Cellular manufacturing – A time based analysis to the layout problem (Seminar report)

7/27/2019 Cellular manufacturing A time based analysis to the layout problem (Seminar report)

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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










13. Input matrix 5x7 10

14. Results of 5x7 matrix using algorithm II 10







21. Detailed test results 19

22. Additional test results 19


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1

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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2

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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3

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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4

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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5

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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7

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).




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15


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16


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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).




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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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REFERENCES

[1] Surjit Angra, Rakesh Sehgal, Z. Samsudeen Noori, 2008. Cellular manufacturing-A time

based analysis to the layout problem. Int. J. Production Economics 112, 427438

[2] Das, K., Lashkari, R.S., Sengupta, S., 2007. Reliability consideration in the design and

analysis of cellular manufacturing systems. International Journal of Production Economics

105, 243262.

[3] Burbridge, J.L., 1963. Production flow analysis. Journal of Institution of Production

Engineers, London 42, 742-748.

[4] Defersha, F.M., Mingyuan, C., 2006. A comprehensive mathematical model for the design

of cellular manufacturing systems. International Journal of Production Economics 103,

767-783.

[5] Yin, Y., Yasuda, K., 2006. Similarity coefficient methods applied to the cell formation

problem: A taxonomy and review. International Journal of Production Economics 101,

329-352.

Documents

Cellular manufacturing – A time based analysis to the layout problem (Seminar report)