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Cellular manufacturing A time based
analysis to the layout problem
SEMINAR REPORT
Submitted in partial fulfillment of the requirement for the award of the degree of
Master of Technology
in
Industrial Engineering and Management
(Mechanical Engineering)
by
VIPIN N. (Roll No. : M120496ME)
DEPARTMENT OF MECHANICAL ENGINEERING
NATIONAL INSTITUTE OF TECHNOLOGY CALICUT
NIT CAMPUS PO, CALICUT
KERALA, INDIA 673601
APR - 2013
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CERTIFICATE
This is to certify that the report entitled Cellular manufacturing A time based
analysis to the layout problem is a bonafide record of the seminar presented by Vipin N.
(Roll No. : M120496ME), in partial fulfillment of the requirements for the award of degree
in Master of Technology in Mechanical Engineering (Industrial Engineering and
Management) from National Institute of Technology Calicut.
Dr. T. Radha Ramanan
(ME6194 Seminar)
Dept. of Mechanical Engineering
Dr. R. Sridharan
Head of the Department
Dept. of Mechanical Engineering
Place : NIT Calicut
Date : 11-04-2013
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ABSTARCT
A cellular manufacturing system is an application of group technology principles to
production. This involves processing groups of similar components in a dedicated cluster of
dissimilar machines. In this paper, an approach that forms the cluster based on the processing
time is suggested. For even distribution of workload, workload balancing is carried out in the
second phase of the model, i.e., a time-based model. The time-based model is compared with
the workload-based model using a commonality score. The performance of the time-based
model is compared by means of workload deviation and deviation index. The validity of the
approach is tested by application to the problems from the literature and the results are
presented. The results indicate that the time-based model gives better even distribution of
workload as compared to the workload-based model.
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i
CONTENTS
List of symbols ii
List of tables iii
1 Introduction 1
2 Proposed model 5
2.1 Problem representation 5
2.2 Problem statement 5
2.2.1 Grouping criteria of the selected algorithms 5
2.2.2 Data requirements 5
2.3 Methodology 6
2.3.1 Algorithm I 6
2.3.2 Algorithm II 6
2.4 Analysis of the time-based model 12
3 Examples 14
3.1 Workload-based model using commonality 14
3.2 Time-based model for even distribution of workload 17
4 Results, discussion and conclusion 19
References 21
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ii
LIST OF SYMBOLS
Mi machine number
Pj part number
tij processing time of part j in machine i
flexibility factor
Cij commonality score between machines i and j
Tf total time of the cell
Tmax maximum processing time
s number of similar facility
k effective time per facility
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iii
LIST OF TABLES
1. Machine Part matrix 5x7 6
2. Incidence matrix with time values 5x7 7
3. Results of 5x7 matrix using algorithm I 7
4. Machine Part matrix 7x14 14
5. Incidence matrix with time values 7x14 14
6. Results of 7x14 matrix using algorithm I 15
7. Machine Part matrix 5x6 15
8. Incidence matrix with time values 5x6 15
9. Results of 5x6 matrix using algorithm I 15
10. Machine Part matrix 15x10 16
11. Incidence matrix with time values 15x10 16
12. Results of 15x10 matrix using algorithm I 16
13. Input matrix 5x7 10
14. Results of 5x7 matrix using algorithm II 10
15. Input matrix 7x14 17
16. Results of 7x14 matrix using algorithm II 17
17. Input matrix 5x6 17
18. Results of 5x6 matrix using algorithm II 18
19. Input matrix 15x10 18
20. Results of 15x10 matrix using algorithm II 18
21. Detailed test results 19
22. Additional test results 19
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CHAPTER 1
INTRODUCTION
The layout or arrangement of equipments in the work area is an inevitable problem in all
industrial plants. The layout decisions receive intensive attention in production and operations
management. The type of manufacturing systems, either explosive or implosive, the physical
arrangements of machines and equipments, storage area, human work area and other elements
critically affect operating efficiency, system capacity and system flexibility. These factors in turn
continuously affect the operating costs and degree of satisfaction. Group technology is a
manufacturing philosophy whose main idea is to capitalize on similar, recurrent activities. It is a
philosophy with broad applicability, potentially affecting all areas of manufacturing organization.
The idea behind group technology is to decompose a manufacturing system into sub-systems in
order to improve the efficiency of the manufacturing system. One specific application of group
technology is cellular manufacturing systems, which involves processing collections of similar
parts on dedicated clusters of dissimilar machines or manufacturing processes for increasing
productivity.
In the past two decades or so, cellular manufacturing has been emerging as an important
manufacturing concept. It has probably had a greater input on increasing manufacturing
productivity than any other manufacturing concept. Cellular manufacturing is the application of
group technology principles to production parts that have similar processing requirements and/or
geometrical shapes that are classified into part families. The equipment requirements for each part
family are determined subsequently or simultaneously to the identification of part families. The
required equipment may then be moved and grouped into machine cells. These machine cells
consist of groups of functionally dissimilar machine types and are dedicated to the production of
one or more part families.
In addition to the simplification of management control through the creation of smaller sub-
systems, cellular manufacturing also leads to reduced materials handling, reduced set-up time,
reduced work- in-progress, reduced throughout time and improved sequencing and scheduling on
the shop floor. Hence, there exists a substantial interest in cellular manufacturing systems as a
primary source of improving the productivity of manufacturing operations. One of the first
problems encountered in implementing cellular manufacturing is that of cell formation. If thenumber of cells is high, then the size of the cell is reduced, which increases the intercell moves.
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For the past two decades, a number of methods have been developed for machine-part cell
formation. Most of them used the one-zero incidence matrix. The basis for the incidence matrix
was suggested by Burbridge (1963, 1971, 1977, 1982) in his production flow analysis. The
methods have relied on both classification and coding approach and direct analysis of production
process. The objective of the methods is to form clusters that should have the minimum number of
voids (0s inside the diagonal block) and minimum exceptional elements (1s outside the diagonal
block) so that the intercell moves are minimized.
The approach using a similarity coefficient was first suggested by Mc Auley (1972). The
basis of the method is to measure the similarity between each pair of machines and then to group
the machines into families based on their similarity measurements. In most of the cases, the
Jaccard coefficient (Sokal and Sneatch) is used. That is the number of components that visits both
machines divided by the number of components that visits at least one of the machines.
Rajagopalan and Batra (1975) developed group theory, which contains three phases. In the
first phase, preliminary machine groups are formed using the similarity co-efficient. The second
phase uses a graph-partitioning algorithm to merge the machine groups to form cells by
minimizing intercell moves. Finally, components are allocated to the cells by evaluating machine
loads, set-up times and number of machines required in a cell. The main drawback of this approachis the high density of the graph when large numbers of machines are involved.
Seifoddini and Wolfe (1986) improved Mc Auleys (1972) method in three ways. They
added a technique that duplicates the machines to eliminate bottleneck parts. They employed an
average linking cluster analysis and techniques that reduce the amount of data storage required for
their processing. This, however, led to an increase in computational complexity. Vanneli and Ravi
Kumar (1986) proposed a method to find the minimum number of bottleneck cells for grouping
part- machine families and considered a cell formation that integrates the issue of cell formation
and within-cell material flows using the similarity coefficient approach to cluster parts and
machines. But, this approach failed to take into account the issues of number of cells and
duplication. Purcheck (1974) developed a mathematical approach for solving the grouping
problems. The machines and parts can be represented as a path along the edges of a lattice
diagram. The lattice diagram grows exponentially as the set is enlarged and hence its usefulness is
limited.
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The concept of production flow analysis was first introduced by Burbridge (1963, 1971,
1977, 1982). The aim of the technique was to find out the families of machines and parts by a
progressive analysis of the information contained in the route sheet. The Burbridge approach
consists of three levels of analysis. They are factory flow analysis, group analysis and line
analysis. The first stage makes use of the process route number in order to obtain an overall picture
of the present state of material flow. In the next stage, information is obtained by sorting
components into packs and finally a layout in each group is found which give the nearest
approximation to the line flow. Component flow analysis was first used in 1971. McCorrnick et al.
(1972) developed a matrix clustering technique named the bond energy algorithm. This maximizes
the sum of all products of nearest-neighbour elements in the pennuted matrix. First, it finds the
optimal column pennutation and then finds the optimal row pennutation. Clustering is known to be
non-polynominally complete and hence, for large- scale problems, heuristic procedures are widely
used.
King (1980) suggested the rank order clustering method (ROC). This approach sorts rows
(and then columns) of a matrix in descending order of their binary weights. He also suggested a
relaxation procedure that determines the number of duplicate machines required to eliminate the
bottlenecks. The ROC 2 algorithm developed by King and Nakornchai (1982) improves on the
original ROC by applying a quicker sorting procedure. Askin and Subramanian (1987) used a
binary clustering algorithm for grouping parts and machines. They evaluated the configurations
based on fixed and variable machine costs, set-up costs, cycle inventory, work in process inventory
and material handling. Ballakur and Stevdel (1987) proposed a within-cell utilization-based
clustering. In that, machines are assigned to cells based on workload and cell size, and parts are
assigned to cells such that the majority of its operations to be performed are within the cells. This
approach also identifies, whether additional machines are needed due to overloads.
Logendram (1990) developed an approach that is based on workload to minimize the total
intercell and intracell movements. He gave more weightage to the intercell moves for calculating
the workload. He considered the processing time also. Mackulak and Cochran (1993) gave a group
technology classification and clustering algorithms in cellular manufacturing. Delvale et al. (1994)
presented a heuristic workload-based model to form cells by minimizing intercellular movements.
Crama and Oasten (1996) in their paper discussed a few models for machine-part grouping in
cellular manufacturing.
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Most process-oriented techniques use only the information available on the part route
sheets. In this paper, a model for even distribution of workload based on commonality score and
time is suggested. In the suggested model, the clustering of parts is based on the zero-one matrix.
For the time-based algorithm, the input matrix uses the time values instead of 1s. For comparison,
however, random time values are given and according to that part grouping is done. In addition,
workload deviation and deviation index for comparing the solution of two algorithms are also
suggested.
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CHAPTER 2
PROPOSED MODEL
2.1. Problem representation
The problem in cellular manufacturing consists of information from a route card, arranged
in the form of a one-zero matrix. The column of the matrix represents the components and the row
of the matrix represents the machines. This one-zero matrix is also called incidence matrix. A one
(1) entry in row i and column j indicates that part j has an operation scheduled on machine i. A
zero (0) indicates that it does not.
2.2. Problem statement
The most important and primary step in cellular manufacturing is to group parts with
similar design features or processing requirements into families and form associated machines into
machine cells. A number of algorithms have been developed for forming manufacturing cells. The
objective of this work is to form cells that should be of even distribution of workload and compare
the new approach to the selected model. The two algorithms used are
1. a workload-based model (using a commonality score) and
2. a time-based model for even distribution of workload.
2.2.1. Grouping criteria of the selected algorithms
In the first algorithm, the first phase is the formation of machine groups based on the com-
monality score which indicates similarity between the machines. Final grouping of parts is based
on the processing time.
In the second algorithm, the grouping of machines and parts is based on the processing
time by keeping in mind the even distribution of workload. Finally, balancing the workload of the
cells is carried out.
2.2.2. Data requirements
These models use input data associated with common machine cell, part family problems.
Some of the following data are needed to apply the two algorithms suggested in Section 2.2:
(i) total number of machines (Mi) (i = 1,2,...,M) (rows),
(ii) total number of parts (Pj) (j = 1,2,...,N) (columns),
(iii) processing time of the parts (tij),
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(iv) number of cell
(v) flexibility fact
(vi) maximum wor
2.3. Methodology
Random members tha
time values. The zero-one inc
an input to the algorithms. B
based. However, for the algor
2.3.1. Algorithm I
The steps in the workload-
following three stages.
Stage I: Commonality
Compute the similarity coeffi
Where Cij is the commonalit
aik, ajk are machine and part i
parts, respectively.
6
s [C],
r () >[>1],
load deviation (Max WLD).
t are generated by the computer using C-pr
idence matrixes are taken from the literature
asically, both the algorithms used in the pre
thm the workload basis is only for part alloc
ased model (using commonality score) c
ient called commonality score which is defi
score between machines i and j, N is
ncidence matrixes where rows and columns
ogram are used as input
or using randomness as
sent work are workload
ation.
n be grouped into the
ed as
he total number of parts
represent machines and
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Stage II: Linear cell clustering
The various steps involved are:
1. Select the highest commonality score that has not yet been considered in the clustering process.
Assume it is the commonality for machine pair(ij). Three states may exist as given below.
(a). Neither machine i nor machine j has yet been assigned to a machine cell. In such a
case, a new cell is created containing only these two machines.
(b). Machine i has been previously assigned to a cell but j has not. In this case, machine j is
added to the cell that already contains machine i.
(c). Machines i and j are already assigned to the same cell; therefore, this commonality
score is redundant and can be ignored.
2. Repeat the above process till all the machines are allotted to any one of the potential clusters.
Stage III: Assignment phase
The various steps involved are:
1. For each part evaluate its cumulative processing time (in this case number of operations that a
part has in a particular cell).
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2. Assign this part to a cell that contributes to the highest cumulative processing time (in this case
maximum number of operations).
3. Repeat step (2) till all the parts are admitted to any one of the existing potential clusters.
4. Compute the workload deviation and deviation index.
2.3.2. Algorithm II
The time-based model develops clusters of machines and parts into cells according to the
processing time. The objective of this algorithm is to form clusters that should have even
distribution of workloads. For that, selections of time values are in a fashion of maximum and
minimum. Total time of the cell (Tf) should be limited within the maximum processing time (Tmax)
in a cell. The other constraints are number of machines and parts per cell. The following
assumptions are made to form the model:
1. uniform machine utilization in all the cells is preferred,
2. no intercellular movement of parts.
The steps involved are grouped into the following two stages.
Stage I: Cell clustering
The salient steps are:
Step 1: First the possible number of machines and parts to be allotted to a cell is decided. There are
two possibilities:
1. If the total number of machines (M) and parts (N) are an integer multiple of the number of
machines and parts in a cell, then all F cells in the system will have the same number of
machines and parts.
2. If not, the first (F-1) cells will have a certain configuration and the Fth cell is of different
configuration.
For the first (F-1) cells, m is the M/F (fractional part to be truncated), n the N/F (fractional part to
be truncated) where F is the total number of cells, m the number of machines in the first (F- 1)
cells and n the number of parts in the first (F-1) cells.
For the Fth cell,
m'= M[(F 1)m],
n' = N[(F 1)n],
where m is the number of machines in the Fth cell and n the number of parts in the Fth cell.
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Step 2: The total processing time of the jobs in the system is
Where tij is the processing time of job j on machine i
Step 3: To avoid maximum variability in the total processing time of the parts in all cells. The total
processing time of the jobs in a cell = T/F:
Tmax = (T/F)(> 1),
where Tmax is the total processing time in a cell.
The larger the values of the flexibility factor (), the more the flexibility in allocating the
operations. The value of a nearer to 1 is preferred.
Step 4:
1. Select the maximum processing time element from the input matrix. Allocate the part and
machine which corresponds to that element to the cell.
2. Check if the machine is previously allocated to that cluster, then count it column = column
+ 1, otherwise row = row+1.
3. Check whether the row count is equal to m or the column count is equal to n; then stop the
allocation to this cluster.
Step 5: Form an array (S1) which contains the time element belonging to the processing times of
the allocated (in previous step) parts in various machines and the time elements belonging to the
parts which need processing in the allocated machine except the selected time element.
Step 6: Check whether the total processing of the allocated parts in the cluster exceeds Tmax; if so,
stop the allocation to this cluster.
Step 7: Combine the arrays previously formed and the total array (initially the total array is a null
array). Select the minimum processing time elements from the array and allocate the part and the
machine to the cell.
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Step 8:
1. If the machine just allocated is equal to the machine which is already present in the cell,
then count column = column+1, otherwise row = row+1.
2. Check whether the row count is equal to m or the column count is equal to n ; then
stop the allocation to this cluster.
Step 9:
(i) For the minimum time element, the presence of time elements which are in the machine number
(row) and in the part number (column) except the allocated time element are selected and form an
array S2.
(ii) Combine the arrays, array (S2) and already formed array (S1) in step 7. This is the total array.
Step 10: Check whether the total processing time in the cluster exceeds or is equal to Tmax then
stop allocation to this cell, otherwise select the minimum time element from the total array and
allocate the corresponding machine and part to the cluster.
Step 11: Form an array (S1) that contains the time elements which are in the machine number
(row) and in the part number (column) that is assigned in step 10 except the selected time element.
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Step 12:
1. If the machine just allocated to the cluster is equal to the machine already present in the
cluster, then count column = column+ 1, otherwise row = row+ 1.
2. Check whether the count of column is equal to n and the count of row is equal to m;
then stop the allocation to this cluster, otherwise go to step 7.
Step 13:
For every allocation of machine and part, the processing times are counted. This is the
effective processing time of that cell. Check whether allocations for the first (F- 1) cells are over;
then allocation is to be done for the final cell. Otherwise repeat from step 4 by initializing the
counts.
Step 14: For the final cell, the unallocated machines and parts to the first (F-1) cells are allocated
to the final cell. The processing timings are counted.
Stage II: Balancing of workload
If alternative preferences of maximum and minimum time elements are not considered,
then there are chances for the first cell to be complete with very few operations with very high
elements. Therefore, in order to achieve uniform machine loading, alternate preferences for
maximum and minimum time elements are considered, i.e., machine duplication is carried out to
balance the workload.
In this phase, the degree of workload deviation in the system is reduced within the permissible
Max. WLD. This is done by means of increasing the number of facilities (manpower as well as
number of similar machines) to the particular cell as per the following steps:
1. (i)
(ii) Set i = 1.
2. (i) Number of similar facility (s) = i (teff/tmin) (truncate fractional part).
(ii) Effective time per facility (k) = i(teff/s).
3. Check whether workload deviation
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If the condition is not satisfied, count ii +1 and repeat step 2, otherwise repeat the steps
for other cells.
4. Finally calculate deviation index (DI) and workload deviation (WLD) for the balanced cell.
2.4. Analysis of the time-based model
This model forms clusters, taking workload distribution as a primary objective. The
machine parts are grouped into families according to the processing times. Each one of the
machine groups are dedicated to any one of the part families.
The number of manufacturing cells to be formed depends upon the total cost incurred. The
total cost includes set-up cost, cost associated with bottleneck operation and material handling
cost. Management should take a decision regarding the number of cells. The decision should
optimize the set-up cost with material handling cost and bottleneck operation cost.
The size of the cell is the next criterion. In the first phase, the model considers that there isno possibility of duplicating the machines, and bottleneck operations are carried out by outsiders.
The maximum number of machines and parts are limited by values [M/F and N/F]. The size of the
cell is determined by this (M/F) factor and the availability. The performance of cell formation is
measured by workload deviation and deviation index. These figures should be as low as possible in
order to attain even distribution of workload. The other factor to limit the size of the cell is the
maximum time Tmax (T/F)a to a cell.
The second phase minimizes the workload of each cell within the maximum allowable limit
(i.e., Max. WLD), which is given by the components. For this purpose, an increase in the number
of facilities (machines as well as parts) is carried out. Therefore, cell formation is done by taking
number of machines per number of parts per cell, maximum allowable time to a cell and maximum
workload deviation as limiting factors.
The result from the first phase is improved in the second phase. Moreover, machines and
parts are split evenly. For all the test problems, the percentage to be considered for Max. WLD and
flexibility factor is 20%.
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The concept of line balancing is applicable to manufacturing cells. It is important that
utilization of the expensive machine is high, even if it means that utilization of the other machines
in the cell is relatively low. On the other hand, workload is to be evenly spread among the
machines in the cells as much as possible. The expensive machine is referred to as the key
machine . The other machines are referred to as supporting machines.
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CHAPTER 3
EXAMPLES
In this section, four examples from the literature [2] are considered to illustrate the
implementation and comparison of the suggested algorithms. Four examples are given in the form
of a simple zero-one machine-part matrix. First, the problems are analyzed using a workload-based
model using commonality and then the same problems are analyzed using a time-based model for
even distribution of workload.
3.1. Workload-based model using commonality
The examples considered are of 5 x 7 machine- part, 7 x 14 machine-part, 5 x 6 machine-
part and 15 x 10 machine-part problems. Tables 1, 4, 7 and 10 shows a 5 x 7, 7 x 14, 5 x 6 and 15 x
10 machine-part matrix, respectively, and Tables 2, 5, 8 and 11 give the respective incidence
matrix with time values. Suggested machine grouping and part grouping in various cell numbers as
well as the total processing time for each cell, workload deviation and deviation index have also
been calculated and are shown in Tables 3, 6, 9 and 12.
Example 1: 5 x 7 machine-part problem.
Example 2: 7 x 14 machine-part problem (Tables 4-6).
Example 3: 5 x 6 machine-part problem (Tables 7-9).
Example 4: 15 x 10 machine-part problem (Tables 10-12).
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3.2. Time-based model for even distribution of workload
The four example problems considered in Section 3.1 are solved using algorithm II
described in Section 2.3.2. The flexibility and maximum workload are uniformly considered as 20
for all the problems. Tables 13, 15, 17 and 19 show the input matrix for 5 x 7, 7 x 14, 5 x 6 and 15
x 10 machine-part problems, respectively, and Tables 14, 16, 18 and 20 show the respective results
of cell formation.
Example 1: 5 x 7 machine-part problem.
Example 2: 7 x 14 machine-part problem (Tables 15 and 16).
Example 3: 5 x 6 machine-part problem (Tables 17 and 18).
Example 4: 15 x 10 machine-part problem (Tables 19 and 20).
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CHAPTER 4
RESULTS, DISCUSSION AND CONCLUSION
The time-based model and the workload- based model (using commonality score) are
tested for the example problems. These problems are taken from the literature and also by
generating the matrix through the random number method. The results are tabulated in Table 21.
The results indicate that the time-based model for even distribution of workload gives better results
than the workload- based model (using commonality score). The minimum value of workload
deviation and deviation index indicates the good performance of the cell formation procedure.
For additional computational experience on the two algorithms (workload-based model and
time- based model), four more problems are solved. Table 22 shows individual problem sizes, the
number of cells and additional test results.
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The time-based model forms cells with a distributed workload as evenly as possible, for
jobs with operation times. The first phase of the two-phase clustering methodology proposed forms
machine-part clusters such that the workload is distributed as uniformly as possible. The second
phase improves the uniformity in the line loading. The second phase considers the maximum
workload deviation specified by the management.
The results show the performance measures such as percentage of workload deviation and
deviation index for different problems solved using the two algorithms. In the tables, we observe
that the performance of the time-based model is best.
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