Design of clustered manufacturing systems-an enhanced and developed optimisation approach.
Gnanasekaran, J.S. ; Shanmugasundaram, S.
Introduction
The cluster approach is a philosophy that exploits the proximity
among the attributes of given objects. Cellular manufacturing (CM) is an
application of GT in manufacturing. CM involves processing a collection
of similar parts (part families) on dedicated cluster of machines or
manufacturing processes (cells). The cell formation problem in cellular
manufacturing systems is the decomposition of the manufacturing systems
into cells. Part families are identified such that they are fully
processed within a machine group.
The cells are formed to capture the inherent advantages of GT such
as reduced setup times, reduced in-process inventories, improved product
quality, shorter lead time, reduced tool requirements, improved
productivity, better overall control of operations, etc. The clustering
method can simplify a complex system by focusing on several groups than
handling all the elements individually. The purpose of the clustering
methodology is to separate a complex system into mutually exclusive
clusters, which have homogeneous properties and use the same or similar
resources. An optimal clustering result can more easily manage the
design and R&D tasks rather than control entire system or detailed
elements. The clustering techniques involve a complicated process, which
determines the fittest number of clusters and the size of combination
simultaneously. As a result, traditional clustering methods are
investigated and new clustering methodologies are developed.
Objectives and Organisation of Paper
The objective of the paper is as follows:- * To provide an enhanced
and developed optimization approach on BEA clustering
* To provide future research directions considering manufacturing
engineering requirements, manufacturing logistics and supply chain
systems.
* To introduce and integrate the Nearest Neighbors Technique (NNT)
and best neighbors Clustering (BNC) in the optimization using BEA.
* To observe the efficiency and effectiveness of the methodology,
results, and their managerial implications are analyzed
Section 3 discuses the brief literature review on cluster
algorithms, Section 4 gives brief theoretical issues of interest when
discussing about Bond energy Algorithm (BEA). Section 5 comprises the
application of cluster algorithms and presented the EDOA for the
segregation of best clusters. Section 6 consist the concurrent
engineering environment and manufacturing logistics activities with a
case study and its results. Finally Section 7 implies the concluding
section with the theoretical/managerial implications of process and
gives recommendations for further research.
Literature Review
* In 1963, Burbidge initially generated a clustering methodology
that was applied to the manufacturing industry involving a machine
economic flow analysis problem. It was thought advantageous in the
analysis of production to group product parts and manufacturing machines
into cellular systems, thereby effectively reducing production
processing time, resulting from the various interactions among parts and
machines. Clusters can be grouped according to similar features of
system components, and this particular property can reorganize a system
into meaningful and structured subsystems
* In 1990, Kusiak and Park applied clustering analysis to the
scheduling of a large amount of design activities and resources of a
complex and large-scale system. Based on concurrent concepts, the design
problem for such a complex system can be broken down into groups of
activities to simplify the scheduling management.
* The primary problem in the clustering method is how to break down
the binary matrix into diagonal form sub-matrices and how to allocate
all 1's of the binary matrix into those sub-matrices. Majority of
the studies have been applied to machine-part cellular forming, the
clustering method has also been applied to many other practical
problems, for example, Burbidge (1963) and King (1980) in production
flow analysis, McCormick et al. (1972) in data recognition, and Kusiak
and Park (1990) in product design scheduling.
* Kusiak (1990) stated that there is three represented formulations
of GT: matrix, mathematical, and graph formulations. Normally, the
interaction among parts and machines can be depicted by a zero-one
binary matrix, the columns and rows of which represent parts and
machines, respectively, and if a column and a row have an interaction
with one other, the matrix element will be set to 1, otherwise, 0.
* Phipps Arabie and Lawrence J. Hubert (1990) were examined the
bond energy algorithm of McCormick et.al (1972) the context of related
strategies of data analysis that seek to solve problems in production
research, imaging, and related engineering problems.
* According to the study of Brimson in 1991, functions are
aggregated by activities, and activity analysis is used to decompose a
large, complex system into elemental processes.
* Furthermore, Yoshikawa (1994) stated that a new product can be
improved by assigning activity costs to individual functions and
focusing efforts on such function groups with the greatest portion of
costs associated with individual activities.
Bond Energy Algorithm (BEA)
The Bond Energy Algorithm developed by McCormick, Schweitzer and
White (1972) is to identify and display the natural variable groups or
clusters that occur in complex data arrays. They proposed a measure of
effectiveness (ME) such that an array that possesses dense clumps of
numerically large elements will have a large ME when compared with the
same array the rows and columns of which have been permuted so that
numerically large elements are more uniformly distributed throughout the
array. When all the rows and columns of the matrix are rearranged, then
there is (M! X N!) Total permutations are possible. The BEA
systematically reduces the number of permutations. The purpose of the
Bond Energy Algorithm (BEA) IS to identify and display natural variable
groups and clusters that occur in complex data arrays. In addition, the
algorithm seeks to uncover and display the associations and
interrelations of these groups with one another. These tasks are
accomplished by permuting the rows and columns of an input data array in
such a way as to push the numerically larger array elements together. It
has been found that the relations among variables existing in data
arrays are more easily identifiable when the arrays are permuted into a
form in which dense clumps of numerically large array elements emerge.
Informative permutations of the input data array (i.e., those that best
display the groupings and interrelations) can be found via a measure of
clumpiness of an array, which assumes large values when associated with
the more informative row and column permutations.
The BEA Measure of Effectiveness
The Measure of effectiveness (ME) used in the bond energy algorithm
in such a way that an array, which possesses dense clumps of numerically
large elements, will have a large ME when compared to the same array
whose rows and columns have been permuted so that its numerically large
elements are more uniformly distributed throughout the array. The ME of
an array is the sum of the bond strengths in the array, where the bond
strength between two nearest-neighbor elements is defined as their
product. Maximizing the ME by row and column permutations serves to
create strong 'bond energies' by driving the larger array
elements together.
Existing BEA Computational Procedures
The BEA expression separated into two forms i.e. row wise and
column wise computations for maximizing ME. The problem was reduced by
two separate optimizations. The expressions for column order and row
order computations are given below.
Column Order Computation
Maximize ME = [m.summation over (i=1)][n.summation over (j=1)]
[a.sub.ij][[a.sub.i-1,j] + [a.sub.i+1,j]]
Where,
ME = MEASURE OF EFFECTIVENESS
m = Number of Rows in the data incidence matrix
n = Number of Columns in the data incidence matrix
[a.sub.ij] = Location of Cell element, i.e., the element
'a' is placed in the ith row and jth column.
With the initialization [a.sub.0,j] = [a.sub.m+1,j = 0]
Row Order Computation
Maximize ME = [m.summation over (i=1)][n.summation over (j=1)]
[a.sub.ij][[a.sub.i,j-1] + [a.sub.i,j+1]]
Where,
ME = MEASURE OF EFFECTIVENESS
m = Number of Rows in the data incidence matrix
n = Number of Columns in the data incidence matrix
[a.sub.ij] = Location of Cell element, i.e., the element
'a' is placed in the ith row and jth column.
With the initialization [a.sub.i.0] = [a.sub.I,n+1 = 0]
The Procedure for finding optimal column/row order is as follows:-
(1) Place one of the columns arbitrarily, Set j=1
(2) Try placing individually each of the remaining n-j columns in
each of the possible locations (to the left and right of the j columns
already placed), and compute each column's contribution to the ME.
(3) Place the columns that gives the largest ME value together with
first referenced column
(4) Increment j by 1 and repeat until j = n
(5) When all the columns have been placed, repeat the procedure on
the rows using row order computation expression.
Enhanced And Developed Optimisation Approach (EDOA)
Enhanced Optimization Approach
From the above computational procedure, the existing BEA is
enhanced through the direct and combined application of the BEA
expression is given below.
Maximize ME = 1/2 [m.summation over (i=1)][n.summation over (j=1)]
[a.sub.ij][[a.sub.i,j-1] + [a.sub.i,j+1] + [a.sub.i1,j] + [a.sub.i+1,j]
Where,
ME = MEASURE OF EFFECTIVENESS
m = Number of Rows in the data incidence matrix
n = Number of Columns in the data incidence matrix
[a.sub.ij] = Location of Cell element, i.e., the element
'a' is placed in the ith row and jth column.
With the initialization [a.sub.0,j] = [a.sub.m+1,j = [a.sub.i.0] =
[a.sub.I,n+1] = 0
The enhancement has been achieved through the improvement of
cluster efficiency by the summation of left, right, top and bottom
element of any [a.sub.ij] cell element in the data incidence matrix and
multiplied by the same element [a.sub.ij] and the whole divided by 2
gives the cell contribution or ME value for the particular element
[a.sub.ij]. The summations of all elements' contribution available
in the incidence matrix are the total contribution or total ME or
produce the Total Bond Energy. The total bond energy before clustering
called here as Initial Measurement of Effectiveness and after clustering
called as final Measurement of Effectiveness. The problem is here also
reduced by two separate optimizations by using the same BEA expression.
Using the enhanced BEA flow chart as shown in Figure 1 does the optimal
column/row order computations. The application of Best Neighbors
Clustering (BNC) interacting with this enhancement results the highest
bond energy and interaction density, whenever the degree of interacting
elements (Number of 1's) comes closer with various combination
occurrences row wise/ column wise during the column/row order
computations. On the other hand, whenever if any non-interacting element
(Number of 0's, i.e. empty cells) comes closer, No such bond energy
developed. The effect of this enhancement increases the cluster
efficiency.
[FIGURE 1 OMITTED]
Enhanced and Developed Optimization Approach (EDOA)
The enhanced BEA was enriched by a developed clustering approach
through the application of tie breaking choice as mentioned in the
enhanced and developed optimization approach (EDOA) as shown in Figure
2. The column computation started as first and computes the optimal
column order sequence and starts the row computation and computes the
optimal row order sequence. Two similar treatments are applied for rows
and columns from data array called as Data Incidence Matrix. Rearrange
columns order optimal sequence from data array called as Structured
Incidence Matrix. The rearrangement of row order optimal sequence from
the structured incidence matrix called as Combined Incidence Matrix. The
final solution is in the form of combined incidence matrix and it
consist of self-contained clusters and it forms a Block Diagonal Matrix.
A detailed procedural step of EDOA is as follows:
(1) Find Initial Measure of Effectiveness (ME) for the given data
incidence matrix using the BEA Expression
(2) Set j=1.
(3) Select a column or row arbitrarily.
(4) Calculate the Measure of Effectiveness (ME) for each of the
remaining n-j columns (m-j rows) with the jth column (jth row).
(5) Place individually the column(s) row(s) from n-j column(s) m-j
row(s) with jth column (jth rows), and those, which have largest ME(s)
next to (below) jth column or jth rows.
(6) For calculation of ME, for any j and j+1 columns (rows),
nearest neighbors technique is also followed.
(7) Select large ME column (row) contribution as reference and
compare with n-j columns (rows) and compute ME again. If any tie occurs
choose a tie breaking choice.
(8) Continue the same procedure until all ME values becomes Zero or
formation of first row or column order block.
(9) Now choose j+1 i.e. new unallocated column (row) for next
comparison/computation and so on.
(10) Continue until (j=n) or (j=m).
(11) The process will stop when j=n or j=m, otherwise continue the
procedure as per detailed BEA flow chart. (Figure 5.4)
(12) Rearrangement of columns or rows for getting block diagonal or
checkerboard clusters (if any).
(13) Find Maximum Measure of Effectiveness i.e. final Measure of
Effectiveness (ME). This value always larger than initial measure of
Effectiveness.
(14) The Total Bond Energy (TBE) results the final measurement of
effectiveness after the clustering process.
[FIGURE 2 OMITTED]
Case Study
A Case Study is presented for this problem to test and validate the
EDOA. The study was mainly focused on logistics concerns and supplier
activities relationship between a main industry and a chain connecting
with their suppliers. They are followed the regular manufacturing
practices including product design and development, tool design, die
design, raw material planning, scheduling, inventory, manufacturing,
storage and warehousing etc. The problem is found in this juncture is to
make an interlink between the main industry and segregate the various
logistic and logistic design activities involved in manufacturing
activities from product design and development to the disposal of
products and to the customer. The study took all necessary steps to link
all the activities held between the manufacturers and suppliers. The
paper is based on both desk research and field research project into
providing a logistics support perspective to the product design process.
EDOA Methodology
According the product design interfaces with logistics and the
interactions between modules and design parameters, the formulation
process starts. A cell entry, say [a.sub.ij] receives either 1 or 0,
corresponding to binary element procedure. The entry 1 or 0 indicates
that a particular design parameter does or does not belong to the
respective module. The interactions between modules and design
parameters can be represented in a binary module design parameter
incidence matrix. The assignment of binary values is inherently a
technical task and requires the possession of knowledge and skills as
they pertain to a particular logistics design. The methodology presented
here allows the generation of multiple incidence matrices. Each of these
matrices can be explored and solved, and the results can be evaluated
for their effectiveness. On the other hand, the design team members can
hold discussions and changes can be made to only one incidence matrix
until an agreement is achieved. The ME measures the density of the bond
between any two elements of the matrix. When the ME numerical value is
greater, then the bond between the elements is greater or vive-versa.
The EDOA methodology is used here to maximize the system
effectiveness to achieve rich or best clusters so as to minimize the
time and cost to the related activities considered in this study. The
existing Bond Energy Algorithm (BEA) was applied to this study and
tested for cluster efficiency. But it forms lesser efficiency clusters.
The Initial Measurement of System Effectiveness (MSE) for the existing
data is 21 and the final MSE for existing method gives only 81 after
clustering. The clusters formed for the existing method as shown in
Figure 3. Hence it is proposed to introduce the above mentioned enhanced
and developed optimization approach (EDOA) for computational purpose to
get rich clusters to the appropriate family of logistic design. The
methodology used in this paper generates modules that are cohesive,
bounded and contains a self-contained group of activities. For effective
implementation of integrated logistics design, each module solves one
clearly defined segment of the total system.
Results
The Initial MSE value for the study as same as 21 and the final MSE
value obtained was 99 after clustering. The system effectiveness is
maximized and hence the clustering process releases highest bond energy
and the solution consist optimal bond energy. The EDOA results are shown
in Figure 4. Here the computational procedures are drastically increased
due to the reference selection of column/row large ME. This will be
continued until all ME values becomes zero to form a row / Column order
block. Then only the next choice of unallocated column/ row allowed as
reference in computations. The effect of this process, the clustering
efficiency was much improved. Hence whatever the data suggested by the
mutual agreement between the logistician and design engineer of any
manufacturing firms, the EDOA achieves a best clustering approach and
results an effective clustering.
Conclusion
The objective of EDOA in a logistic design has been attained
through clustering. The design for logistics model results with four
module families with related design parameters. The above study produced
high bond energy clusters by the incremental rise in the system
effectiveness when comparing the existing optimization approach..
This approach reduces the scattering of data and hence there will
be a chance of the occurrence of perfect block diagonal also, if the
relevance of data is appropriate. Many times it results the block
checkerboard cluster types also. EDOA Clustering Software is also
specially developed for this research and it is also tested and
validated through this study.
References
[1] Andrew Kusiak (1992) "Concurrent Engineering Automation,
Tools and Techniques" John Wiley & sons, Inc. New York,
p.535-544.
[2] Blanchard, B.S. and Fabrycky, W.J. (1998). Systems Engineering
and Analysis (3rd Ed). Upper Saddle River, NJ: Prentice Hall.
[3] Burbidge L, "Production flow analysis," The
Production Engineer, vol. 42,pp. 742-752, 1963.
[4] Gnanasekaran J.S, and Dr. Shanmugasundaram S. (2003)
"Concurrent Engineering Approach for Modeling to the
Logistics", Proceedings of International Conference on Mechanical
Engineering, Dhaka, Bangladesh, ICME2003-AM-31.
[5] Gnanasekaran J.S. and Dr.S.Shanmugasundaram (2007)
"Logistics Integrated Product Design under Concurrent Engineering
Environment", International Conference on Manufacturing Engineering
and Engineering Management (ICMEEM 2007) under World Congress on
Engineering (WCE 2007) held at London, U.K., July 2-4, 2007.
[6] Gnanasekaran J.S. and Dr.S.Shanmugasundaram (2008) "Role
Of Manufacturing Logistics in Indian Automobile Industries -A Case
Study", International Journal of Applied Engineering Research,
Volume 3, Number 9, pp 1205-1215
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"Pioneer-manufacturing achievements through concurrent
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(IMEC-2004) Kuwait, December 5-8, 2004.
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"Optimization in designing for logistics support- A Concurrent
engineering approach", Proceedings of International conference on
e-manufacturing, Bhopal, India, pp359-365.
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"Manufacturing Logistics-Research Implications", National
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January6-7, 2006
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"Problem decomposition and data reorganization by a clustering
technique". Operations Research 20 (5), 993-1009.
[15] Phipps Arabie And Lawrence J. Hubert (1990), "The Bond
Energy Algorithm Revisited", IEEE Transactions On Systems, Man, And
Cybernetics, Vol. 20, No. 1, January/February.
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J.S. Gnanasekaran (1) and S. Shanmugasundaram (2)
(1) Professor, Department of Mechanical Engineering, Sri Krishna
College of Engineering and Technology, Coimbatore-641008. India.
E-mail:jsgsekar@yahoo.com
(2) Principal, Rajarajeswari Engineering College, Adayalampattu,
Chennai-600 095. India, E-mail: sssundaramgct@yahoo.com
Figure 3: Existing BEA Clustering.
DESIGN PARAMETERS
BEA 1 21 26 2 8 13 17 23 25
MODULES 1 1 1 1 1
13 1 1 1 1 1 1 1 1 1
2
5
3
6
8
4
14
7
9
10
11
12 1 1 1 1 1
15 1 1 1 1 1 1
DESIGN PARAMETERS
BEA 29 3 4 14 18 30 5 6 9
MODULES 1 1
13 1
2 1 1 1 1 1
5 1 1 1 1 1
3 1 1 1
6 1 1 1
8 1 1 1
4
14
7 1 1 1 1 1
9 1
10
11
12
15 1
DESIGN PARAMETERS
BEA 12 15 27 7 10 11 16 19 20
MODULES 1 1
13 1
2 1
5 1
3 1 1 1 1 1
6 1 1 1 1
8 1 1 1
4 1
14 1
7
9 1
10 1
11 1
12
15
DESIGN PARAMETERS
BEA 22 28 24
MODULES 1
13
2
5
3
6
8
4 1 1
14 1 1
7
9
10
11
12
15
Figure 4: EDOA Clustering.
DESIGN PARAMETERS
ES1 1.1 1.2 4.1 4.2 7.1 9.1 11 12
BE 1 2 7 8 13 17 21 23
MODULES MF1 1 1 1 1 1
12 1 1 1 1
13 1 1 1 1 1 1 1 1
15 1 1 1 1 1
MF2 2
5
7
MF3 3
6
8
9
10
MF4 4
11
14
ES1 1.1 1.2 4.1 4.2 7.1 9.1 11 12
DPF1
DESIGN PARAMETERS
ES1 12 13 13 15 2.1 2.2 5.2
BE 24 25 26 29 3 4 10
MODULES MF1 1 1 1
12 1 1
13 1 1 1
15 1 1
MF2 2 1 1 1
5 1 1 1
7 1 1
MF3 3
6
8
9
10
MF4 4
11
14
ES1 12 13 13 15 2.1 2.2 5.2
DPF1 DPF2
DESIGN PARAMETERS
ES1 7.2 9.2 15 3.1 3.2 5.1 6.1 6.2
BE 14 18 30 5 6 9 11 12
MODULES MF1 1
12
13
15
MF2 2 1 1 1
5 1 1 1
7 1 1 1
MF3 3 1 1 1 1 1
6 1 1 1 1 1
8 1 1 1 1
9 1
10
MF4 4
11
14
ES1 7.2 9.2 15 3.1 3.2 5.1 6.1 6.2
DPF2 DPF3
DESIGN PARAMETERS
ES1 8.1 8.2 10 14 10 11 14
BE 15 16 19 27 20 22 28
MODULES MF1 1
12
13
15
MF2 2
5
7
MF3 3 1 1 1
6 1 1
8 1 1 1
9 1
10 1
MF4 4 1 1 1
11 1
14 1 1 1
ES1 8.1 8.2 10 14 10 11 14
DPF3 DPF4
DPF: DESIGN PARAMETER FAMILY
MF: MODULE FAMILY
