1 Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne Teerawut Tunnukij Christian...

Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne

1

Teerawut Tunnukij

Christian Hicks


2

Road Map

Facilities layout design

Facilities layout design

Start

GT/CMGT/CM

Clustering methods

Clustering methods

Benefits of GT/CM to facilities layout design

• General problems of clustering methods

• Suitable methods for the solutions

GAsGAs

• Components of GAs• Problems of the classical GAs for solving the cell formation problem

GGAsGGAs

Developed GGA

Developed GGA

General structure & components of the developed GGA

Comparisons & performance

Comparisons & performance

Performance & benefits of the proposed GGA

Goal


3

Select machines for each operation and specify operation sequences

The facilities layout design

Layout DesignLayout Design

Transportation System Design Transportation System Design

Job AssignmentJob Assignment

Cell FormationCell Formation Group machines into cells

Assign cells within plants and machines within cells

Design aisle structure and select material handling equipment


4

Group Technology & Cellular Manufacturing

Clustering Methods

Manufacturing cells

Manufacturing cells

have been used for identifying

Based upon

Group Technology

A philosophy that aims to exploit similarities and achieve efficiencies by grouping.

GT has been applied to manufacturing systems known as Cellular Manufacturing (CM).


5

Manufacturing Layout

Process (Functional) Layout

Process (Functional) Layout Group (Cellular) LayoutGroup (Cellular) Layout

Like resources placed togetherResources to produce like products placed together

T T T

MM M T

M

SG CG CG

SG

D D D

D

T T T CG CG

T T T SG SG

M M D D D

M M D D D

A cluster or cell


7

The benefits of CM

Cellular Manufacturing

Cellular Manufacturing

Main benefits

• Reduced throughput time

• Reduced work in progress

• Improved material flows

Others• Reduced inventory

• Improved use of space

• Improved team work

• Reduced waste

• Increased flexibility

Reduced Manufacturing

Costs


8

Clustering Methods

A large number of clustering methods

have been developed

A large number of clustering methods

have been developed

Part family grouping

Part family grouping

Machine grouping

Machine grouping

Machine-part grouping

Machine-part grouping

Can be classified into

Form part families and then group machines into cells.

Form machine cells based upon similarities in part routing and then allocate parts to cells.

Form part families and machine cells simultaneously.


9

Clustering Methods

Part family groupingPart family grouping Machine groupingMachine grouping

Machine-part groupingMachine-part grouping

Classification & Coding

Similarity coefficient-based Methods

Graph theoretic

Machine-Part incidencematrix-based Methods

• Most of these methods have exploited the machine-part matrix as the initial information to identify potential manufacturing cells.

Mathematical Programming-based Methods

HeuristicMethods

Meta-heuristicMethods


10

A machine-part incidence matrix

1 2 3 4 5 61 1 1 12 1 1 1 13 1 1 14 1 1 1 1

1 3 6 2 4 52 1 1 1 11 1 1 14 1 1 1 13 1 1 1

(a) the original matrix (b) a rearranged matrix into block-diagonal forms

Exceptional elements

Parts Parts

Ma

ch

ine

s

Ma

ch

ine

s


11

General problems of clustering methods

Conventional methods do not always produce a desirable solution.

Conventional methods do not always produce a desirable solution.

There are many ‘exceptional elements’ (machines & parts that cannot be assigned to cells).

There are many ‘exceptional elements’ (machines & parts that cannot be assigned to cells).

The cell formation problem has been shown to be a non-deterministic polynomial (NP) complete problem.

The cell formation problem has been shown to be a non-deterministic polynomial (NP) complete problem.

Meta-heuristic methods

Meta-heuristic methods

• Good methods for the solution

• SA, TS, GAs


12

Genetic Algorithms (GAs)

• GAs are one of the meta-heuristic algorithms. They are stochastic search techniques for approximating optimal solutions within complex search spaces.

• The technique is based upon the mechanics of natural genetics and selection.

• The basic idea derived from an analogy with biological evolution, in which the fitness of individual determines its ability to survive and reproduce, known as ‘the survival of the fittest’.


13

GAs: The main components

GAsGAs

1. Genetic representation1. Genetic representation

2. Method for generating the initial population

2. Method for generating the initial population

3. Evaluation function3. Evaluation function

4. Reproduction selection scheme

4. Reproduction selection scheme

5. Genetic operators5. Genetic operators

6. Mechanism for creating successive generations

6. Mechanism for creating successive generations

7. Stopping Criteria7. Stopping Criteria

8. GA parameter settings8. GA parameter settings


14

GAs: The cell formation problem

• Venugopal and Narendran (1992) were the first researchers to apply GAs to the cell formation problem.

1 2 3 4 5 61 1 2 3 2 1

6 parts (or machines)

Cell number Chromosome:Cell 1: 1,2,6Cell 2: 3,5Cell 3: 4

The general chromosome representation

The general chromosome representation

A potential solution


15

GAs: The problem of the classical GAs

• The standard gene encoding scheme includes significant redundancy when representing a grouping problem (Falkenauer 1998)

A B A C

C A C B

1 2 1 3

3 1 3 2

All chromosomes represent the same solution

All chromosomes represent the same solution

This repetition problem• increases the size of the

search space;• reduces the effectiveness

of the GAs.


16

Grouping Genetic Algorithms (GGAs)

• The GGA, introduced by Falkenauer (1998), is a specialised GA tool that has been adapted to suit and handle the structure of grouping problems.

• The GGA differs from the classical GAs in two important aspects:1. The special gene encoding scheme;2. The special genetic operators.

• De Lit et al. (2000) first applied the GGA to solve the cell formation problem with the fixed maximum cell size.


17

The developed GGA: The general structure

StartEncodeGenes

GeneratePopulation

Population Genetic Operation

Parent 1

Crossover operation

Parent 2

Offspring 1

Offspring 2

Parent 1 Offspring 1

Mutation operation

Chromosome

Repair Process

Check & remove empty cells

Check no. of cells 2≤C≤min(M-1,P-1)

Check & replace duplicate cell no.

Check & relocate unassigned parts

& machines

Evaluate Fitness

Grouping efficacy

Roulette Wheel

Stop

Terminate?

Number of generation

Yes

No

Chromosome selection

Create population for the next generation

Randomly combine genes with a repair process

Integer representing a cell number

Chromosome

Chromosome

Random selection

1 2 3 4

4.1

56

7


24

The analysis of performance

A simple CFP A simple CFP

1 2 3 4 5 6 7 81 1 1 12 1 1 1 1 13 1 1 1 1 14 1 1 15 1 1 1

1 4 7 2 3 5 6 81 1 1 14 1 1 15 1 1 12 1 1 1 1 13 1 1 1 1 1

(a) The 5x8 original matrix

(b) The 5x8 matrix after clustered

-5

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

1 3 5 7 9 11 13 15 17 19

Generation

Fit

nes

s

Best Fitness Avg. Fitness

0.0

0.2

0.4

0.6

0.8

1.0

1 3 5 7 9 11 13 15 17 19

Generation

Fit

nes

s

Best Fitness Avg. Fitness

the performance of the GGA proposed by Yasuda, et al. (2005)

the performance of the developed GGA


25

Data set Size ZODIAC GRAFICS Cheng & others’ GA

CF-GGA Yasuda and others’ GGA

Developed GGA

CR1 24×40 100.00 100.00 100.00 100.00 100.00 100.00

CR2 24×40 85.11 85.11 85.11 85.11 85.11 85.11

CR3 24×40 73.03 NA 73.03 NA 73.03 73.51

CR4 24×40 73.51 73.51 NA 73.29 73.51 73.51

CR5 24×40 20.42 43.27 49.37 48.98 48.98 53.21

CR6 24×40 18.23 44.51 44.67 46.81 45.00 46.04

CR7 24×40 17.61 41.61 42.50 44.14 41.90 43.66

KN1 16×43 53.76 54.39 53.89 53.70 55.43 56.88


Comparisons of five clustering algorithms Comparisons of five clustering algorithms

• CR1-CR7 obtained from Chandrasekharan and Rajagopalan (1989)• KN1 obtained from King and Nakornchai (1982)


26


0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

90.00

100.00

CR1 CR2 CR3 CR4 CR5 CR6 CR7 KN1

ZODIAC

GRAFICS

Cheng & others’ GA

CF-GGA

Yasuda and others’ GGA

Developed GGA

Gro

up

ing

eff

ica

cy


27

Conclusions

• The developed GGA including a repair process was developed for solving the CFP without the predetermination of the No. of manufacturing cells and the No. of machines within the cell.

• The developed GGA was applied to well-known data sets from the literature and was compared to other methods. The results show the developed GGA is effective, performs very well, and outperforms other selected methods in most cases.

• The designed parameter experiment suggests that the large no. of population size have more chance to obtain the better solution, and using the range 0.6-0.7 for probability of crossover and the range 0.2-0.3 for probability of mutation tends to produce the better solution.


28

Further Work

• Develop the proposed GGA to be able to consider important parameters such as operation sequences and others.

• Apply the developed GGA to a data set obtained from a collaborating company.


29


30

References

Aytug, H., Khouja, M. and Vergara, F. E., 2003, Use of genetic algorithms to solve production and operations management problems: A review, International Journal of Production Research, 41(17), 3955-4009.

Brown, E. C. and Sumichrast, R. T., 2001, CF-GGA: A grouping genetic algorithm for the cell formation problem, International Journal of Production Research, 39(16), 3651-3669.

Chandrasekharan, M. P. and Rajagopalan, R., 1989, GROUPABILITY: An analysis of the properties of binary data matrices for group technology, International Journal of Production Research, 27(6), 1035-1052.

Cheng, C. H., Gupta, Y. P., Lee, W. H. and Wong, K. F., 1998, TSP-based heuristic for forming machine groups and part families, International Journal of Production Research, 36(5), 1325-1337.

De Lit, P., Falkenauer, E. and Delchambre, A., 2000, Grouping genetic algorithms: An efficient method to solve the cell formation problem, Mathematics and Computers in Simulation, 51(3-4), 257-271.


31

References

Dimopoulos, C. and Zalzala, A. M. S., 2000, Recent developments in evolutionary computation for manufacturing optimization: Problems, solutions, and comparisons, IEEE Transactions on Evolutionary Computation, 4(2), 93-113.

Falkenauer, E., 1998, Genetic Algorithms and Grouping Problems (New York: John Wiley & Sons).

Gallagher, C. C. and Knight, W. A., 1973, Group Technology (London: Gutterworth).

Gallagher, C. C. and Knight, W. A., 1986, Group Technology Production Methods in Manufacture (New York: Wiley).

Hyer, N. L. and Wemmerlov, U., 1984, Group Technology and Productivity, Harvard Business Review, 62(4), 140-149.

King, J. R. and Nakornchai, V., 1982, Machine-Component Group Formation in Group Technology - Review and Extension, International Journal of Production Research, 20(2), 117-133.

Kumar, C. S. and Chandrasekharan, M. P., 1990, Grouping Efficacy - a Quantitative Criterion for Goodness of Block Diagonal Forms of Binary Matrices in Group Technology, International Journal of Production Research, 28(2), 233-243.


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References

Srinivasan, G. and Narendran, T. T., 1991, GRAFICS. A nonhierarchical clustering algorithm for group technology, International Journal of Production Research, 29(3), 463-478.

Venugopal, V. and Narendran, T. T., 1992, Genetic algorithm approach to the machine-component grouping problem with multiple objectives, Computers & Industrial Engineering, 22(4), 469-480.

Wemmerlov, U. and Hyer, N. L., 1989, Cellular manufacturing in the US industry: a survey of users, International Journal of Production Research, 27(9), 1511-1530.

Wu, Y., 1999, Computer aided design of cellular manufacturing layout, Ph.D. Thesis, School of Engineering and Applied Science, University of Durham.

Yasuda, K., Hu, L. and Yin, Y., 2005, A grouping genetic algorithm for the multi-objective cell formation problem, International Journal of Production Research, 43(4), 829-853.

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