FlowAnalysis in fluid mechanics presentation

Flow Analysis
• Factors that Affect the Flow Pattern
• Flow Analysis Information
• Flow Patterns
a. Flow within Workstations b. Flow within Departments
c. Flow between Departments
• Flow Planning
• Measuring Flow
• Types of Layout
a. Fixed Location b. Product
c. Group Technology d. Process
e. Hybrid
• Flow Dominance Measure
• Techniques for Machine Cell Formation
a. Row and Column Masking Algorithm
b. Single Linkage Clustering c. Average Linkage clustering

Factors that Affect the Flow Pattern
• Number of parts in each product
• Number of operations on each part
• Sequence of operations in each part
• Number of subassemblies
• Number of units to be produced
• Product versus process type layout
• Desired flexibility
• Locations of service areas
• The building
• . . . .

Flow Analysis Information
• Assembly Chart
• Operations Process Chart
• Flow Process Chart
• Multi-Product Process Chart
• Flow Diagram
• From-To Chart

Assembly Chart
It is an analog model of the assembly
process. Circles with a single link denote
basic components, circles with several
links denote assembly
operations/subassemblies, and squares
represent inspection operations. The
easiest method to constructing an
assembly chart is to begin with the
original product and to trace the product
disassembly back to its basic components.

Operations Process Chart
By superimposing the route sheets and
the assembly chart, a chart results that
gives an overview of the flow within
the facility. This chart is operations
process chart.

Flow Process Chart
This chart uses circles for operations,
arrows for transports, squares for
inspections, triangles for storage, and
the letter D for delays. Vertical lines
connect these symbols in the
sequence they are performed.

Multi-Product Process Chart
This chart is a flow process chart
containing several products.

Flow Diagram
It depicts the probable
movement of materials in the
floor plant. The movement is
represented by a line in the plant
drawing.

From-To Chart
This chart is a matrix that
contains numbers representing a
measure (units, unit loads, etc.)
of the material flow between
machines, departments,
buildings, etc.

Flow Patterns: Flow within Workstations
Motion studies and ergonomics considerations are important in
establishing the flow within workstations. Flow within workstations
should be:
• Simultaneous: coordinated use of hands, arms and feet.
• Symmetrical: coordination of movements about the center of the
body.
• Natural: movements are continuous, curved, and make use of
momentum.
• Rhythmical and Habitual: flow allows a methodological and
automatic sequence of activities. It should reduce mental, eye and
muscle fatigue, and strain.

Flow Patterns: Flow within Departments
• The flow pattern within departments depends on the type of
department.
• In a product and/or product family department, the flow follows the
product flow.
1 machine/operator
1 machine/operator 2 machines/operator
1 machine/operator
More than 2
machines /operator
END-TO-END
BACK-TO-BACK FRONT-TO-FRONT
CIRCULAR
ODD-ANGLE

Flow Pat.: Flow within Departments (cont.)
• In a process department, little flow should occur between workstations
within departments. Flow occurs between workstations and isles.
Aisle
Aisle
Aisle
Dependent on interactions among workstations
available space
size of materials
Uncommon
Aisle
Aisle
One way
One way
PARALLEL PERPENDICULAR DIAGONAL

Flow Pat.: Flow between Departments
• Flow between departments is a criterion often used to evaluate flow
within a facility.
• Flow typically is a combination of the basic horizontal flow patterns
shown below. An important consideration in combining the flow
patterns is the location of the entrance (receiving department) and exit
(shipping department).
Straight
U flow
Serpentine
L flow
S flow
Circular
flow
Simplest. Separate
receiving/shipping
crews
Very popular.
Combine receiving
/shipping. Simple to
administer
When line is too long
Similar to straight.
It is not as long.
Terminate flow.
Near point of origin

Flow within a facility considering the
locations of entrance and exit
At the same location
On adjacent sides

Flow within a facility considering the
locations of entrance and exit (cont.)
On the same side but
at opposite ends
On opposite sides

Vertical Flow Pattern
Flow between buildings exists
and the connection between
buildings is elevated
Ground level ingress (entry)
and egress (exit) are required
Ground level ingress (entry)
and egress (exit) occur on the
same side of the building
Travel between floors occurs on
the same side of the building
Some bucket and belt
conveyors and escalators result
in inclined flow
Backtracking occurs due to the
return to the top floor

Flow Planning
• Planning effective flow involves combining the above patterns with adequate isles
to obtain progressive movements from origin to destination.
• An effective flow can be achieved by maximizing directed flow paths, reducing
flow, and minimizing the costs of flow.
• A directed flow path is an uninterrupted flow path progressing directly from
origin to destination: the figure below illustrates the congestion and undesirable
intersections that may occur when flow paths are interrupted.
Uninterrupted flow paths
Interrupted flow paths

Flow Planning (cont.)
• The reduction of flow can be achieved by work simplification including:
1. Eliminating flow by planning for the delivery of materials, information, or people
directly to the point of ultimate use and eliminate intermediate steps.
2. Minimizing multiple flows by planning for the flow between two consecutive points
of use to take place in as few movements as possible.
3. Combining flows and operations whenever possible by planning for the movement of
materials, information, or people to be combined with a processing step.
• Minimizing the cost of flow can be achieved as follows:
1. Reduction of manual handling by minimizing walking, manual travel distances, and
motions.
2. Elimination of manual handling by mechanizing or automating flow.

Measuring Flow
1. Flow among departments is one of the most important factors in the arrangement of departments
within a facility.
2. Flows may be specified in a quantitative manner or a qualitative manner. Quantitative measures
may include pieces per hour, moves per day, pounds per week. Qualitative measures may range
from an absolute necessity that two departments show be close to each other to a preference that
two departments not being close to each other.
3. In facilities having large volumes of materials, information, a number of people moving between
departments, a quantitative measure of flow will typically be the basis for the arrangement of
departments. On the contrary, in facilities having very little actual movement of materials,
information, and people flowing between departments, but having significant communication
and organizational interrelation, a qualitative measure of flow will typically serve as the basis for
the arrangement of departments.
4. Most often, a facility will have a need for both quantitative and qualitative measures of flow and
both measures should be used.
5. Quantitative flow measure: From-to Chart
Qualitative flow measure: Relationship (REL) Chart

Quantitative Flow Measurement
• A From-to Chart is constructed as follows:
1. List all departments down the row and across the column following the overall
flow pattern.
2. Establish a measure of flow for the facility that accurately indicates equivalent
flow volumes. If the items moved are equivalent with respect to ease of
movement, the number of trips may be recorded in the from-to chart. If the items
moved vary in size, weight, value, risk of damage, shape, and so on, then
equivalent items may be established so that the quantities recorded in the from-to
chart represent the proper relationships among the volumes of movement.
3. Based on the flow paths for the items to be moved and the established measure of
flow, record the flow volumes in the from-to chart.

Example 1
Stores
Turning
Milling
Press
Plate
Assembly
Warehouse
– 6 12 9 1 4 –
– – 3 – 4 – –
– – – – 7 2 –
– – – – 3 1 1
– 1 3 – – 4 3
1 – – – – – 7
– – – – – – –
Stores
Turning
Milling
Press
Plate
Assembly
Warehouse
Stores
Milling
Turning
Press
Plate
Assembly
Warehouse
– 12 6 9 1 4 –
– – – – 7 2 –
– 3 – – 4 – –
– – – – 3 1 1
– 3 1 – – 4 3
1 – – – – – 7
– – – – – – –
Stores
Milling
Turning
Press
Plate
Assembly
Warehouse
From-to Chart
Original Flow Pattern Revised Flow Pattern

Flow Patterns
Store
Turning
Milling
Press
Plate
Assembly
Warehouse
Stores Turning Milling
Warehouse Assembly Plate
Press
Stores Press Plate Assembly
Turning Milling Warehouse
Stores Milling Warehouse
Turning Press Plate Assembly
Straight-line flow U-shaped flow
W-shaped flow
S-shaped flow

Flow Patterns (cont.)
Store
Turning
Milling
Press
Plate
Assembly
Warehouse
Stores Turning Milling
Warehouse Assembly Plate
Press
Stores Press Plate Assembly
Turning Milling Warehouse
Stores Milling Warehouse
Turning Press Plate Assembly
Straight-line flow U-shaped flow
W-shaped flow
S-shaped flow

Qualitative Flow Measurement
• A Relationship (REL) Chart is constructed as follows:
1. List all departments on the relationship chart.
2. Conduct interviews of surveys with persons from each department listed on the
relationship chart and with the management responsible for all departments.
3. Define the criteria for assigning closeness relationships and itemize and record the
criteria as the reasons for relationship values on the relationship chart.
4. Establish the relationship value and the reason for the value for all pairs of
departments.
5. Allow everyone having input to the development of the relationship chart to have
an opportunity to evaluate and discuss changes in the chart.

Relationship Chart
Code Reason
1 Frequency of use high
2 Frequency of use medium
3 Frequency of use low
4 Information flow high
5 Information flow medium
6 Information flow low
Rating Definition
A Absolutely Necessary
E Especially Important
I Important
O Ordinary Closeness OK
U Unimportant
X Undesirable
1. Directors conference
room
2. President
3. Sales department
4. Personnel
5. Plant manager
6. Plant engineering office
7. Production supervisor
8. Controller office
9. Purchasing department
I
1
O
5
U
6
O
5
A
4
I
4
U
6
I
4
I
1
U
6
I
4
O
5
A
4
O
5
O
5
U
3
O
5
O
5
O
5
O
5
E
4
O
2
U
6
O
5
O
5
O
5
U
3
U
6
E
4
O
4
U
3
I
4
I
4
U
3
O
5
U
6

Types of Layout
Volume
High
Medium
Low
Low Medium High Variety
Product
Planning
Department
Fixed Materials
Location
Planning
Department
Process
Planning
Department
Product
Family
Planning
Department
Product
Layout
Fixed Location
Layout
Group Technology
Layout
Process
Layout

Fixed Product Layout
Lathe Press Grind
Weld Assembly
Paint
S
t
o
r
a
g
e
W
a
r
e
h
o
u
s
e

Fixed Product Layout (cont.)
• Advantages
1. Material movement is reduced.
2. Promotes job enlargement by allowing individuals or teams to perform the “whole job”.
3. Continuity of operations and responsibility results from team.
4. Highly flexible; can accommodate changes in product design, product mix, and product volume.
5. Independence of production centers allowing scheduling to achieve minimum total production
time.
• Limitations
1. Increased movement of personnel and equipment.
2. Equipment duplication may occur.
3. Higher skill requirements for personnel.
4. General supervision required.
5. Cumbersome and costly positioning of material and machinery.
6. Low equipment utilization.

Product Layout
Drill Grind Drill
Lathe
Drill
Drill
S
t
o
r
a
g
e
W
a
r
e
h
o
u
s
e
A
s
s
e
m
b
l
y
Lathe
Bend
Lathe
Mill
Press
Drill

Product Layout (cont.)
• Advantages
1. Since the layout corresponds to the sequence of operations, smooth and logical flow lines result.
2. Since the work from one process is fed directly into the next, small in-process inventories result.
3. Total production time per unit is short.
4. Since the machines are located so as to minimize distances between consecutive operations, material
handling is reduced.
5. Little skill is usually required by operators at the production line; hence, training is simple, short, and
inexpensive.
6. Simple production planning control systems are possible.
7. Less space is occupied by work in transit and for temporary storage.
• Limitations
1. A breakdown of one machine may lead to a complete stoppage of the line that follows that machine.
2. Since the layout is determined by the product, a change in product design may require major
alternations in the layout.
3. The “pace” of production is determined by the slowest machine.
4. Supervision is general, rather than specialized.
5. Comparatively high investment is required, as identical machines (a few not fully utilized) are
sometimes distributed along the line.

Process Layout
Lathe Drill Weld
Mill
Drill
Grind
S
t
o
r
a
g
e
W
a
r
e
h
o
u
s
e
Lathe
Lathe
Mill
Mill
Lathe
Mill
Paint
Grind
Assembly
Assembly
Paint
Weld

Process Layout (cont.)
• Advantages
1. Better utilization of machines can result; consequently, fewer machines are required.
2. A high degree of flexibility exists relative to equipment or man power allocation for specific
tasks.
3. Comparatively low investment in machines is required.
4. The diversity of tasks offers a more interesting and satisfying occupation for the operator.
5. Specialized supervision is possible.
• Limitations
1. Since longer flow lines usually exist, material handling is more expensive.
2. Production planning and control systems are more involved.
3. Total production time is usually longer.
4. Comparatively large amounts of in-process inventory result.
5. Space and capital are tied up by work in process.
6. Because of the diversity of the jobs in specialized departments, higher grades of skill are
required.

Group Layout
Drill Grind Assembly
Drill
Weld
Assembly
S
t
o
r
a
g
e
W
a
r
e
h
o
u
s
e
Lathe
Assembly
Grind
Press
Mill
Lathe
Paint
Drill
Drill
Press
Grind
Assembly

Group Layout (cont.)
• Advantages
1. Increased machine utilization.
2. Team attitude and job enlargement tend to occur.
3. Compromise between product layout and process layout, with associated advantages.
4. Supports the use of general purpose equipment.
5. Shorter travel distances and smoother flow lines than for process layout.
• Limitations
1. General supervision required.
2. Higher skill levels required of employees than for product layout.
3. Compromise between product layout and process layout, with associated limitations.
4. Depends on balanced material flow through the cell; otherwise, buffers and work-in-process
storage are required.
5. Lower machine utilization than for process layout.

Hybrid Layout
• Combination of the layouts discussed.
• A sample hybrid layout that has characteristics of group, process and product
layout is shown in the following figure.
• A combination of group layout in manufacturing cells, product layout in assembly
area, and process layout in the general machining and finishing section is used.
TM
TM TM
TM TM
DM
BM

Flow Dominance Measure
• Notations:
M: number of activities.
Nij: number of different types of items moved between activities i and j.
fijk: flow volume between i and j for item k (in moves/time period).
hijk: equivalence factor for moving item k with respect to other items moved
between i and j (dimensionless).
wij: equivalent flow volume specified in from-to chart (in moves/time
period),
w = f h .
ij ijk ijk
k
Nij


1

Flow Dominance Measure (cont.)
• Flow dominance measure = f =
where
f f
f f
U
'
U L


f
w M w
M 1
w
, w =
w
M
f M
M M 1
(M 1)(M 1)
, f M
1
(M 1)(M 1)
'
ij
2 2 2
j 1
M
i 1
M
2
1
2
ij
j 1
M
i 1
M
2
U
2
2 L 2














 


 
 





 
 










1
2
1
2
• fis the coefficient of variation.
• fL and fU are lower and upper bounds on f, respectively (fL  f fU).
• The upper bound fU is only guaranteed to work when each process plan includes all activities.
In this case, 0  f 1.

Flow Dominance Measure (cont.)
Three cases :
1. f  0  a few dominant flows exist.  product layout.
 can use operations process chart as starting point for developing layout and
material handling system design.
 quantitative measures principal source of activity relationship.
2. f  1  many nearly equal flows exist.
 any layout equally good with respect to flows .
 qualitative measures principal source of activity relationship.
3. 0 << f << 1  no dominant flows exist.  difficult to develop layout.
 process or product family layout .
 both quantitative and qualitative measures important source of activity
relationship.

Example 2
• Given three machines (activities) labeled 1, 2 & 3,
Product
A
B
C
Process Plan
1 - 2 - 3
2 - 1
3 - 1 - 2
Quantities/Shift
10
5
15
• Assume Product B is twice as “difficult” to move as A or C  hijB = 2 and hijA = hijC = 1
To
From
1
2
3
1
0
2  5
10
1  15
15
2
110
1  15
25
0
0
3
0
1  10
10
0
Equivalent
Flow Volume
From-To Chart
 w12 = 25,
w21 = 10, etc

Example 2 (cont.)
M = 3 and
f
3 1
6.67
= .352
f 3
3 3 1
(3 1)(3 1)
= 1.984 and f 3
1
(3 1)(3 1)
f
'
2
U
2
2 L 2

    








 
 





 
 





 




( ) ( . )
.
. .
. .
.
25 10 10 15 3 6 67
1
0 75
1 984 1 352
1 984 0 75
0 5122
2 2 2 2 2 2
1
2
1
2
1
2
w =
(25 10 10 15)
3
6.67
2
  

 no dominant flows exist
(likely, since 3 different process plans)

Qualitative Measures
• Closeness values (A, E, I, O, U, X) used to indicate physical proximity
requirements between activities.
• Relationship Chart can only show symmetric relationships, as compared to
From-to Chart (wij  wji possible).
• Relationship Chart is starting point for developing layout when 0 << f  1.
– If f  1, then don’t need to consider flow (only qualitative relationship)
– If f <<1, then one can convert equivalent flow volumes to closeness values so that
material flow relationships can be considered along with qualitative relationship.
– If f  0, then can still convert to relationship chart if significant qualitative
relationship exists, otherwise, just use operations process chart.

Conversion Method
• To convert equivalent flow volumes to closeness values for the example
problem, use wij + wji to make them symmetric.
• Conversion relations :
20 < wij + wji  A w12 + w21 = 25 + 10  A
12 < wij + wji  20  E w13 + w31 = 0 + 15  E
5 < wij + wji  12  I w23 + w32 = 10 + 0  I
0 < wij + wji  5  O
wij + wji = 0  U A
I
E
Machine 1
Machine 2
Machine 3

Group Technology
• Group Technology (GT) is a management philosophy that attempts to group
products with similar design or manufacturing characteristics, or both.
• Cellular Manufacturing (CM) is an application of GT that involves grouping
machines based on the parts manufactured by them.
• The main objective of CM is to identify machine cells and part families
simultaneously, and to allocate part families to machine cells in a way that
minimizes the intercellular movement of parts.
• Potential benefits of CM:
* Setup time reduction. * Improvement in quality.
* Work-in-process (WIP) reduction. * Improvement in material flow.
* Material handling cost reduction. * Improvement in machine utilization.
* Direct/indirect labor cost reduction. * Improvement in space utilization.
* Improvement in employee moral.

Group Technology (cont.)
• A cellular manufacturing system (CMS) designer must consider a number of
constraints:
– Available capacity of machines in each cell cannot be exceeded.
– Safety and technological requirements pertaining to the location of equipment and
processes must be met.
– The size of a cell and the number of cells must not exceed a user-specified value.
• Design analysis begins with a machine-part indicator matrix A = [aij] of size
m×n, where m is the number of machines and n the number of parts.
Typically the matrix consists of 0 and 1 entries:
– aij = 1 indicates that part j is processed by machine i.
– aij = 0 indicates that part j is not processed by machine i.
• Analysis attempt to rearrange the rows and columns of the matrix to get a
block diagonal form as shown in the following example.

Example 3
Initial Machine Part
Processing Matrix
Rearranged Machine-Part
Processing Matrix
P1 P2 P3 P4 P5 P6
M1
M2
M3
M4
M5
M6
M7
1 – – – – –
– 1 – 1 – 1
– 1 – 1 1 –
1 – 1 – – –
– 1 – – – 1
1 – 1 – – –
– – – – 1 1
Part
Machine
P1 P3 P2 P4 P5 P6
M1
M4
M6
M2
M3
M5
M7
1 – – – – –
1 1 – – – –
1 1 – – – –
– – 1 1 – 1
– – 1 1 1 –
– – 1 – – 1
– – – – 1 1
Part
Machine

Row and Column Masking (R&CM) Algorithm
1. Draw a horizontal line through the first row. Select any 1 entry in the matrix
through which there is only one line.
2. If the entry has a horizontal line, go to step 2a. If the entry has a vertical line,
go to step 2b.
2a. Draw a vertical line through the column in which this 1 entry appears. Go to
step 3.
2b. Draw a horizontal line through the row in which this 1 entry appears. Go to
step 3.
3. If there is any 1 entries with only one line through them, select any one and go
to step 2. Repeat until there are no such entries left. Identify the corresponding
machine cell and part family. Go to step 4.
4. Select any row through which there is no line. If there are no such rows, stop.
Otherwise, draw a horizontal line through this row, select any 1 entry in the
matrix through which there is only one line, and go to step 2.

Example 3 Solution
Identification of the First Machine
Cell and Part Family
Identification of the Second Machine
Cell and Part Family
P1 P2 P3 P4 P5 P6
M1
M2
M3
M4
M5
M6
M7
1 – – – – –
– 1 – 1 – 1
– 1 – 1 1 –
1 – 1 – – –
– 1 – – – 1
1 – 1 – – –
– – – – 1 1
Part
Machine
2
3
4
1 5
P1 P2 P3 P4 P5 P6
M1
M2
M3
M4
M5
M6
M7
1 – – – – –
– 1 – 1 – 1
– 1 – 1 1 –
1 – 1 – – –
– 1 – – – 1
1 – 1 – – –
– – – – 1 1
Part
Machine
2
3
4
7
1 5 8 6

Single Linkage (S-Link) Clustering
Algorithm
• S-Link is the simplest of all clustering algorithms based on the similarity
coefficient method.
• The similarity coefficient between two machines is defined as the number of
parts visiting the two machines divided by the number of parts visiting either
of the two machines.
1. pairwise similarity coefficients between machines are calculated and stored in
the similarity matrix.
2. The two most similar machines join to form the first machine cell.
3. The threshold value (the similarity level at which two or more machine cells
join together) is lowered in predetermined steps and all machine/machine cells
with the similarity coefficient greater than the threshold value are grouped into
larger cells.
4. Step 3 is repeated until all machines are grouped into a single machine cell.

Example 4: Initial Machine Part Matrix
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P20 P21 P22
M1
M2
M3
M4
M5
M6
M7
M8
M9
M10
M11
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 – – – –
Part
Machine

Example 4: Initial Similarity Coefficient Matrix
M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11
M1
M2
M3
M4
M5
M6
M7
M8
M9
M10
M11
–
0.08 –
0.00 0.43 –
1.00 0.08 0.00 –
0.80 0.00 0.00 0.80 –
0.00 0.80 0.50 0.00 0.00 –
0.00 0.00 0.10 0.00 0.00 0.00 –
0.00 0.25 0.50 0.00 0.00 0.27 0.45 –
0.00 0.00 0.00 0.00 0.00 0.00 0.83 0.36 –
0.43 0.45 0.23 0.43 0.43 0.36 0.00 0.17 0.00 –
0.00 0.00 0.00 0.00 0.00 0.00 0.57 0.37 0.67 0.00 –
Machine
Machine

Example 4: Dendrogram Based on S-Link
M1 M4 M5 M2 M6 M3 M8 M10 M7 M9 M11
Machine
0.00
0.25
0.50
0.75
1.00
Similarity
Levels

Example 4: Machine Part Groups using S-Link
M5
M1
M4
M10
M2
M6
M3
M8
M7
M9
M11
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
Part
Machine

Average Linkage (A-Link) Clustering Algorithm
• The similarity coefficient between two machine cells is defined as the average
of pairwise similarity coefficients between all members of the two cells.
1. Compute pairwise similarity coefficients between machines and construct the
similarity coefficient matrix.
2. Merge the two most similar machines into a single machine cell.
3. Compute the similarity coefficients between the newly formed machine cell
and the remaining cells. Revise the similarity coefficient matrix.
4. The threshold value (the similarity level at which two or more machine cells
join together) is lowered in predetermined steps and all machine/machine cells
with the similarity coefficient greater than the threshold value are grouped into
larger cells. Repeat steps 3 and 4 until all machines are grouped into a single
machine cell.

Example 4: Revised Similarity Coefficient Matrix I
(M1,M4) (M2,M6) M3 M5 (M7,M9) M8 M10 M11
(M1,M4)
(M2,M6)
M3
M5
(M7,M9)
M8
M10
M11
–
0.04 –
0.00 0.47 –
0.80 0.00 0.00 –
0.00 0.00 0.05 0.00 –
0.00 0.26 0.50 0.00 0.41 –
0.43 0.41 0.23 0.43 0.00 0.17 –
0.00 0.00 0.00 0.00 0.62 0.36 0.00 –
Machine Cell
Machine
Cell

Example 4: Revised Similarity Coefficient Matrix II
(M1,M4 ,M5) (M2,M6) M3 (M7,M9,M11) M8 M10
(M1,M4,M5)
(M2,M6)
M3
(M7,M9,M11)
M8
M10
–
0.02 –
0.00 0.47 –
0.00 0.00 0.03 –
0.00 0.26 0.50 0.39 –
0.43 0.41 0.23 0.00 0.17 –
Machine Cell
Machine
Cell

Example 4: Revised Similarity Coefficient Matrices III & IV
(M1,M4 ,M5) (M2,M6) (M3,M8) (M7,M9,M11)M10
(M1,M4,M5)
(M2,M6)
(M3,M8)
(M7,M9,M11)
M10
–
0.02 –
0.00 0.37 –
0.00 0.00 0.21 –
0.43 0.41 0.20 0.00 –
Machine Cell
Machine
Cell
(M1,M4,M5,M10) (M2,M6, M3,M8) (M7,M9,M11)
(M1,M4,M5,M10)
(M2,M6, M3,M8)
(M7,M9,M11)
–
0.02 –
0.00 0.11 –
Machine Cell
Machine
Cell

Example 4: Dendrogram Based on A-Link
M1 M4 M5 M10 M2 M6 M3 M8 M7 M9 M11
Machine
0.00
0.25
0.50
0.75
1.00
Similarity
Levels

Example 4: Machine Part Groups using A-Link
M5
M1
M4
M10
M2
M6
M3
M8
M7
M9
M11
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
Part
Machine

Comparison
• R&CM is the simplest clustering algorithm.
• A major disadvantage of R&CM is that when the machine part matrix contains one or more
bottleneck machines (machines that belong to more than one cell) or exceptional parts (parts
that are processed in more than one cell), the algorithm may provide a solution with all
machines in a cell and all parts in a corresponding part family.
• The major advantages of S-Link are its simplicity and minimal computational requirement.
In S-Link, once pairwise similarity coefficients are computed and the similarity coefficient
matrix is constructed, the matrix can be used to develop the dendrogram which represents the
machine cells at different threshold values.
• The major drawback of S-Link is the chaining problem. Due to the chaining problem, two
machine cells may join together just because two of their members are similar while the
remaining members may remain far apart in terms of similarity.
• The chaining problem of S-Link can be overcome by using A-Link. Since in A-Link two
machine cells merge based on the overall similarity coefficient between all their members, it
is unlikely that two similar members in two cells cause the cells to merge while other
members are not similar enough. A-Link provides a more reliable solution to the machine
cells formation problem.

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