Layout algorithms, Optimisation, Production lines.

1. INTRODUCTION

The fumniture industry is experiencing a very competitive era like many others, thus striving hard to find methods to
reduce manufacturing costs, improve quality etc. As part of a productivity improvement program in a manufacturing
company herein called (The Company = TC) we conducted a project to optimize the layout design of the production
line at the shop floor of this company aiming at overcoming the current problems attributed to the inefficient layout. It
was decided to apply a number of layout modelling techniques to generate a near optimal layout based on formal
methods that are rarely used in practice. The modelling techniques used are Graph Theory, Bloc Plan, CRAFT,
Optimum Sequence and Genetic Algorithm. These layouts were then evaluated and compared using three criteria
namely Total Area, Flow * Dist and the Adjacency Percentage. Total Area refers to the area occupied by the
production line for each model developed. Flow * Dist calculates the sum of products of the flow and the distance
between every two facilities. Adjacency Percentage calculates the percentage of the facilities that meet the
requirement of being adjacent.
Selection of the best layout was also done formally usingmulti-criteriadecision making approach AHP (Satty, 1980)
using Expert Choice software. The best layout was compared with the existing layout to demonstrate improvements
gained by formal approaches to layout design.
The definition of a plant layout problem is to find the best arrangement of physical facilities to provide an efficient
operation (Hassan and Hogg, 1991). The layout affects the cost of material handling, lead time and throughput. It
hence affects the overall productivity and efficiency of the plant. According to Tompkins and White (1984) the design
of facilities has been around throughout recorded history and indeed town facilities that were designed and built are
described in the ancient

* Corresponding Author
history of Greece and the Roman Empire. Among the first who studied this problem are Amour and Buffa et al.
(1964). Little seems to have been published in the 1950's. Francis and White (1974) were the first who collected
and updated the early research on this area. Later research has been updated by two studies the first by Domschke
and Drexl (1985) and the other by Francis et al. (1992). Hassan and Hogg (1991) reported an extensive study on
the type of data required in the machine layout problem. The machine layout data is considered in a hierarchy;
depending on how detailed the layout is designed. When the layout required is only to find the relative arrangement
of machines, data representing machine number and their flow relationships are sufficient. However, if a detailed
layout is needed, more data is required. In finding data some difculties may arise especially in new manufacturing
facilities where the data is not yet available. Whenthe layout is developed for modern and automated facilities, the
required data cannot be obtained from historical data or from similar facilities since they may not exist.
Mathematical modelling has been suggested as a way to get an optimal solution for the facility layout problem.
Since the first mathematical model developed by Koopmans and Beckmann (1957) as a quadratic assignment
problem, interest in the area has attracted considerable growth. This opened up a new and interesting field for the
researcher. In searching for a solution to the facility layout problem, researchers launched themselves into
developing mathematical models. Houshyar and White (1993) looked at layout problem as
aninteger-programmingmodel while Rosenblatt (1986) formulated the layout problem as a dynamic programming
model. Palekar et al. (1992) deal with uncertainty and Shang (1993) uses amulti-criteriaapproach. On the other
hand, Leung (1992) presented a graph theory formulation.

Green andAl-Hakim(1985) used a GA to find the part family as well as the layout between cells. In his formulation,
he limited the arrangement of cell as either linear single row or linear double row. The developed algorithm is more
towards the cells system layout, or the layout of production floor, rather than the cell layout, or the machine layout.
The actual layout of machines within cells was not considered. Banerjee and Zhou (1995) formulated the facilitis
design optimization problem for asingle-looplayout using genetic algorithms. The developed algorithm is for the cell
systems layout and hence does not consider the layout of machines within cell. Fu and Kaku (1997) presented a
plant layout problem formulation for a job shop manufacturing system where the objective is to minimize the
average Work in Process. They modeled the plant as an open queuing network under a set of assumptions. The
problem reduces to a Queuing Assignment Problem (QAP). Simulation was used to minimize the average Material
Handling costs and minimizing the Average Work in Process.

2. MODELING APPROACHES
Models are categorised depending on their nature, assumptions and objectives. The first generic Systematic L ayout
Planning approach, developed by Muthor (1955), is still a useful scheme specially if supported by other approaches
and assisted by computer. Construction approaches, Hassan and Hogg (1991) for example, build a layout from
scratch while Improvement Methods, Bozer, Meller and Erlebacher (1994) for example, attempt to modify an
existing layout for better results. Optimising methods and also heuristics for layout by is well documented by Heragu
(2007).De-Alvarengaand Gomes (2000) discuss ameta-heuristicapproach as a way to overcome the NP- hard
nature of optimal models.
The various modelling techniques used in this work are Graph Theory, CRAFT, Optimum Sequence, BL _OCPL AN
and Genetic Algorithm. Explained below are parameters that are required by each algorithm in order to model the
same.

Graph Theory
Graph  theory  (Foulds  and  Robinson,  1976;  Giffin  et  al.,  1984;  Kim  and  Kim,  1985;  and  Leung,  
1992)applies  an  edge–weight  maximal  planar  graph  in  which  the  vertices  (V)  represents  the  
facilities and the edges (E) represent adjacencies and Kn  denotes the complete graph of n Vertices.
Given  a  weighted  graph  G,  the  facility  layout  problem  is  to  find  a  maximum  weighted  spanning  
sub-graph G’ of G that is planar.  

This  paper  uses  2  different  kinds  of  approaches  to  model  the  case  study.  The  first  approach  is  the  
Delta-hedron  method  by  Foulds  and  Robinson  (1976).  The  method  involves  simple  insertion  with  
an initial K4, and vertices are then inserted one by one according to a benefit criterion. The second
approach used is the wheel expansion algorithm (Green and Al-Hakim, 1985). Here the initial K4 is
obtained  by  selecting  an  edge  having  the  highest  weight  and  then  applying  two  successive  vertex  
insertion  according  to  the  benefit  criteria.  The  algorithm  then  proceeds  with  an  insertion  process,  
called the wheel expansion procedure. A wheel on n vertices is defined as a cycle on (n-1) vertices
(termed the rim), such that each vertex is adjacent to one additional vertex (termed the hub). Let W
be a wheel having the hub x. Select two vertices k and l, which are the rims of this cycle. A vertex y
from  the  set  of  unused  vertices  is  then  inserted  to  this  wheel  in  the  current  partial  sub-graph  such  
that y is  a  hub  of  the  new  wheel  W′ containing k, l and x as  its  rims,  and  all  rims  in  W  are  now  
adjacent to vertex x or vertex y. By inserting each unused vertex successively in the above fashion,
the final maximal planar sub graph is obtained.


Using CRAFT

CRAFT  (Computerized  Relative  Allocation  of  Facilities  Technique)  uses  a  pair  wise  exchange  to  
develop  a  layout  (Buffa  et  al.,  1964;  Hicks  and  Lowan,  1976).  CRAFT  does  not  examine  all  
possible  pair  wise  exchange  before  generating  an  improved  layout.  The  input  data  includes  
dimensions  of  the  building  and  facilities,  flow  of  material  or  frequency  of  trips  between  facility  
pairs and cost per unit load per unit distance. The product of the flow (f) and distance (d) provides
the cost of moving materials between 2 facilities. The cost reduction is then calculated based on the
pre and post exchange material handling cost contribution.  


Optimum Sequence  

The method of solution starts with an arbitrary sequential layout and tries to improve it by switching
two departments in the sequence (Heragu, 1997). At each step, the method computes the
flow*distance changes for all possible switches of two departments and chooses the most effective
pair. The two departments are switched and the method repeats. The process stops when no switch
results  in  a  reduced  cost.  The  input  required  to  generate  a  layout  using  Optimum  Sequence  are  
mainly dimensions of the building and facilities, the flow of material or frequency of trips between
facility pairs and cost per unit load per unit distance.


Using BLOCPLAN

BLOCPLAN  is  an  interactive  program  used  to  develop  and  improve  both  single  and  multi  storey  
layout (Green and Al-Hakim, 1985). It is a simple program which generates good initial layouts due
to its flexibility based on several imbedded options. It uses both quantitative and qualitative data to 84                                                                                                                                           

Pinto and Shayan  generate  several  block  layouts  and  their  measure  of  fitness. 

The  user  can  choose  the  relative  solutions based on circumstances.  


Genetic Algorithm  

There are numerous ways of formulating facilities Layout problems through genetic
algorithms(GA).  Banerjee,  Zhou,  and  Montreuil(1997)  applied  GA  to  cell  layout..    Slicing  
tree  structure  was  first  suggested  by  Otten  (1982)  as  a  way  to  represent  a  class  of  layouts.  The  
approach was later used by many authors including Tam and Chan (1995) who used it to solve
the  unequal  area  layout  problem  with  geometric  constraints.  The  GA  algorithm  used  in  this  
work  was  developed  by  Shayan  and  Chittilappilli  (2004)  based  on  slicing  tree  structures  (STC).  It  
codes  a  tree  structured  candidate  layout  into  a  special  structure  of  2  dimensional  chromosomes  
which shows the relative location of each facility in a slicing tree. Special schemes are available to
manipulate the chromosome in GA operations (Tam and Li, 1991). A new “cloning” operation was
also  introduced  in  Shayan  and  Al-Hakim  (1999).    The  chosen  solution  through  GA  is  then  
converted  to  a  slicing  layout.  It  starts  with  one  initial  block  that  contains  all  the  facilities.  As  the  
layout  constructing  algorithm  progresses,  new  partitions  are  made  and  facilities  are  assigned  
between  newly  generated  blocks,  until  there  is  only  one  facility  in  each  block.  Meanwhile  the  
coordinates of each facility is also calculated. Rectilinear distance between centroids of facilities is
used  to  evaluate  the  fitness  of  the  respective  chromosome.  When  the  GA  terminates,  a  drawing  
procedure  takes  over  to  print  the  layout  using  the  stored  values  of  the  coordinates.    The  objective  
function has a penalty term to avoid narrow slices.  


3. EXPERIMENTATION VIA A CASE STUDY

To  test  the  performance  of  the  methods  described  before,  they  were  all  applied  to  a  real  case  
scenario  in  furniture  manufacturing.  The  Company  manufactures  9  different  styles  of  Chairs,  2-
Seaters  and  3-Seaters  respectively.  Production  of  all  the  styles  follows  the  same  set  of  operations  
but  involve  different  raw  materials.  5  parts  namely  Seat  cushions,  Back  cushions,  Arms  Seats  and  
Backs are produced internally in batches of varied sizes, in scattered areas (departments).
Movement of parts generates problems such as work in progress, missing parts, shortages,
congestion and wrong placement.  


Each  product  goes  through  11  operations  which  begin  at  Facility  1  –  Cutting  Area  and  end  at  
Facility  11-  Bolt  up  Area.  Each  of  the  final  assembly  can  be  broken  down  into  subassemblies  
named the same. These subassemblies meet up at the Bolt -Up Facility for final assembly. Each of
the subassemblies begin their operations independently and all go through a fixed set of operations
which is shown in the form of an assembly chart in Fig 1. The facilities of the current layout are not
placed according to the sequence of operations.  

Due to this there is no sequential flow of materials, giving rise to work in progress. The interaction
between facilities can be determined using subjective as well as objective measures. The main input
required  for  flow  charts  is  the  demand,  the  quantity  of  materials  produced  and  the  amount  of  
material  that  flows  between  each  machine.  The  flow  of  material  is  calculated  based  on  amount  of  
flow  of  material  traveling  per  10  months  *  Unit  of  measure  which  is  shown  in  Figure  2.  Figure  3  
shows the area of each of the department used in the case study. Figure 4 shows the current layout
of the Case Study.

4. APPLICATION OF THE MODELING APPROACHES
Here the various modelling approaches discussed in section 2 are applied to the case study to
generate alternative layouts for comparison.

4.1 Using Graph Theory
Table 1 shows the comparison of the results using two different approaches of Graph Theory
namely the Foulds and Robinsons method and the Wheels and Rims method. Table 1 it clearly
shows that the Foulds and the Robinsons method is the better of the two results. The results of the
Foulds and Robinsons method are explained in detail in Figures 5-7.

4.2 Using CRAFT
The  input  data  for  CRAFT  is  entered  and  the  initial  cost  for  the  current  layout  is  first  calculated.  
This cost can be reduced using a pair wise comparison as shown in Figures 8,9.

The results obtained by CRAFT are shown in Table 2. Based on the above calculations a new and
improved layout can be drawn which is shown in Figure 10

4.3 Optimum Sequence Algorithm

The  input  data  is  the  same  as  for  CRAFT  except  that  it  follows  a  different  set  of  pair  wise  
comparison.  Table  3  shows  the  results  drawn  from  the  improved  layout.  Figure  11  shows  the  
improved layout using Optimum Sequence.

4.4 Using BLOCPLAN

The  Flow  matrix  chart  was  converted  to  a  REL  chart  as  shown  in  Figure  12  with  the  following  
parameters:

Table  4  shows  the  results  using  different  kinds  of  approach.  As  seen  the  BLOCPLAN  using  an  
automated search showed better results than using the Construction Algorithm.

4.5 Using Genetic Algorithm

The best solution found by the algorithm is shown in Figure 14. This is then converted to the layout
in Figure 15 for common comparisons with other models.

Table 5 shows the results using Genetic Algorithm.

5. COMPARISONS OF EXPERIMENTATION RESULTS BY AHP

Table  6  summarizes  the  results  obtained  from  all  the  modelling  techniques  versus  the  Current  
Layout for comparison. Section of the best layout will be done based on three factors namely Total
Area (Minimze), Flow * Distance (Maximize) and the Adjacency percentage (Maximize). The main
objective  is  to  reduce  the  WIP  and  organise  a  systematic  flow  of  materials.  As  a  result  the  flow  *  
distance matrix is the most important parameter.  
 

Table 6 Summary of results using all modelling techniques versus the results of the current layout

Table  7  shows  the  mix  ranking  of  the  alternative  layouts  based  on  various  factors.  For  example  
Layout 1 has a poor rank in Area and F*D while is the best in Adjacency. The combination makes it
difficult  to  choose  one  over  the  others.  We  urge  to  use  a  formal  technique,  AHP,  implemented  by  
Expert Choice software

AHPcompares the relative importance of each pair of children with respect to the parent. Once the
pair comparisons is completed, the approach synthesis the results using some mathematical models
to  determine  an  overall  ranking.  Figure  16  shows  the  ranking  of  the  results  achieved  from  all  
algorithms with respect the goal of best choice solution.

The  best  solution  is  achieved  by  BLOCPLAN  (  Automated  Search)  followed  by  Graph  Theory  
using  Foulds  and  Robinsons  Method,  then  Genetic  Algorithm.  The  other  solutions  are  far  worse.  
Note  that  due  to  the  inherent  subjectivities  ranking  is  not  an  absolute  indication  of  better  choice,  
rather it is a recommendation that the user can entertain to suit the needs. 94                                                                                                                                             

We  propose  the  layout  generated  using  BLOCPLAN  using  Automated  Search  to  be  the  chosen  
solution.  When  this  was  decided  a  sensitivity  analysis  was  conducted  to  ensure  that  the  choice  is  
robust. If time allows this should be done for other close alternatives before the choice is made.  

6. CONCLUSIONS

The  goal  in  this  paper  was  to  use  various  modelling  techniques  to  select  the  best  layout  for  a  
furniture  company.  The  best  layout  was  generated  by  BLOCPLAN  using  Automated  Search as figure 17.

Table  9  shows  the  improvements  of  the  proposed  solution  over  the  current  layout.  Note  that  the  
layout shows the blocks and their relative locations. Practical limitations need to be applied to suit
all the needs. Then further details of each block can be planned, if necessary in the same manner.

Table 9: Improvements over the current layout using modeling techniques

The  result  was  quite  satisfactory  to  the  company,  which  did  not  have  any  knowledge  of  the  
scientific approaches.  


REFERENCES


[1] Banerjee  P.,    Zhou  Y.  (1995),  Facilities  layout  design  optimization  with  single  loop  material  flow  
path configuration; Int. Journal of Production Research 33(1); 183-204.

[2] Banerjee  P.,  Zhou  Y.,  Montreuil  B.  (1997),Genetically  assisted  optimization  of  cell  layout  and  
material flow path skeleton; IIE Trans 29(4); 277-292. Layout Design of a Furniture... 95
[3] Bozer Y.A, Meller R.D., Erlebacher S.J. (1994), An improvement type layout algorithm;
International Journal of Production Research 1; 1675-1692.

[4] Buffa E.S., Armour G.C., Vollman T.E. (1964), Allocating facilities with CRAFT; Harvard Business
Review 42; 136-159.

[5] De-Alvarenga A.G., Gomes N.J., Mestria M. (2000), Metaheuristic methods for a class of the facility
layout problems; Journal of Intelligent Manufacturing 11; 421-430.

[6] Domschke  W.,  Drexl    A.  (1985),  Location  and  layout  planning,  An  international  bibliography;  
Springer Verlag, Berlin.  

[7] Foulds  L.R.,  Robinson  D.F.  (1976),  A  strategy  for  solving  the  plant  layout  problem;  Operational
Research Quarterly 27; 845-855.  

[8] Francis  R.L.,  McGinnis  Jr.  L.F.,  White  J.A.  (1992),  2nd  Ed,  Facility  layout  and  location,  An  
analytical approach; Prentice Hall; Englewood Cliffs, NJ.

[9] Fu  M.C.,  Kaku  B.K.  (1997),  Minimizing  work  in  progress  and  material  handling  in  the  facilities  
layout problem; IIE Trans 29; 29-36.

[10] Giffin J.W., Foulds L.R. Cameron D.C. (1984), Drawing a block plan from a REL chart with graph
theory and microcomputer; Computers & Industrial Engineering 10; 109-116.

[11] Green  R.H.,  Al-Hakim  L.  (1985),  A  heuristic  for  facilities  layout  planning;  OMEGA, International
Journal of Management Science 13; 469-474.

[12] Hassan M.M.D., Hogg G.L. (1991), On constructing a block layout by graph theory;
International Journal of Production Research 29; 1263-1278.  

[13] Heragu S.S. (2007), 2nd Ed, Facilities Design; iUniverse Inc., NY.  

[14] Hicks  P.E., Lowan  T.E. (1976),  CRAFT-M  for  layout re-arrangement;  Industrial Engineering 8(5);
30-35.

[15] Houshyar  A.,  White  B.  (1993),  Exact  optimal  solution  for  facility  layout  –  deciding  which  pairs  of  
locations should be adjacent; Computers and Industrial Engineering 24(2); 287-290.

[16] Kim J.Y., Kim Y.D. (1985), Graphic theoretic for unequal sized facility layout  problems; OMEGA,
International Journal of Management Science 23; 391-401.

[17] Koopmans T.C., Beckmann M. (1957), Assignment problems and the location of Economic
Activities; Econometrica 25(1), 53-76.

[18] Leung J.A. (1992), A new graph theoretic heuristic for facility layout, Management Science 38; 554-
605.

[19] Meller R.D., Narayanan V., Vance P.H. (1998), Optimal facility layout design; Operation Research
Letters 23;117-127.

[20] Muther R. (1955), Practical plant layout; McGraw-Hill; New York, NY.  


[21] Otten R.H.J.M. (1982), Automatic floor plan design; Proceedings of the 19th ACM-IEEE
DesignAutomation Conference; 261-267. 96                                                                                                                                            

[22] Palekar  V.S.,  Batta  R.,  Bosch  R.M.,  Elhence  S.  (1992),  Modeling  uncertainties  in  plant  layout  
problems; European Journal of Operations Research 63(2); 347-359.  

[23] Rosenblatt M.J. (1986), The dynamics of plant layout; Management Science 32(1); 76-86.            

[24] Satty T.L. (1980), Analytical hierarchic process; McGraw Hill; New York.  

[25] Shang J.S. (1993), Multicriteria facility layout problem -An integrated approach; European Journal
of Operational Research; 66(3); 291-304                 .  

[26] Shayan E., Al-Hakim L., 1999. "Cloning in layout design problem: A genetic algorithm approach."
Proceedings  of  the  15th  International  Conference  on  Production  Research;    Hillery,  M.,  Lewis, H.  
Eds.), University of Limerick, Ireland; 787-792.  

[27] Shayan E., Chittilappilly A.(2004) , Genetic algorithm for facilities layout problems based on slicing
tree structure; Int. J Production Research; 42(19); 4055–4067.

[28] Tam  K.Y.,  Chan  S.K.  (1998),  Solving  facility  layout  problems  with  geometric  constraints  using  
parallel  genetic  algorithms:  experimentation  and  findings; International  Journal  of  Production  
Research 36(12); 3411-3423.  

[29] Tam  K.Y.,  Li   S.L. (1991), A  hierarchal  approach  to  facility  layout  problem;  International  Journal  
Production Research, 29; 165-184.  

[30] Tompkins  J.A., White J.A. (1984),  Facilities planning; John Wiley & Sons, NY.

Layout Design of a Furniture Prodtction Line Using Formal Method.pdf