CELLULAR MANUFACTURING

Definition

Objectives of Cellular Manufacturing

To reduce WIP inventory To shorten manufacturing lead times To simplify production scheduling To reduce set-up times To provide minimum work part

handling To reduce process variation

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Step 1: Assign binary weight and calculate a decimal weight for each row and column using the following formulas:

Decimal we

Decimal we bpjn p

ight for row i = b

ight for column j =

ipm-p

p=1

m

p=1

n

2

2

n is the total number of rows

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Step 2: Rank the rows in order of decreasing decimal weight values.

Step 3: Repeat steps 1 and 2 for each column.

Step 4: Continue preceding steps until there is no change in the position of each element in the row and the column.

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EXAMPLE:Consider a problem of 5 machines and 10 parts. Try to group them by using Rank Order Clustering Algorithm.

Machines 1 2 3 4 5 6 7 8 9 10

M1 1 1 1 1 1 1 1 1 1

M2 1 1 1 1 1

M3 1 1 1 1

M4 1 1 1 1 1 1

M5 1 1 1 1 1 1 1 1

Components

Table 1

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Machines 1 2 3 4 5 6 7 8 9 10 Decimalequivalent

M1 1 1 1 1 1 1 1 1 1 1007

M2 1 1 1 1 1 451

M3 1 1 1 1 568

M4 1 1 1 1 1 1 455

M5 1 1 1 1 1 1 1 1 1020

29 28 27 26 25 24 23 22 21 20

Binary weight

Components

Table 2

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Binaryweight

Machines 1 2 3 4 5 6 7 8 9 10

24 M5 1 1 1 1 1 1 1 1

23 M1 1 1 1 1 1 1 1 1 1

22 M3 1 1 1 1

21 M4 1 1 1 1 1 1

20 M2 1 1 1 1 1Decimalequivalent 28 27 27 27 28 20 28 26 11 11

29 28 27 26 25 24 23 22 21 20

Binary weight

Components

Table 3

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Binaryweight

Machines 1 5 7 2 3 4 8 6 9 10 Decimalequivalent

24 M5 1 1 1 1 1 1 1 1 1020

23 M1 1 1 1 1 1 1 1 1 1 1019

22 M3 1 1 1 1 900

21 M4 1 1 1 1 1 1 123

20 M2 1 1 1 1 1 115Decimalequivalent 28 28 28 27 27 27 26 20 11 11

29 28 27 26 25 24 23 22 21 20

Binary weight

Components

Table 4

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Similarity Coefficient-Based Approaches

In similarity coefficient methods, the basis is to define a measure of similarity between machines, tools, design features, and so forth and then use it to form part families and machine groups.

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Single-Linkage Cluster Analysis (SLCA):

It is a hierarchical machine grouping method known as single-linkage cluster analysis using similarity coefficients between machines.

The procedure is to construct a tree called a dendrogram.

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The similarity coefficient between two machines is defined as the ratio of the number of parts visiting both machines and the number of parts visiting one of the two machines:

S =

+ Z - Xij

k=1

N

jk ijk

X

Y

ijk

ik

k

N

( )1

where: Xijk = operation on part k performed both on machine i and j,

Yik = operation on part k performed on machine i,Zjk = operation on part k performed on machine j.

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SLCA ALGORITHMS

It helps in constructing dendrograms.

A dendrogram is a pictorial representation of bonds of similarity between machines as measured by the similarity coefficients.

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The steps of algorithm are as follows:

Step 1: Compute similarity coefficients for all possible pairs of machines,

Step 2: Select the two most similar machines to form the first machine cell,

Step 3: Lower the similarity level (threshold) and form new machine cells by including all the machines with similarity coefficients not less than the threshold value,

Step 4: Continue step 3 until all machines are grouped into a single cell.

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EXAMPLE:Consider the matrix of 5 machines and 10 components given below.

Machines 1 2 3 4 5 6 7 8 9 10

M1 1 1 1 1 1 1 1 1 1

M2 1 1 1 1 1

M3 1 1 1 1

M4 1 1 1 1 1 1

M5 1 1 1 1 1 1 1 1

Components

Develop a denrogram and discuss the resulting cell structures.

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Step 1: Determine similarity coefficients between all pairs of machines.

SC = 59 +5-5

= 0.556 12

Machinepairs

M1M2

M1M3

M1M4

M1M5

M2M3

M2M4

M2M5

M3M4

M3M5

M4M5

SC 0.55 0.30 0.67 0.70 0.00 0.83 0.30 0.00 0.50 0.40

Similarity coefficients of machine pairs

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Step 2: Select machines M2 and M4, having the highest similarity coefficients of 0.83 to form the first cell.

Step 3: The next lower coefficient of similarity is between machines M1 and

M5. Use these machines to form the second cell.

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Step 4: The next lower coefficient of similarity is now 0.67 between machines M1 and M4. At this threshold value machines M1, M2, M4, and M5 will form one machine group. The other possible groups will be evaluated by the same way.

0.00

0.50

0.670.70

0.83

M4 M1M2 M3M5

Dendrogram