group technology and

8/11/2019 Group Technology And

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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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(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


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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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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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:


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:


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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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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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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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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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


of 0.33, combine machines

{2, 3, 5, 7} into one cell


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SC values in the fourth iteration


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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