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Application of the Similarity Coefficient Method in
Group Technology
a
Hamid Seifoddini & Philip M. Wolfe
b
a
Industrial Engineering Department , University of Wisconsin-Milwaukee , Milwaukee,
Wisconsin, 53201
b
Garrett Turbine Engine Company , Phoenix, Arizona, 85010
Published online: 06 Jul 2007.
To cite this article: Hamid Seifoddini & Philip M. Wolfe (1986) Application of the Similarity Coefficient Method in Group
Technology, IIE Transactions, 18:3, 271-277, DOI: 10.1080/07408178608974704
To link to this article: http://dx.doi.org/10.1080/07408178608974704
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Application of the Similarity
Coefficient Method in G r o u ~
Technology
HAMID SEIFODDINI
Assistant Profes~or
Industrial Engineering Depanment
University of Wirconrin-Milwaukee
Milwaukee, Wiseansin 53201
PHILIP M. WOLFE
Downloaded by [University of Waterloo] at 13:27 23 February 2015
SENIOR
MEMBER,
AIlE
Garrett Turbine Engine Company
Phoenix. Arizona 85010
Abstract: The Similarity Coefficient Method (SCM) is one of the methods used t o form the machine cells in group
technology applications. Compared t o the other methods, SCM incorporates more flexibility into the machinecomponent grouping process and more easily lends itself to the computer application. The new model improves the
existing models based on SCM by dealing with the duplication of bottleneck machines and by employing special
data storage and analysis techniques which greatly simplify the machine-component grouping process. The duplication
process in the new model is based on the number of inter-cellular moves. Duplication starts with the machine
generating the largest number of inter-cellular moves and continues until no machine generates more inter-cellular
moves than specified by a threshold value. By changing the threshold value, alternative solutions can be examined.
the new model employs the bit-level data storage technique to reduce the storage and computational requirements
of the machine-component grouping process.
Over the last two decades or so group technology has been
emerging as an important scientificprinciple in improving the
productivity of manufacturingsystems. The greatest potential
for application of group technology lies in hatch-type manufacturing where a large number of lots of small sizes are
produced [2,6]. The application of group technology to manufacturing starts with tinding the families of similar parts
(part-families) and forming the associated groups of machines
(machine-cells). This process is referred to as "machine-component grouping." There are differentapproaches to the machine-component grouping problem. In the following sections
some major machine-component grouping models are reviewed and a new model is presented.
Definition of the Pmblem
Most machine-component grouping algorithms employ a
matrix called a "machine-component chart." A machine-
Received May 1985; revired September 1985 and January 1986. Handled by
the Manufacturing and Automated Production Department.
September 1986, IIE Transactions
component chart is an M x N matrix with zero or one entries.
A "one" entry in row i and column j of the matrix indicates
that part j has an operation on machine i; a zero entry indicates it does not. The purpose of a machine-component
grouping algorithm is to find part-families and to form the
associated machine cells such that one or more part-families
can be fully processed within a single machine cell. The result
of a machine-component grouping algorithm (when a machine-component chart is used) is a block diagonal form in
which "one" entries are concentrated around the diagonal of
the matrix.
In practical cases, not all components of a part-family can
always be processed within a single cell. The components
having operations in more than one cell are called "exceptional parts" and the machines processing them are referred
to as "bottleneck machines." The transportation of exceptional parts behveen cells (inter-cellular moves) can be eliminated by assigning a sufficient number of bottleneck
machines to appropriate cells (machine duplication). The way
these problems are handled varies in different approaches.
In the next section some major machine-component grouping
models are reviewed.
0470-817Xi8Si06M)-018U$2200/0
0 1986 " I I E
271
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Background
Production Flow Analysis (PFA) due to Burbidge [2, 31 is
one of the first systematic approaches to machine-component
grouping. PFA has been devised as a manual method, and
while it provides the basic data required to lind the machinecomponent groups, it is not well suited for computer applications [4,8]. There are two other approaches to the problem.
One of them is based on the permutations of rows and columns of the machine-component chart and is referred to as
"machine-component group analysis." Several algorithms
based on this method have been discussed in the literature
[8, 9, 111.
McCormick, Schweitzer, and White [Ill developed a general clustering algorithm called the Bond Energy Algorithm
(BEA). BEA seeks to form a block diagonal form by maximizing the bond energy between adjoining row and column
entries in a matrix. King [8] has developed the Rank Order
Clustering (ROC) algorithm. The ROC algorithm has been
specifically designed for machine-component grouping and
deals with the problem of bottleneck machines [8,9]. Another
algorithm is the Direct Clustering Algorithm (DCA) due to
Chan and Milner [4].
The algorithms based on the machine-component group
analysis method should identify the bottleneck machines, duplicate them, and modify the machine-component chart prior
to formation of the block diagonal form. This process usually
requires human intervention and when a large volume of data
is involved becomes complicated. All of the above approaches
are limited by these constraints.
The third approach to machine-component grouping is
based on the similarity coefficient method. The construction
of machine cells by the Single Linkage Clustering Algorithm
(SLCA) was introduced by McAuley [lo]. He defined the
similarity coefficient between two machines as the number of
components visiting both machines divided by the number of
components visiting either of the two machines. A similarity
matrix containing all painvise similarity coefficients between
machines is an input to a clustering algorithm which forms
the machine cells and presents them in a kind of tree diagram
called a "dendogram" (151. The major drawback of the algorithms based on SCM is that they do not deal with the
duplication of bottleneck machines [a]. In addition, due to
the chaining problem of SLCA two clusters (machine cells)
may join together merely because two of their members are
similar 110, 13, 151.
second, the new model uses an Average Linkage Clustering
(ALC) algorithm to overcome the chaining problem of SLCA
(in ALC, the similarity coefficient between two clusters is
defined as the average of the similarity coefficients between
ail members of the two clusters). Finally, the new model
employs specific data storage and analysis techniques which
greatly simplify the machine-component grouping process
1131.
The mach'ine-component chart is the main input to the
model. The model forms the machine cells and rearranges
the elements in the machine-component chart to represent
the machine-component groups. Since different solutions will
be obtained depending on the similarity level' used, a number
indicating the desired number of machine cells must be used
to choose a specific solution [131.
Duplication in the new model is based on the number of
inter-cellular moves. The model determines this number for
each bottleneck machine and ranks the bottleneck machines
accordingly. The duplication process starts with the machine
generating the largest number of inter-cellular moves and
continues until no machine generates more inter-cellular
moves than specified by the threshold value. Various threshold values are employed as input to the model in order to
generate a set of alternative solutions. The duplication of a
bottleneck machine may change the status of the other bottleneck machines. For this reason the number of inter-cellular
moves for bottleneck machines within the cells involved in
the duplication process should be recalculated after each duplication. All steps in the duplication process are computerized and no human intervention is necessary.
To illustrate the duplication process, a machine-component
chart in which the machine-component groups have been already formed is presented in Figure l . Suppose the threshold
value is one, that means, any machine processing more than
one part from outside cells is a candidate for duplication.
Machines B, C, D, and F in Figure 1 are bottleneck machines.
Machine C processes parts 7 , 8 , and 9 from the middle block
(cell 2). It generates the largest number of inter-cellular
moves and is the first candidate for duplication. The machinecomponent chart after the duplication of this machine is de-
C
A
B
?~~~~
1
D
E
1
1
F
The New Model
The new model employs SCM to form the machine cells.
The algorithms based on SCM are more flexible than the other
machine-component grouping algorithms in forming the machine cells [la, 131. The model improves the existing machinecomponent grouping models based on SCM in three ways:
first, it deals with the duplication of bottleneck machines;
272
1
t
1
G
H
1
1
. . - 8
Figure 1. The Machine-Component Chan. "One" Entries Outside
Blocks Represent the Operations of Exceplional Pans on Bottleneck
Machines.
--
'The Similarity Level is a similarity
(machines) join together.
coefficient at which two or more clusters
IIE Transactions, September 1986
picted in Figure 2. The next candidate for duplication is machine B which processes parts 7 and 10 from cell 2. When
this machine is duplicated, the result will be as presented in
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Figure 2. Machine-Component Chan: Machine C is Duplicated.
Figure 3. As can be seen, the duplication of machines B and
C results in reassignment of part 6 to cell 2. With this change,
machine D is no longer a bottleneck. With the threshold value
equal to one, machine F is not a candidate for duplication
and the final machine-component groups are as presented in
Figure 3.
:
F
G
l1 ; ;
H
1
li
of the data a of binary type, a bit-level data storage technique
is employed to decrease the storage requirement and computational effort. Using this technique, fewer computer words
will be required to store the data in the machine-component
chart. In addition, the computation of similarity coefficients,
identification of exceptional parts, duplication of bottleneck
machines, and formation of the block d~agonalform becomes
simpler [13].
The number of computer words required to store one row
of the machine-component chart as a binary stream is determined as,
1
1
Figure 3. Machine-Component Chatl. Machines Band C are Duplicated.
The algorithmic flow chart of the model is depicted in Figure 4. As the flow chart shows, first, the similarity coefficients
between machines are calculated and a similarity matrix is
constructed. An average linkage clustering algorithm uses the
similarity matrix to form the machine cells. Then, based on
the similarity level which gives the desired number of machine
cells, a specific arrangement of machine-component groups
is chosen. Next, the cells visited by each component are determined, and within each cell the machines visited by that
component are identified. A component is assigned to a cell
based on the number of machines (within the cell) visited by
the component. Finally, the components visiting more than
one cell are identified as exceptional parts and any machine
processing them is considered a bottleneck machine. Bottleneck machines are duplicated to reduce the inter-cellular
moves.
Solution Methodology
The machine-component grouping process involves the
analysis of a large volume of data. Since the major portion
September 1986, IIE Transactions
Figure 4. Algorithmic Flow Chan of the Model
where,
NWORD = Number of computer words
NPART = Number of components
NBITS = Number of bits per computer word.
A machine veclor is defined as an array containing the
information related to the processing of components on a
single machine. Such an array has a dimension of NWORD
and contains the data in one row of the machine-component
chart. If machine vector k is designated by MVL, a new machine vector can be defined as follows,
MVO
=
MVi.OR.MVj
where,
MVO = Machine vector containing the information
related to components visiting machine
ilmachine j
MVi, MV, = machine vectors i and j.
If a bit in MVO is one, its corresponding component has an
operation on either of the two machines i or j. In the same
visited by a component, the corresponding bit in each machine vector is checked. A component is assigned to the cell
which processes it for most of its operations.
To determine the number of inter-cellular moves between
two cells, the corresponding cell vectors are AND'ed and the
number of non-zero bits in the resulting vector is calculated.
Based on the number of inter-cellular moves, the bottleneck
machines are identified and the duplication process is carried
out.
way, the machine vector containing the information related
to components visiting both machines i and j , MVA can he
defined as follows,
MVA
=
MVj.AND.MVj
A non-zero bit in MVA indicates that the corresponding part
in the machine-component chart should be processed on both
machines i and j .
Let NOR and NAND be the numbers of non-zero bits in
MVO and MVA, respectively. Then, the similarity coefficient
between two machines i and j , Sq is calculated as [lo, 131
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S, =
The Results
NAND
NOR
To illustrate the way the model works and to present the
results, a machine-component grouping problem involving 16
machines and 43 components has been chosen as the test
problem. Burbidge [p. 172, 31 has solved this problem using
a manual method. His solution is used to verify the results
of the new model. The initial machine-component chart of
the problem is presented in Figure 5.
Based on the data in Figure 5 , the similarity coefficient
between machines 1 and 2 (with machine vectors MVI and
MV2) can be calculated as follows.
This simple procedure is the basis for the construction of a
similarity matrix containing all pairwise similarity coefficients
between machines. The similarity matrix is accessed by an
average linkage clustering algorithm which brings the similar
machines together. By specifying the desired number of machine cells, a specific solution among the alternative solutions
given by the clustering algorithm will be chosen.
The identification of the exceptional parts and assignment
of parts to machine cells are other major functions of the
model. Exceptional parts are identified by determining the
cells visited by different components. To determine whether
a component has an operation in a specific cell, all machines
within that cell should be checked to see if any of them processes the part for any of its operations. Considering the
number of components and machines involved in real world
situations, this task can be very time consuming. To simplify
the process, the concept of cell vector is very useful. A cell
vector can be defined as an array containing the data related
to the processing of parts in a specific cell and can be obtained
by OR'ing the machine vectors belonging to that cell. A component visits a cell if its related hit in the cell vector ispositive.
If a component visits more than one cell, it is considered an
exceptional part. To identify the machines within the cell
MVO = MVI.OR.MV~
MVA
=
010000000100000000000000000l000100001101010
=
MVl.AND.MV2
=
00000000000000000000OO00000000000001~0010
The numbers of non-zero hits in MVO and MVA are 8 and
2, respectively, and the similarity coefficient between machines 1 and 2 is,
In the same way pairwise similarity coefficients between all
other machines are calculated. The result will be a similarity
Components
1 2 3 4 5 6 7 8 Q 1011 1213141516171819202122232425262728293031323334353637383940414243
1
2
1
1
3
4
5
6
7
8
9
10
11
12
13
14
15
16
1
1
1
1 1 1
1 1 1
1
1
1 1
1
t
1 1
1
1 1 1
1
1
1
1
1
1
1
1 1
1 1 1
1 1
1
1
1
1
1
1 1
1 1
1
1
1
1
1
1
1 1
1 1
1
1
1
1
1
1
1
1
1
1
1 1
1
1
1
1
1
1
1
1
1
1
1
1
1
1 1
1
1
1
1 1 1
1
1 1 1
1
1
1
1
1
1 1
1
1
1
1
1 1 1
1
1
1
1
1
1
1 1
1
1
1
1
1
1
1
1 1
1
1
Fbgure 5.The Original Machine-Component Chan
IIE Transactions, Septernher 1986
Level
Threshold
Value
10
0.00
9
0 09
8
0 17
..
i
I
I
I
I
I
I
I
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i
I
I
I
I
1
I
I
1
Machines
Figure 6. Dendogram For Test Problem
matrix which is accessed by an average linkage clustering
algorithm to form the machine cells. The similarity matrix is
continuously revised to reflect changes due to formation of
new cells.
The dendogram representing the machine cells at different
similarity levels is depicted in Figure 6. At the similarity level
of 0.17, five machine cells are formed. Machines 1, 2, 9, and
16 form the first cell: machines 4, 5, 6, 8, and 15 form the
second, and so on. The resulting machine-component chart,
when the parts are assigned to appropriate cells, is as pre-
sented in Figure 7. Due to a large number of inter-cellular
moves created by bottleneck machines, the block diagonal
form can hardly be realized.
Machine cells 1and 2 are used to illustrate how the number
of intercellular moves between two cells is determined. The
cell vector 1, CVl is constructed by OR'ing the machine
vectors belonging to cell 1.
Components
2 4 7 10182832373840421 5 6 8 9 111214151619202123293133343941431735361325263222242730
Figure 7. Machine-Component Chart Before Considering Bottleneck Machines, Parts are Assigned to Cells. "One" Entries Outside the
Blocks Represent lnterceiluiar Moves
September 1986, 11E Transactions
Cell vector 2, CV2 is constructed by OR'ing its machine
vectors:
CV2
=
MV~.OR.MVs.OR.MV~.0R,MV8.ORRMj~
=
11101111101111111011101l001110l1110011l1111.
The resulting vector from AND
vectors is obtained as follows,
on these two cell
CVA = CV,.AND.CVl
=
010000100000000000OO000000010001OO001101010.
Downloaded by [University of Waterloo] at 13:27 23 February 2015
The non-zero bits in CVA correspond to components having
operations in both cells 1 and 2. The number of non-zero bits
determines how many inter-cellular moves exist between the
two cells. The list of bottleneck machines and the related
number of inter-cellular moves is given in Table 1.
--
7
1
Table 1. Bottleneck Machines and Related InterCellular Moves
Bottleneck
Number of Inter-Cellular
Machines
Moves
.~
6
7
8
Conclusion
The new model forms the machine cells by using the similarity coefficient method. It uses a simple procedure to assign
the components to machine cells in order to create machinecomponent groups. The model employs simple data structure
and analysis techniques to store the data of the machinecomponent chart, to identify the exceptional parts, and to
ternative
duplicate solutions
the bottleneck
and provides
machines.
the user
Finally,
with the
it generates
opportunity
al-
.-..-
-
1
2
4
3
5
The duplication process starts with the machine creating the
largest
number of inter-cellular moves (machine 6 ) and continues until no machine is creating a larger number of intercellular moves than specified. When the lower limit on the
number of inter-cellular moves to be considered critical for
duplication, LIMIT is zero, the result of duplication would
be as presented in Figure 8. As can be seen, the duplication
of bottleneck machines resulted in the elimination of all intercellular moves. When the LIMIT is equal to 2, the resulting
machine-component chart will be as presented in Figure 9.
By changing the value of LIMIT, alternative solutions can be
examined.
2
14
2
7
12
.
to evaluate different options and choose one of them. Methods have been developed to assist the user in making these
choices; this will be the topic of a later paper.
Components
2 4 7 10182832373840425 8 9 141516192123293341436 173435361 1213252631393 112022242730
"7
e
.-
2 1
1 1 1 1 1 1
9 1 1
1 1 1 1 1 1 1
1 1 1
1 1 1
161
1
1
1
1 1
1
5 1
1 1 1
8 1
1
3
14 1
5
15
4
6
' 0 8
11
3
14
6
7
10
6
8
11
12
13
8
1
1
1
1
1
1 1 1
1
1 1
1
1 1
1
1 1 1 1 1 1 1 1 1
1
1 1
1 1
1
1 1 1 1
1
1
1
1
1 1 1 1
1
Figure 8. Final Machine-Component Chart (LIMIT
1
1
1
1
1 1 1 1
1 1
1
1 1 1
1
1
1
1 1 1 1 1 1 1
1 1 1
1
1 1
1
1
1
1 1
1 1
1
1 1 1
=
1
1
1
1
1
1 1 1
0)
IIE Transactions, September 1986
Components
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2 4 7 10182832373840425 8 9 1 4 1 5 1 6 1 9 2 1 2 3 2 9 3 3 4 1 4 3 6 1 7 3 4 3 5 3 6 1 1 2 1 3 2 5 2 6 3 1 3 9 3 11202!2242730
14 1
6
7
10
6
8
11
12
13
8
1
Figure 9. Final Machine-Component Chalt (LIMIT = 2)
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[I] Anderberg, hl. R.. Clutter Analysis for Appliartion, Academic Press,
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[Z] Burbidge, 1. L., "Production Row Analysis:' Semimr on ,he First Steps
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[4] Chan, H. M., and Milncr, D. A., "Direct Clustering Algotithm for
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[71 Kennedy, James N., "A Review of Some Cluster Analysis Methods,"
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[91 King, J. R., and Nakarnchai. V., "Machine-Component Group Formation in Group Technology: Review and Exlension," Int. Jow. Prod.
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1 0 McAuley, I . , "Machine Grouping for Efficient Production," The Produetion Engin~er,Vol. 52, February 1972, pp. 53-57.
[Ill MeCarmick, W. T., Schweiuer, P. I., and White, T. W., "Problem
Demmposition and Data Reorganization by a Cluatcrinx Technique,"
Opelafionr Research, Vol. 52, February 1972, pp. 993.1009.
[I21 Mitrofanou, S. P., Scicn~ijcPrinciples of G ~ o u pTechnoloxy, Pans 1 3 ,
English Translation, National Lending Library for Science and Technology, 1976.
September 1986, IIE Transactions
[13] Seifoddid. Hamid, Cost Bosed M ~ o c h i ~ ~ - C ~ m p oGrouping
nenl
Model:
h G ~ o u pTechnology, unpublished Ph.D, dissertation, Oklahoma State
Uduersity, Stillwater, 1984.
[14] Sneath. P. H., and Sokal, R. R., Numerical Tarommy. W. H . , Freeman
and Company, San Francism, 1973.
[IS] Sokal, R. R.,and Sneath, P. H., Principles of Numerical Taronomy,
Freeman, 1968.
[la] Standiih, T. A , , Data Slnrcture Teehniqurr, Addisan-Wesley, Company,
1980.
Hamid Seifoddini received a BSIE from Tthran Univernty of Technology
and an MS and W D in Industrial Engineering and Management from Oklahoma State University. He is an assistant professor in the Department of
lndustnal Engineering at the University of Wironsin-Milwaukee. He has also
taught a t University of Utah and at Langrton University in Langrton, Oklahoma. H e has taughl courser in quality control, reliability engineering, engineering statistics, industrial automation, and produdion systems. Dr.
Seifoddini has worked for five years as a industrial engineer in a number of
manufacturing organizations. His primary reaching and research interests are
computer applications (simulation and mkrocomputers); quality mnuol and
reliability, and operations research.
Philip M.Wolfe received a BSIE and a BS in business administration from
the University of Missouri. He also has MS and PhD degrees in industrial
engineering from Arvona State University. Dr. Wolfe i$ manager, operational
planning at the Garren Turbine Engine Company in Phoenix, Arizona. Previously, he was professor in the School of Industrial Engineering and Management at Oklahoma State University and has over fiheen years of computer
experience in designing, developing and implementing data processingsystems.
Dr. Wolfe has authored numerous articles in the thrust area of computer
software and hardwarc in addition to his new book. "Basic Engjncering and
Scientific Programs for the IBM Personal Computer." Dr. Wolfc is a senior
member of 11E.