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Group Technology and
Facility Layout
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Group Technology and
Cellular Manufacturing
Group technology (GT)
A management philosophy that attempts to group
products with similar design or manufacturing
characteristics, or both.
Cellular manufacturing (CM)
An application of GT that involves grouping
machines based on the parts manufactured.
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Objective of CM
Identify machine cells and part familiessimultaneously
Allocate part families to machine cells in a way
that minimizes the intercellular movement of parts.
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CM Concept in Layout
Develop the layout of machines within the cells soas to minimize inter- and intracellular material-
handling costs.
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Benefits of CM application Set-up time reduction Work-in-process inventory reduction
Material-handling cost reduction
Direct and indirect labor cost reduction
Improvement in quality Improvement in material flow
Improvement in machine utilization
Improvement in space utilization
Improvement in employee morale
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A GT Cell
Machine 1
Machine 2
Machine 3
Machine 4
Machine 5
Materials in
Finished
goods out
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Traditional Job Shop vs CM
Job shop environment Machines are grouped on the basis of their
functional similarities
CM environment
Machines are grouped into cells, with each cell
dedicated to the manufacture of a specific part
family
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Arrangement of Cells in
a Job Shop Environment
TM
TM TM
TM DM
DM DM
DM
VMM VMM BM BM
BM = broaching machine
DM = drilling machine
TM = turning machine
VMM = vertical milling machine
Routing of partsP1,P3,P9Routing of partsP2,P4,P7,P8
Routing of partsP5,P6,P10
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Arrangement of Cells
in a CM SystemTM DM
DM
DM
VMM
BM BM
BM = broaching machine
DM = drilling machine
TM = turning machine
VMM = vertical milling machine
VMM TM
DM
TM TM
Routing of partsP1,P3,P9Routing of partsP2,P4,P7,P8
Routing of partsP5,P6,P10
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Sample Part-Machine Processing
Indicator Matrix
M a c h i n e
M1 M2 M3 M4 M5 M6 M7
P
a
rt
P1 1 - - 1 - 1 -
P2 - 1 1 - 1 - -
P3 - - - 1 - 1 -
P4 - 1 1 - - - -
P5 - - 1 - - - 1
P6 - 1 - - 1 - 1
][ ija
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Rearranged Processing
Indicator Matrix
M a c h i n e
M1 M4 M6 M2 M3 M5 M7
P
a
rt
P1 1 1 1 - - - -
P3 - 1 1 - - - -
P2 - - - 1 1 1 -
P4 - - - 1 1 - -
P5 - - - - 1 - 1
P6 - - - 1 - 1 1
][ ija
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Case of Exceptional Parts
The rows (parts) corresponding to the 1s that lieoutside the diagonal block.
When exceptional parts are removed, a block
diagonal structure is easily identified.
If it is wanted that cells are completely
independent with no intercellular movement of
material, exceptional parts must be subcontracted
out.
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Processing Indicator Matrix
(Case of Exceptional Parts)
M a c h i n e
M1 M4 M6 M2 M3 M5 M7
P
a
rt
P1 1 1 1 - - - -
P3 - 1 1 - - - -
P2 1 - - 1 1 1 -
P4 - - - 1 1 - -
P5 - - - - 1 - 1
P6 - - - 1 - 1 1
][ ija
Exceptional part
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Case of Bottleneck Machines
Bottleneck Machines Machines corresponding to the columns that
contain exceptional elements, i.e., elements outside
the block diagonal structure.
Two or more part families share the machines. If the columns corresponding bottleneck machines
are removed, then mutually separable clusters or
machine cells and part families can be identified.
Additional copies of machines are needed
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Processing Indicator Matrix
(Case of Exceptional Parts)
M a c h i n e
M1 M4 M6 M2 M3 M5 M7
P
a
rt
P1 1 1 1 - - - -
P3 - 1 1 - - - -
P2 1 - - 1 1 1 -
P4 - - - 1 1 - -
P5 - - - - 1 - 1
P6 - - - 1 - 1 1
][ ija
Bottleneck machine
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Using Nonbinary in Part-Machine
Processing Indicator Matrix
Binary matrix representation Only informs whether or not a part is processed on
a machine
Nonbinary matrix representation
Flexible because it allows to capture other
relationships between each part-machine pair (e.g.,
cost of processing a part on a machine, processing
time)
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Modifying Part-Machine Processing
Indicator Matrix
Creating additional columns Number of parts to be manufactured
Batch size for each part
Sequence of machines visited by a part can be
recorded
Operation sequence for each part is a critical factor
in identification of machine cells
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Operation Sequence
Definition of operation sequence
k if part i visits machinej for the kthoperation
xij=
0 otherwise
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Processing Indicator Matrix showing
Sequence of Operations
M a c h i n e
M1 M4 M6 M2 M3 M5 M7
P
a
rt
P1 2 3 1 - - - -
P3 - 1 2 - - - -
P2 3 - - 1 4 2 -
P4 - - - 2 1 - -
P5 - - - - - 1 2
P6 - - - 1 - 2 3
][ ija
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Clustering Approach
Attempt to uncover and display similar clusters orgroups in an input object-object or object-attribute
data matrix.
Rearrange rows and column of the input matrix
typically a binary matrix
that determineswhether or not a part is processed on a particular
machine (i.e., a block diagonal is identified)
Use process plan or part routing information
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Input Matrix
M1 M2 M3 M4 M5 M6 M7
P
a
rt
P1 1 - - 1 - 1 -
P2 - 1 1 - 1 - -
P3 - - - 1 - 1 -
P4 - 1 1 - - - -
P5 - - 1 - - - 1
P6 - 1 - - 1 - 1
][ ija
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Common Clustering Algorithms
Rank order clustering
Row and column masking
Similarity coefficient
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Rank Order Clustering (ROC)
Algorithm
ROC algorithm: Determine a binary value for each row and column
Rearrange the rows and columns in descending
order of their binary values
Identify clusters.
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Steps of ROC Algorithm
Step 1:Assign binary weight BWj= 2
m-jto each columnj ofthe part-machine processing indicator matrix.
Step 2:
Determine the decimal equivalent DE of the binaryvalue of each row i using the formula
m
j
ij
jm
i aDE1
2
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Steps of ROC Algorithm
Step 3:Rank the rows in decreasing order of their DE values.Break ties arbitrarily. Rearrange the rows based on thisranking. If no rearrangement is necessary, stop;otherwise go to step 4.
Step 4:For each rearranged row of the matrix, assign binaryweight BWi= 2
n-i.
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Steps of ROC Algorithm
Step 5:
Determine the decimal equivalent DE of the binaryvalue of each columnj using the formula
Step 6:
Rank the columns in decreasing order of their DEvalues. Break ties arbitrarily. Rearrange the columns
based on this ranking. If no rearrangement isnecessary, stop; otherwise go to step 1.
n
i
ij
in
j aDE1
2
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Example Part-machine processing indicator matrix
M1 M2 M3 M4 M5 M6 M7
P
a
r
t
P1 1 - - 1 - 1 -
P2 - 1 1 - 1 - -
P3 - - - 1 - 1 -
P4 - 1 1 - - - -P5 - - 1 - - - 1
P6 - 1 - - 1 - 1
][ ija
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Step 2:
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Step 2:
Determine the decimal equivalent (DE) of the binary
value for each row i
M1 M2 M3 M4 M5 M6 M7 Binary Value
64 32 16 8 4 2 1
P
a
r
t
P1 1 - - 1 - 1 - 74
P2 - 1 1 - 1 - - 52
P3 - - - 1 - 1 - 10
P4 - 1 1 - - - - 48P5 - - 1 - - - 1 17
P6 - 1 - - 1 - 1 37
][ ija
Binary Weight
Step 3:
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Step 3:
Rank the row in decreasing order of their DE value and
rearrange them based on this ranking
M1 M2 M3 M4 M5 M6 M7
P
a
r
t
P1 1 - - 1 - 1 -
P2 - 1 1 - 1 - -
P4 - 1 1 - - - -
P6 - 1 - - 1 - 1P5 - - 1 - - - 1
P3 - - - 1 - 1 -
][ ija
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Step 5:
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Step 5:
Determine the decimal equivalent (DE) of the binary
value for each columnj
M1 M2 M3 M4 M5 M6 M7
32 28 26 33 20 33 6
P
a
r
t
P1 1 - - 1 - 1 - 32
P2 - 1 1 - 1 - - 16
P4 - 1 1 - - - - 8
P6 - 1 - - 1 - 1 4P5 - - 1 - - - 1 2
P3 - - - 1 - 1 - 1
][ ija
Binary Value
Binary Weight
Rank the column in decreasing order of their DE value
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Rank the column in decreasing order of their DE value
and rearrange them based on this ranking (Break ties
arbitrarily).
M4 M6 M1 M2 M3 M5 M7
P
a
r
t
P1 1 1 1 - - - -
P2 - - - 1 1 1 -
P4 - - - 1 1 - -
P6 - - - 1 - 1 1P5 - - - - 1 - 1
P3 1 1 - - - - -
][ ija
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Step 1:
Assign binary weight (BW) to each columnj
M4 M6 M1 M2 M3 M5 M7
64 32 16 8 4 2 1
P
a
r
t
P1 1 1 1 - - - -
P2 - - - 1 1 1 -
P4 - - - 1 1 - -
P6 - - - 1 - 1 1P5 - - - - 1 - 1
P3 1 1 - - - - -
][ ija
Binary Weight
Step 2:
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Step 2:
Determine the decimal equivalent (DE) of the binary
value for each row i
M4 M6 M1 M2 M3 M5 M7
64 32 16 8 4 2 1
P
a
r
t
P1 1 1 1 - - - - 112
P2 - - - 1 1 1 - 14
P4 - - - 1 1 - - 12
P6 - - - 1 - 1 1 11P5 - - - - 1 - 1 5
P3 1 1 - - - - - 96
][ ija
Binary Weight
Binary Value
Step 3:
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Step 3:
Rank the row in decreasing order of their DE value and
rearrange them based on this ranking
M4 M6 M1 M2 M3 M5 M7
P
a
r
t
P1 1 1 1 - - - -
P3 1 1 - - - - -
P2 - - - 1 1 1 -
P4 - - - 1 1 - -P6 - - - 1 - 1 1
P5 - - - - 1 - 1
][ ija
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Step 4:
Assign binary weight (BW) to each row i
M4 M6 M1 M2 M3 M5 M7
P
a
r
t
P1 1 1 1 - - - - 32
P3 1 1 - - - - - 16
P2 - - - 1 1 1 - 8
P4 - - - 1 1 - - 4P6 - - - 1 - 1 1 2
P5 - - - - 1 - 1 1
][ ija
Binary Weight
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Row and Column Masking (R&CM)
Algorithm
Step 1:Draw a horizontal line through the first row. Select
any 1 entry in the matrix through which there is
only one line.
Step 2:
If the entry has a horizontal line, go to step 2a. If
the entry has a vertical line go to step 2b.
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Row and Column Masking (R&CM)
Algorithm
Step 2a:Draw a vertical line through the column in which
this 1 entry appears. Go to step 2.
Step 2b:
Draw a horizontal line through the row in which this
1 entry appears. Go to step 3.
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Row and Column Masking (R&CM)
Algorithm
Step 3:If there are any 1 entries with only one line through them, selectany one and go to step 2. Repeat until there are no such entries left.Identify the corresponding machine cell and part family. Go to step4.
Step 4:
Select any row through which there is no line. If there are no suchrows, stop. Otherwise, draw a horizontal line through the row,select any 1 entry in the matrix through which there is only one line,and go to step 2.
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Example Part-machine processing indicator matrix
M1 M2 M3 M4 M5 M6 M7
P
a
r
t
P1 1 - - 1 - 1 -
P2 - 1 1 - 1 - -
P3 - - - 1 - 1 -
P4 - 1 1 - - - -
P5 - - 1 - - - 1
P6 - 1 - - 1 - 1
][ ija
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Example
M1 M2 M3 M4 M5 M6 M7
P
a
r
t
P1 1 - - 1 - 1 -
P2 - 1 1 - 1 - -
P3 - - - 1 - 1 -
P4 - 1 1 - - - -
P5 - - 1 - - - 1
P6 - 1 - - 1 - 1
][ ija
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Example
M1 M2 M3 M4 M5 M6 M7
P
a
r
t
P1 1 - - 1 - 1 -
P2 - 1 1 - 1 - -
P3 - - - 1 - 1 -
P4 - 1 1 - - - -
P5 - - 1 - - - 1
P6 - 1 - - 1 - 1
][ ija
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Example
M1 M2 M3 M4 M5 M6 M7
P
a
r
t
P1 1 - - 1 - 1 -
P2 - 1 1 - 1 - -
P3 - - - 1 - 1 -
P4 - 1 1 - - - -
P5 - - 1 - - - 1
P6 - 1 - - 1 - 1
][ ija
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Example
M1 M2 M3 M4 M5 M6 M7
P
a
r
t
P1 1 - - 1 - 1 -
P2 - 1 1 - 1 - -
P3 - - - 1 - 1 -
P4 - 1 1 - - - -
P5 - - 1 - - - 1
P6 - 1 - - 1 - 1
][ ija
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M1 M2 M3 M4 M5 M6 M7
P
a
r
t
P1 1 - - 1 - 1 -
P2 - 1 1 - 1 - -
P3 - - - 1 - 1 -
P4 - 1 1 - - - -
P5 - - 1 - - - 1
P6 - 1 - - 1 - 1
][ ija
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M1 M2 M3 M4 M5 M6 M7
P
a
r
t
P1 1 - - 1 - 1 -
P2 - 1 1 - 1 - -
P3 - - - 1 - 1 -
P4 - 1 1 - - - -
P5 - - 1 - - - 1
P6 - 1 - - 1 - 1
][ ija
Column 1, 4, 6M1,M4,M6in cell 1
Row 1, 3P1,P3in cell 1
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M1 M2 M3 M4 M5 M6 M7
P
a
r
t
P1 1 - - 1 - 1 -
P2 - 1 1 - 1 - -
P3 - - - 1 - 1 -
P4 - 1 1 - - - -
P5 - - 1 - - - 1
P6 - 1 - - 1 - 1
][ ija
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M1 M2 M3 M4 M5 M6 M7
P
a
r
t
P1 1 - - 1 - 1 -
P2 - 1 1 - 1 - -
P3 - - - 1 - 1 -
P4 - 1 1 - - - -
P5 - - 1 - - - 1
P6 - 1 - - 1 - 1
][ ija
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M1 M2 M3 M4 M5 M6 M7
P
a
r
t
P1 1 - - 1 - 1 -
P2 - 1 1 - 1 - -
P3 - - - 1 - 1 -
P4 - 1 1 - - - -
P5 - - 1 - - - 1
P6 - 1 - - 1 - 1
][ ija
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M1 M2 M3 M4 M5 M6 M7
P
a
r
t
P1 1 - - 1 - 1 -
P2 - 1 1 - 1 - -
P3 - - - 1 - 1 -
P4 - 1 1 - - - -
P5 - - 1 - - - 1
P6 - 1 - - 1 - 1
][ ija
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M1 M2 M3 M4 M5 M6 M7
P
a
r
t
P1 1 - - 1 - 1 -
P2 - 1 1 - 1 - -
P3 - - - 1 - 1 -
P4 - 1 1 - - - -
P5 - - 1 - - - 1
P6 - 1 - - 1 - 1
][ ija
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M1 M2 M3 M4 M5 M6 M7
P
a
r
t
P1 1 - - 1 - 1 -
P2 - 1 1 - 1 - -
P3 - - - 1 - 1 -
P4 - 1 1 - - - -
P5 - - 1 - - - 1
P6 - 1 - - 1 - 1
][ ija
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M1 M2 M3 M4 M5 M6 M7
P
a
r
t
P1 1 - - 1 - 1 -
P2 - 1 1 - 1 - -
P3 - - - 1 - 1 -
P4 - 1 1 - - - -
P5 - - 1 - - - 1
P6 - 1 - - 1 - 1
][ ija
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M1 M2 M3 M4 M5 M6 M7
P
a
r
t
P1 1 - - 1 - 1 -
P2 - 1 1 - 1 - -
P3 - - - 1 - 1 -
P4 - 1 1 - - - -
P5 - - 1 - - - 1
P6 - 1 - - 1 - 1
][ ija
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Part Family
M a c h i n e
M1 M4 M6 M2 M3 M5 M7
P
a
rt
P1 1 1 1 - - - -
P3 - 1 1 - - - -
P2 - - - 1 1 1 -
P4 - - - 1 1 - -
P5 - - - - 1 - 1
P6 - - - 1 - 1 1
][ ija
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Similarity Coefficient (SC) Algorithm
SC algorithms are derived from numerictaxonomy and attempt to measure the similaritycoefficient (SC) between pair of machines orparts.
Most of SC algorithms use the Jaccard similaritycoefficient.
For a pair of machines, the Jaccard coefficient isdefined as the number of parts that visit bothmachines divided by the number of parts that visit
at least one machines
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Similarity Coefficient
The Jaccard coefficient:
where aij= 1 if part k requires processing on
machine i, aij= 0 otherwise.
n
k
kjkikjki
n
k
kjki
ij
aaaa
aa
s
1
1
Example
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Example Part-machine processing indicator matrix
M1 M2 M3 M4 M5 M6 M7
P
a
r
t
P1 1 - - 1 - 1 -
P2 - 1 1 - 1 - -
P3 - - - 1 - 1 -
P4
- 1 1 - - - -
P5 - - 1 - - - 1
P6 - 1 - - 1 - 1
][ ija
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SC values in the second iteration
)3,5()3,2( ,max SCSC
Using a threshold value
of 0.5, combine machines
{1, 4, 6} and {2, 3, 5} intotwo cells, respectively
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SC values in the third iteration
Using a threshold value
of 0.33, combine machines
{2, 3, 5, 7} into one cell
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SC values in the fourth iteration
Using a threshold value
of 0.01, no further combining of cells is posible
A solution with two cells is obtained;
cell 1 consists of machines 1, 4 and 6.
cell 2 consists of machines 2, 3, 5 and 7
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