Genetic Algorithms in Manufacturing
6.9 A Case Study
6.9.2 Machine Grouping
The next step in the cell formation process is to group machines into a diagonal MCS matrix using genetic algorithm as previously discussed. The objective here is to maximize the MCS coefficients of adjacent machines. The simulation result for the genetic algorithm can be seen in Figure 6.9, and the corresponding diagonal MCS matrix is shown in Table 6.8.
3 14 7 3 15 2 15 100 1 12 10 5 9
TABLE 6.6 The Best Alternat ive Routing s for Ea ch Par t Part No.
FIGURE 6.8 The GA simulat ion to find parts’ optimum process routing s.
FIGURE 6.9 The GA simulat ion for machine grouping . 0
20 40 60 80
1 11 21 31 41 51
Generation No.
Max Min Average
Diagonalization of MCS matrix
4 6 8 10 12
1 11 21 31 41 51
Generation No.
Fitness
Max Min Average
summarized in Table 6.10.
6.9.4 Layout Design
Figure 6.11 shows the factory site for positioning the 17 machines in this case study. The site has been divided into 24 positions to cater to compulsory and economic machine duplications. In this case, there is no need for compulsory machine duplication, and the layout of the 17 machines can be optimized using the genetic algorithm previously described. The resultant layout is shown in Figure 6.12. This result has been achieved after 155 generations using a population size of 120. The material handling cost for this layout is $12,765 per year.
The next step is to consider machine duplication in order to minimize the number of intercellular movements (economic machine duplication). Table 6.11 indicates the number of intercellular movements due to each bottleneck machine. It can be seen from this table that machine 13 creates the most number of intercellular movements. Therefore, this should be the first machine to be considered for duplication in cell 4. There is now a total of 18 machines (instead of 17 machines), and the layout for these 18 machines needs to be optimized again, using the same GA as in the case of 17 machines. Figure 6.13 shows the layout for 18 machines. The difference in material handling cost between this layout and the previous layout is $1845 per year, which is $580 more than duplication cost of machine 13. As a result, the duplication of machine 13 is justified. Next, machine 4 is selected to be duplicated in cell 3, resulting in a total of 19 machines. The genetic algorithm is run again, and the optimum layout for these 19 machines is shown in Figure 6.14. The difference in material handling cost between this layout and the previous layout (for 18 machines) is $956, which is $193 less than the duplication cost of machine 4. As a result, this duplication is not economically justified. For the same reason, machines 11 and 8 cannot be economically duplicated. Therefore, the final layout design is as indicated in Figure 6.13, with a total of 18 machines.
6.10 Conclusion
This chapter has presented an integrated methodology cellular manufacturing system design that covers both the cell formation process and cellular layout. The methodology is based on a new concept of similarity coefficients, and the use of genetic algorithms as an optimization tool. In comparison with previous works, this methodology takes into account in the design process all relevant production data such process routings and production volumes of parts. The issue of the interaction between layout procedure and machine duplication to justify economic machine duplications is also addressed.
The GA-based optimization tool used in this work is not only robust and able to handle large-scale problems, but also parallel in nature, and hence can reduce computational time significantly. Another advantage of the genetic algorithm is that it is independent of the objective function and the number constraints.
Defining Terms
Bottleneck machine: A machine that is required by parts from different part families.
Clustering procedure: A procedure for clustering machines into machine groups and parts into part families.
Exceptional element: A part that needs one or more machines from different cells in its process routing.
Intercell layout: Arrangement of machines for the whole cellular manufacturing system, which may include many machine cells.
Intracell layout: Arrangement of machines within a cell.
3 0 0.194 1 0.004 0 0.009 0.194 0 0 0.009 0.03 0.009 0.032 0.189 0.194 0 0
4 0.004 0.01 0.004 1 0.094 0.057 0.01 0.094 0.004 0.057 0.053 0.057 0.057 0.029 0.01 0.076 0.004
5 0.004 0 0 0.094 1 0.01 0 0.094 0.004 0.01 0.006 0.01 0.01 0 0 0.076 0.004
6 0 0.015 0.009 0.057 0.01 1 0.015 0.01 0 0.199 0.212 0.235 0.218 0.036 0.015 0.01 0
7 0 0.244 0.194 0.01 0 0.015 1 0 0 0.015 0.036 0.015 0.038 0.225 0.244 0 0
8 0.016 0 0 0.094 0.094 0.01 0 1 0.016 0.01 0.006 0.01 0.01 0 0 0.076 0.016
9 0.073 0 0 0.004 0.004 0 0 0.016 1 0 0 0 0 0 0 0.004 0.073
10 0 0.015 0.009 0.057 0.01 0.199 0.015 0.01 0 1 0.19 0.199 0.195 0.36 0.015 0.01 0
11 0 0.036 0.03 0.053 0.006 0.212 0.036 0.006 0 0.19 1 0.212 0.225 0.058 0.036 0.006 0
12 0 0.015 0.009 0.057 0.01 0.235 0.015 0.01 0 0.199 0.212 1 0.218 0.036 0.015 0.01 0
13 0 0.038 0.032 0.057 0.01 0.218 0.038 0.01 0 0.195 0.225 0.218 1 0.06 0.038 0.01 0
14 0 0.225 0.189 0.029 0 0.036 0.225 0 0 0.036 0.058 0.036 0.06 1 0.225 0 0
15 0 0.244 0.194 0.01 0 0.015 0.244 0 0 0.015 0.036 0.015 0.038 0.225 1 0 0
16 0.004 0 0 0.076 0.076 0.01 0 0.076 0.004 0.01 0.006 0.01 0.01 0 0 1 0.004
17 0.073 0 0 0.004 0.004 0 0 0.016 0.073 0 0 0 0 0 0 0.004 1
©2001 CRC Press LLC
1 0.0727 0.0727 1 0.0041 0.0165 0.0041 0.0041
16 0.0041 0.0041 0.0041 1 0.0759 0.0759 0.0759 0.0103 0.0103 0.0103 0.0103 0.0057 8 0.0165 0.0165 0.0165 0.0759 1 0.0938 0.0938 0.0103 0.0103 0.0103 0.0103 0.0057 5 0.0041 0.0041 0.0041 0.0759 0.0938 1 0.0938 0.0103 0.0103 0.0103 0.0103 0.0057
4 0.0041 0.0041 0.0041 0.0759 0.0938 0.0938 1 0.0572 0.0572 0.0572 0.0572 0.0526 0.029 0.0103 0.0103 0.0103 0.0043
10 0.0103 0.0103 0.0103 0.0572 1 0.1992 0.1992 0.1951 0.1901 0.0364 0.0146 0.0146 0.0146 0.0087
12 0.0103 0.0103 0.0103 0.0572 0.1992 1 0.2349 0.2184 0.212 0.0364 0.0146 0.0146 0.0146 0.0087
6 0.0103 0.0103 0.0103 0.0572 0.1992 0.2349 1 0.2184 0.212 0.0364 0.0146 0.0146 0.0146 0.0087
13 0.0103 0.0103 0.0103 0.0572 0.1951 0.2184 0.2184 1 0.2253 0.0602 0.0384 0.0384 0.0384 0.0325
11 0.0057 0.0057 0.0057 0.0526 0.1901 0.212 0.212 0.2253 1 0.0581 0.0364 0.0364 0.0364 0.0304
14 0.029 0.0364 0.0364 0.0364 0.0602 0.0581 1 0.2246 0.2246 0.2246 0.1892
15 0.0103 0.0146 0.0146 0.0146 0.0384 0.0364 0.2246 1 0.2438 0.2438 0.194
2 0.0103 0.0146 0.0146 0.0146 0.0384 0.0364 0.2246 0.2438 1 0.2438 0.194
7 0.0103 0.0146 0.0146 0.0146 0.0384 0.0364 0.2246 0.2438 0.2438 1 0.194
3 0.0043 0.0087 0.0087 0.0087 0.0325 0.0304 0.1892 0.194 0.194 0.194 1
©2001 CRC Press LLC
1 180 200 240 200 180
16 80 115 240 200
8 180 160 130 230 240 100
5 160 260 230 120 100
4 80 130 115 120 200 125 100
10 90 90 105 110 130 125 100 95
12 180 180 95 100 210 220 260 250 200 190
6 180 180 190 200 210 220 260 250 200 190
13 180 180 190 200 210 220 260 250 200 190 260
11 90 90 95 100 105 110 130 250 95 95
14 190 110 130 110 130 105 105 100 100 95
15 220 260 220 260 210 210 200 200 190 105
2 110 130 110 130 105 105 100 100 190 210
7 220 260 220 260 210 210 200 200 190 105
3 220 260 210 210 200 200 190 210
©2001 CRC Press LLC
4 17,1,9 25,20,12,23,3
FIGURE 6.10 The GA simulat ion for maximizing a djacent par ts’ similar ity in the machine–par t matrix.
FIGURE 6.11 The site of a factory divided into 24 positions of equal siz e.
maximizing adjacent parts' similarity in machine-component matrix
7000 9000 11000 13000 15000 17000
1 11 21 31 41 51 61 71
Generation No.
Fitness value
Max Min Average
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FIGURE 6.12 The first layout design with no machine duplicat ion.
FIGURE 6.13 The layout for 18 machines, after the duplicat ion of machine 13 in cell 4.
FIGURE 6.14 The new layout after duplicat ion of machine 4 in cell 3, giving a t otal of 19 machines.
TABLE 6.11 Number of Intercellular M ovements Created by the Bottleneck Machines
Machine no. 8 4 13 11
From cell no. 2 2 3 3
Duplicated in cell no. 1 3 4 4
For part no. 25 5,14 6 17
Number of intercellular movements 180 225 260 95
17 1 9 10
14 15 2 12 13
7 3 5 4 11 6
13 8 16
17 1 9 10 13
14 15 2 12 6
7 3 5 4 11 4
13 8 16
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For Further Information
A more complete discussion on genetic algorithms, including extensions and related topics, can be found in The Handbook of Genetic Algorithms by L. Davis, Van Nostrand Reinhold, New York, 1991 and Genetic Algorithms + Data Structure = Evolution Programs by Z. Michalewicz, Springer-Verlag, New York, 1994.
The International Journal of Production Research frequently publishes articles on advances in cellular manufacturing systems.