Comparison of Cell formation techniques in Cellular manufacturing using three cell formation algorithms

Prabhat Kumar Giri Int. Journal of Engineering Research and Applications www.ijera.com
ISSN: 2248-9622, Vol. 6, Issue 1, (Part - 5) January 2016, pp.98-101
www.ijera.com 98 | P a g e
Comparison of Cell formation techniques in Cellular
manufacturing using three cell formation algorithms
Prabhat Kumar Giri1
, Dr.S. K. Moulick2
1
(Research scholar ,Dr. C.V. Raman University, Bilaspur(C.G.),India)
2
(Department of Mechanical Engineering, BIT-Durg, India)
ABSTRACT
In the present era of globalization and competitive market, cellular manufacturing has become a vital tool for
meeting the challenges of improving productivity, which is the way to sustain growth. Getting best results of
cellular manufacturing depends on the formation of the machine cells and part families. This paper examines
advantages of ART method of cell formation over array based clustering algorithms, namely ROC-2 and DCA.
The comparison and evaluation of the cell formation methods has been carried out in the study. The most
appropriate approach is selected and used to form the cellular manufacturing system. The comparison and
evaluation is done on the basis of performance measure as grouping efficiency and improvements over the
existing cellular manufacturing system is presented.
Keywords - Neural Network, ART Model, Group Technology
I. INTRODUCTION
Group Technology is a manufacturing
philosophy in which similar parts are identified.
Machines on which these parts are to be processed
are grouped together to form a GT cell. The purpose
of GT cell is that the Cellular manufacturing system
is result of implementation of GT to the production.
The number of benefit has been achieved by
implementation of CMS, like material handling, cost
reduction; work in process inventory reduction, set-
up time reduction, and equipment cost reduction,
direct/indirect labor cost reduction, improvement
of quality, improvement in space utilization and
employees satisfaction etc.
Formation of part families and machine cells is
the key step towards the design of cellular
manufacturing system (CMS). The input data are
derived from route sheet. These data are in the form
of zero-one matrices. The rows represent the
machines and columns represent parts. Elements of
the matrix ‘aij’ will be ‘1’ if the jth component is
processed on ith machine. If it is not ‘aij’ will be
zero. The output is obtained in the form of block
diagonal structure. Each block represents a machine
cell and a part family. Number of research work has
been done in the last decades for cell formation. The
researchers have proposed number of algorithms for
cell formation using production flow analysis. In this
paper it is presented that ART algorithm is found
better over array based cell formation techniques.
II. LITERATURE SURVEY
Survey of literature has been carried out to
identify the findings and directions given by
researchers. The contribution and directions of
selected research work reported in the literature have
been presented below:
The problem was originally identified by Murthy
and Srinivasan [1]. They used simulated annealing
(SA) and heuristics algorithms (HA) for fractional
cell formation. In other research, Srinivasan and
Zimmers [2] used a neighborhood search algorithm
for fractional cell formation.
The architecture of the ART1 is based on the
idea of adaptive resonant feedback between two
layers of nodes, as developed by Grossberg [3]. The
ART1 Model described in Carpenter and Grossberg
[4] was designed to cluster binary input patterns.
Dagli and Huggahalli [5] and Chen and Park [6] also
modified the ART1 in their works to improve its
performance in GT cell formation. But their
modifications are not suitable for fractional cell
formation. Miin-Shen Yang and Jenn- Hwai Yang [7]
proposed a modified ART1 neural learning
algorithm. In modified ART1, the vigilance
parameter can be simply estimated by the data so that
it is more efficient and reliable than Dagli and
Huggahalli’s method for selecting a vigilance value.
M. Murugan and Selladurai[8] proposed an Art
Modified Single Linkage Clustering approach (ART-
MOD-SLC) to solve cell formation problems in
Cellular Manufacturing. In this study, an ART1
network is integrated with Modified Single Linkage
Clustering (MOD-SLC) to solve cell formation
problems. The Percentage of Exceptional Elements
(PE), Machine Utilization (MU), Grouping
Efficiency (GE) and Grouping Efficacy (GC) are
considered as performance measures. This proposed
heuristic ART1 Modified Single Linkage Clustering
(ART-MOD-SLC) first constructs a cell formation
RESEARCH ARTICLE OPEN ACCESS

using an ART1 and then refines the solution using
Modified Single Linkage Clustering (MOD-SLC)
heuristic. ART1 Modified Single Linkage Clustering
has been applied to most popular examples in the
literature including a real time manufacturing data.
According to P. Venkumar and A. Noorul Haq [9] the
GT cell formation by any known algorithm/heuristics
results in much intercell movement known as
exceptional elements. In such cases, fractional cell
formation using reminder cells can be adopted
successfully to minimize the number of exceptional
elements. The fractional cell formation problem is
solved using modified adaptive resonance theory1
network (ART1). The input to the modified ART1 is
machine-part incidence matrix comprising of the
binary digits 0 and 1. This method is applied to the
known benchmarked problems found in the literature
and it is found to be equal or superior to other
algorithms in terms of minimizing the number of the
exceptional elements. The relative merits of using
this method with respect to other known
algorithms/heuristics in terms of computational speed
and consistency are presented. Yong Yina and
Kazuhiko Yasudab[10] gave a comprehensive
overview and discussion for similarity coefficients
developed to date for use in solving the cell
formation (CF) problem. Despite previous studies
indicated that similarity coefficients based method
(SCM) is more flexible than other CF methods, none
of the studies has explained the reason why SCM is
more flexible. They tried to explain the reason
explicitly. They also developed a taxonomy to
clarify the definition and usage of various similarity
coefficients in designing CM systems. Existing
similarity (dissimilarity) coefficients developed so far
are mapped onto the taxonomy. Additionally,
production information based similarity coefficients
are discussed and a historical evolution of these
similarity coefficients is outlined. Finally,
recommendations for future research are suggested.
Chang-Chun Tsai and Chung-ying Leewe [11]
presented a multi-functional MP (mathematical
programming) model that incorporates the merits of
related CF (Cell Formation) models based on the
systematic study of MP models. The proposed model
can offer the suitable modules that include the
different objective functions and constraints for user
to solve the related problem. In addition, analysis
results demonstrate that the proposed model’s
performance to outperform the other related models.
Jose Fernando Goncalves and Mauricio G.C.
Resende [12] presented a new approach for obtaining
machine cells and product families. The approach
combines a local search heuristic with a genetic
algorithm. Computational experience with the
algorithm on a set of group technology problems
available in the literature is also presented the
approach produced solutions with a grouping efficacy
that is at least as good as any results previously
reported in literature and improved the grouping
efficacy for 59% of the problems.
III. METHODOLOGY
Proposed methodology uses the Adaptive
Resonance Theory (ART) neural network to solve the
cell formation problem in group technology (GT).
The advantage of using an ART network over the
other conventional methods, like ROC (Rank order
clustering) and DCA (Direct clustering Analysis) are
the fast computation and outstanding ability to handle
large-scale industrial problems.
A. Rank order clustering2 (ROC-2)
ROC-2 was developed by King and Nakoranchai
(1982) to overcome the limitations of ROC. ROC-2
can identify block diagonal structure (of machine part
incidence matrix) very quickly. Therefore it is found
practicable to apply in an interactive manner even for
large matrices.
Algorithm:
Step 1 Start from the last column, move the rows
with positive entries to the top of the matrix.
Step 2 Repeat step 1 for all the columns.
Step 3 Start from the last row, move the columns
with positive entries to the left of the matrix.
Step 4 Repeat step 3 for all rows.
Step 5 Compare the matrix with the previous result.
If the matrices are different go to step 1 otherwise go
to Step 6.
Step6 Print the final machine-component incidence
matrix.
B. Direct clustering analysis (DCA):
In this method, the initial matrix is rearranged
according to the row and column assignments. After
rearrangement the rows and columns are rearranged
to form the clustered part- machine incidence matrix.
Algorithm:
Step 1 The row and column ranks are found by
adding their corresponding positive entries.
Step 2 The matrix is rearranged according to the
ranks.
Step 3 Start from the first row, move the columns
with positive entries to the left of the matrix
Step 4 Repeat the step 3 for all the rows.
Step 5 Start from the first column, move the rows
with positive entries to the top.
Step 6 Repeat the step 5 for all the columns.
Step 7 Compare the matrix with the previous result. If
the matrices are different go to step 3 otherwise go to
step 8.
Step 8 Print the final machine component incidence
matrix

C. Adaptive Resonance Theory(ART) :
An artificial neural network is built on a number
of simple processing elements called neurons. These
neurons are often recognized into a sequence of
layers. All layers of the network are linked by
weights, which are adapted using a learning
algorithm. The structure of a neural network could be
characterized by interconnection architecture among
neurons, the activation function for conversion of
input into outputs, and the learning algorithm.
Algorithm:
Step1 : Define the number of neurons in the input
layer Nin and number of neurons in the output layer
Nout and select a value for vigilance parameter, ρ
Nin = the number of columns (parts ) of machine-part
incidence matrix.
Nout = the maximum expected number of machine
cells.
Step 2 : Enable all the output units and initialize top
down weights Wt
and bottom up weights Wb
Wt
ij = 1 = tij(0)
1 1
(0)
1 1
b
ij ij
in
W b
N N
  
 
Wt
ij = top down weight from neuron j in the
output layer to neuron i in the input layer.
b
ijW  Bottom –up weight from neuron i in the
input to neuron j in the output layer.
Step3 : Present a machine vector X to input layer , X
consist of zero/one element ix .
Step4: compute machining scores for all the enabled
output nodes
b
j ij i
i
Net W x 
Where Netj is the output of neuron j in the output
layer
Step5: Select a node with the largest value of
matching score as best matching exemplar let this
node be j’. In the event of a tie, the unit on the left is
selected
 , max jj j
Net net
Step6: Vigilance test (i,e test of similarity with best
matching exemplar)
Compute the following:
i
i
X x  (norm of vector X)
' '. .t t
j ij iW X W x 
Let X = New pattern and Y= exemplar
So the Euclidean distance =  
2
i ix y
If  
2
i ix y  ρ, go to step 8, else go to step 7.
Step7: Disable best exemplar temporarily
Since the vector X does not belong to cluster
j’, the output of node j’ selected in step 5 is
temporarily disabled and removed from future
competitions; go to step4.
Step8: Adapt best matching exemplar
'
'
'
.
0.5 .
t
ij ib
ij t
ij i
W x
W
W x


Step9: Enable any node s disabled in step7 and go
to step3.
D. Measure of Performance
To measure the efficiency of the group grouping
efficiency is considered as measuring parameter
represented by η,
 1 21q q    
Where
1
1
d
k
r r
r
e
M N




0
2
1
1 k
r r
r
e
mn M N


 
 
  
  
 

m = Number of machines (rows)
n = Number of parts (columns)
Mr = Number of machines in the r-th cell
Nr = Number of parts in the r-th family
ed = Number of 1’s within the machine /parts group
e0 = Number of 1’s outside the machine/parts group
k = Number of clusters
 = Grouping efficiency
q = Weighting factor (0< q <1)
Grouping efficiency (GE) ranges from 0 to 1. A
GE with a value closed to 1.0 means that the solution
matrix has a perfect structure. In this paper the
solutions are evaluated in terms of GE and
Exceptional Element (EE).
IV. TEST PROBLEMS
To check the efficiency and working of proposed
methodology, few test problems are generated
randomly
Problem No. Matrix Size Minimum Threshold
1 20x15 0.9
2 20x15 0.5
3 20x15 0.6
4 20x15 0.7

The results obtained are given in table below.
V. CONCLUSION
The neural network based on adaptive resonance
theory (ART) can be effectively used for machine-
part cell formation using the information from route
sheet of parts. The industries seeking to reframe their
existing facilities to cellular layout can derive
maximum benefit from the proposed methodology.
Usually the implementation of GT is a continuous
process. Different methods may be found more useful
or can give better results for different kind of
products. The neural network can effectively execute
the dynamic characteristic of GT implementation.
REFERENCES
[1] Murthy CVR, Srinivasan G (1995)
Fractional Cell formation in group
technology. International Journal of
Production Research 33(5):1323–1337
[2] Srinivasan G, Zimmers EW Jr (1998)
Fractional cell formation – issues and
approaches. International Journal of
Industrial Engineering –Theory and
Application Practice 5:257–264
[3] Grossberg S (1976) Adaptive pattern
classification an universal recording: parallel
development and coding of neural feature
detectors. Biol Cybern 23:187–202
[4] GCarpenter GA, Grossberg S (1987) A
massively parallel architecture for a self-
organizing neural pattern recognition
machine. Comput Vision Graph Image
Process 37:54–115
[5] Dagli C, Huggahalli R (1995) Machine-part
family formation with the adaptive
resonance theory paradigm. Int J Prod Res
33(4):893–913
[6] Chen DS, Chen HC, Park JM (1996) An
improved ART neural net for machine cell
formation. Journal of Materials Processing
Technology 61:1–6
[7] Miin-Shen Yang and Jenn- Hwai Yang
Machine-part cell formation in group
technology using a modified ART1 method
European Journal of Operational Research
188 (2008) 140–152
[8] M. Murugan and Selladurai(2011)vol. 5,3:
199-212 Jordon Journal of Mechanical and
Industrial Engineering
[9] P. Venkumar and A. Noorul Haq Fractional
cell formation in group technology using
modified ART1 neural networks,
International Journal of Advanced
Manufacturing Technology (2006) 28: 761–
765
[10] Yong Yina and Kazuhiko Yasudab
Similarity coefficient methods applied to the
cell formation problem: A taxonomy and
review Int. J. Production Economics 101
(2006) 329–352
[11] Chang-Chun Tsai and Chung-ying Leewe
(2006) International Journal of advanced
manufacturing technology Volume 30, Issue
3-4, 309-318
[12] Jose Fernando Goncalves and Mauricio
G.C. Resende, An evolutionary algorithm
for manufacturing cell formation Computers
& Industrial Engineering 47 (2004) 247–273
Pro
ble
m
No.
Calculated
efficiency
(%)by ART
algorithm
Calculated
efficiency(%)
by DCA
algorithm
Calculated
efficiency
(%)by ROC
algorithm
1 72.00 63.23 67.00
2 66.15 52.00 62.24
3 66.00 61.08 65.14
4 61.50 58.25 59.28

Comparison of Cell formation techniques in Cellular manufacturing using three cell formation algorithms

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