Abstract
There has been extensive scheduling research relating to use of existing dispatching rules along with/without new dispatching rules and compared their performance behavior in job-shop, flow-shop, open-shop, flexible manufacturing system, and single machine with unit capacity environments using various scheduling objectives. However, it appears that there is no comparative study on analysis of dispatching rules for scheduling bottleneck batch processing machine in discrete parts manufacturing, particularly the diffusion furnace (DF) in semiconductor manufacturing (SM). This study addresses this research issue. For that, this study first, proposes the mathematical models for dynamic scheduling (DS) of DF to optimize the due-date based scheduling objectives: Total weighted tardiness, on-time delivery rate, total earliness/lateness, and maximum lateness. Due to the computational intractability of each the proposed mathematical models for large-scale problem, this study proposes greedy heuristic algorithm (GHA) based on due-date based dispatching rules (DDR). Because, dispatching rules are widely used in the SM industry. Accordingly, in this study twenty variants of GHA-DDR are proposed by considering various due-date based dispatching rules to compare the effects of due-date based dispatching rules in DS of DF. From the series of computational analysis carried out in this study, it is observed empirically that the proposed variants of GHA based on apparent tardiness cost (ATC) and batch ATC (BATC) dispatching rules yield consistently better solution for most of the scheduling objectives considered in this study. This observation is further verified by statistical analysis: Friedman test and Nemenyi multiple comparison test.
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Appendices
Appendix 1: A LINGO set code for the proposed mathematical model for DS-DF to minimize TWT
Appendix 2: Performance analysis of each of the twenty proposed variants of GHA-DDR in comparison with optimal TWT based on Relative Percentage Deviation (RPD)
Problem instances | Optimal TWT | RPD of each of the proposed variants of GHA-DDR in comparison with optimal TWT | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
GHA-DDR1 | GHA-DDR2 | GHA-DDR3 | GHA-DDR4 | GHA-DDR5 | GHA-DDR6 | GHA-DDR7 | GHA-DDR8 | GHA-DDR9 | GHA-DDR10 | ||
1 | 111 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 68.47 | 68.47 | 0.00 |
2 | 111 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 68.47 | 68.47 | 0.00 |
3 | 222 | 16.22 | 16.22 | 16.22 | 16.22 | 16.22 | 16.22 | 16.22 | 0.00 | 0.00 | 16.22 |
4 | 311 | 3.54 | 3.54 | 3.54 | 3.54 | 3.54 | 3.54 | 3.54 | 43.41 | 43.41 | 3.54 |
5 | 461 | 34.06 | 49.89 | 49.89 | 49.89 | 34.06 | 34.06 | 27.55 | 29.28 | 32.75 | 34.06 |
6 | 112 | 308.93 | 308.93 | 308.93 | 308.93 | 308.93 | 308.93 | 308.93 | 308.93 | 308.93 | 308.93 |
7 | 247 | 78.14 | 78.14 | 78.14 | 78.14 | 78.14 | 78.14 | 78.14 | 47.37 | 47.37 | 78.14 |
8 | 325 | 18.77 | 18.77 | 18.77 | 18.77 | 18.77 | 18.77 | 18.77 | 11.08 | 11.08 | 18.77 |
9 | 200 | 11.00 | 28.50 | 28.50 | 28.50 | 11.00 | 11.00 | 63.50 | 11.00 | 11.00 | 11.00 |
10 | 182 | 6.59 | 6.59 | 6.59 | 6.59 | 6.59 | 6.59 | 6.59 | 6.59 | 6.59 | 6.59 |
11 | 120 | 83.33 | 83.33 | 83.33 | 83.33 | 83.33 | 83.33 | 83.33 | 83.33 | 83.33 | 83.33 |
12 | 429 | 77.62 | 77.62 | 77.62 | 77.62 | 77.62 | 77.62 | 77.16 | 80.19 | 80.19 | 77.62 |
13 | 76 | 125.00 | 125.00 | 125.00 | 125.00 | 125.00 | 125.00 | 125.00 | 92.11 | 92.11 | 125.00 |
14 | 56 | 225.00 | 225.00 | 225.00 | 225.00 | 225.00 | 225.00 | 225.00 | 225.00 | 225.00 | 225.00 |
15 | 120 | 91.67 | 91.67 | 91.67 | 91.67 | 91.67 | 91.67 | 91.67 | 91.67 | 91.67 | 91.67 |
Problem instances | RPD of each of the proposed variants of GHA-DDR in comparison with optimal TWT | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
GHA-DDR11 | GHA-DDR12 | GHA-DDR13 | GHA-DDR14 | GHA-DDR15 | GHA-DDR16 | GHA-DDR17 | GHA-DDR18 | GHA-DDR19 | GHA-DDR20 | |
1 | 0.00 | 0.00 | 0.00 | 8.11 | 9.91 | 9.91 | 9.91 | 9.91 | 9.91 | 109.01 |
2 | 0.00 | 0.00 | 0.00 | 236.94 | 9.91 | 15.32 | 15.32 | 15.32 | 15.32 | 15.32 |
3 | 16.22 | 16.22 | 16.22 | 5.86 | 8.11 | 10.81 | 10.81 | 10.81 | 10.81 | 27.03 |
4 | 3.54 | 3.54 | 3.54 | 47.59 | 5.79 | 13.50 | 13.50 | 13.50 | 13.50 | 31.83 |
5 | 34.06 | 34.06 | 34.06 | 34.06 | 36.23 | 36.23 | 36.23 | 36.23 | 36.23 | 48.59 |
6 | 308.93 | 308.93 | 308.93 | 192.86 | 12.50 | 12.50 | 12.50 | 12.50 | 12.50 | 30.36 |
7 | 78.14 | 78.14 | 78.14 | 47.37 | 23.08 | 23.08 | 23.08 | 23.08 | 23.08 | 23.08 |
8 | 18.77 | 18.77 | 18.77 | 4.92 | 7.69 | 7.69 | 7.69 | 7.69 | 7.69 | 7.69 |
9 | 11.00 | 11.00 | 11.00 | 319.00 | 8.00 | 1.50 | 8.00 | 1.50 | 1.50 | 44.50 |
10 | 6.59 | 6.59 | 6.59 | 6.59 | 6.59 | 6.59 | 6.59 | 6.59 | 6.59 | 0.00 |
11 | 83.33 | 83.33 | 83.33 | 335.00 | 73.33 | 73.33 | 75.00 | 73.33 | 73.33 | 127.50 |
12 | 77.62 | 77.62 | 77.62 | 23.54 | 23.54 | 23.54 | 23.54 | 23.54 | 23.54 | 23.54 |
13 | 125.00 | 125.00 | 125.00 | 496.05 | 15.79 | 15.79 | 15.79 | 15.79 | 15.79 | 15.79 |
14 | 225.00 | 225.00 | 225.00 | 271.43 | 271.43 | 271.43 | 271.43 | 271.43 | 271.43 | 271.43 |
15 | 91.67 | 91.67 | 91.67 | 23.33 | 23.33 | 23.33 | 23.33 | 23.33 | 23.33 | 23.33 |
Appendix 3: Performance analysis of each of the twenty proposed variants of GHA-DDR in comparison with optimal OTD rate based on RPD
Problem instances | Optimal OTD rate | RPD of each of the proposed variants of GHA-DDR in comparison with optimal OTD rate | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
GHA-DDR1 | GHA-DDR2 | GHA-DDR3 | GHA-DDR4 | GHA-DDR5 | GHA-DDR6 | GHA-DDR7 | GHA-DDR8 | GHA-DDR9 | GHA-DDR10 | ||
1 | 0.667 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
2 | 0.714 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
3 | 0.625 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
4 | 0.670 | 17.08 | 17.08 | 17.08 | 17.08 | 17.08 | 17.08 | 17.08 | 17.08 | 17.08 | 17.08 |
5 | 0.600 | 16.67 | 16.67 | 16.67 | 16.67 | 16.67 | 16.67 | 16.67 | 16.67 | 33.33 | 16.67 |
6 | 0.700 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 85.71 | 85.71 | 71.43 |
7 | 0.700 | 42.86 | 42.86 | 42.86 | 42.86 | 42.86 | 42.86 | 42.86 | 28.57 | 28.57 | 42.86 |
8 | 0.700 | 28.57 | 28.57 | 28.57 | 28.57 | 28.57 | 28.57 | 28.57 | 14.29 | 14.29 | 28.57 |
9 | 0.900 | 44.44 | 44.44 | 44.44 | 44.44 | 44.44 | 44.44 | 44.44 | 44.44 | 44.44 | 44.44 |
10 | 0.800 | 12.50 | 12.50 | 12.50 | 12.50 | 12.50 | 12.50 | 12.50 | 12.50 | 12.50 | 12.50 |
11 | 0.800 | 25.00 | 25.00 | 25.00 | 25.00 | 25.00 | 25.00 | 25.00 | 25.00 | 25.00 | 25.00 |
12 | 0.600 | 66.67 | 66.67 | 66.67 | 66.67 | 66.67 | 66.67 | 50.00 | 50.00 | 50.00 | 66.67 |
13 | 0.800 | 25.00 | 25.00 | 25.00 | 25.00 | 25.00 | 25.00 | 25.00 | 37.50 | 37.50 | 25.00 |
14 | 0.700 | 28.57 | 28.57 | 28.57 | 28.57 | 28.57 | 28.57 | 28.57 | 28.57 | 28.57 | 28.57 |
15 | 0.800 | 25.00 | 25.00 | 25.00 | 25.00 | 25.00 | 25.00 | 25.00 | 25.00 | 25.00 | 25.00 |
Problem instances | RPD of each of the proposed variants of GHA-DDR in comparison with optimal OTD rate | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
GHA-DDR11 | GHA-DDR12 | GHA-DDR13 | GHA-DDR14 | GHA-DDR15 | GHA-DDR16 | GHA-DDR17 | GHA-DDR18 | GHA-DDR19 | GHA-DDR20 | |
1 | 0.00 | 0.00 | 0.00 | 25.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 25.00 |
2 | 0.00 | 0.00 | 0.00 | 60.00 | 0.00 | 20.00 | 20.00 | 20.00 | 20.00 | 20.00 |
3 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 20.00 | 20.00 | 20.00 | 20.00 | 20.00 |
4 | 17.08 | 17.08 | 17.08 | 17.08 | 17.08 | 33.67 | 33.67 | 33.67 | 33.67 | 17.08 |
5 | 16.67 | 16.67 | 16.67 | 16.67 | 50.00 | 50.00 | 50.00 | 50.00 | 50.00 | 33.33 |
6 | 71.43 | 71.43 | 71.43 | 71.43 | 42.86 | 42.86 | 42.86 | 42.86 | 42.86 | 28.57 |
7 | 42.86 | 42.86 | 42.86 | 28.57 | 42.86 | 42.86 | 42.86 | 42.86 | 42.86 | 42.86 |
8 | 28.57 | 28.57 | 28.57 | 42.86 | 28.57 | 28.57 | 28.57 | 28.57 | 28.57 | 28.57 |
9 | 44.44 | 44.44 | 44.44 | 66.67 | 33.33 | 11.11 | 33.33 | 11.11 | 11.11 | 44.44 |
10 | 12.50 | 12.50 | 12.50 | 12.50 | 12.50 | 12.50 | 12.50 | 12.50 | 12.50 | 0.00 |
11 | 25.00 | 25.00 | 25.00 | 12.50 | 25.00 | 25.00 | 25.00 | 25.00 | 25.00 | 37.50 |
12 | 66.67 | 66.67 | 66.67 | 33.33 | 33.33 | 33.33 | 33.33 | 33.33 | 33.33 | 33.33 |
13 | 25.00 | 25.00 | 25.00 | 37.50 | 37.50 | 37.50 | 37.50 | 37.50 | 37.50 | 37.50 |
14 | 28.57 | 28.57 | 28.57 | 42.86 | 42.86 | 42.86 | 42.86 | 42.86 | 42.86 | 42.86 |
15 | 25.00 | 25.00 | 25.00 | 12.50 | 12.50 | 12.50 | 12.50 | 12.50 | 12.50 | 12.50 |
Appendix 4 Performance analysis of each of the twenty proposed variants of GHA-DDR in comparison with optimal TE/L based on RPD
Problem instances | Optimal TE/L | RPD of each of the proposed variants of GHA-DDR in comparison with optimal TE/L | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
GHA-DDR1 | GHA-DDR2 | GHA-DDR3 | GHA-DDR4 | GHA-DDR5 | GHA-DDR6 | GHA-DDR7 | GHA-DDR8 | GHA-DDR9 | GHA-DDR10 | ||
1 | 40 | 55.00 | 55.00 | 55.00 | 55.00 | 55.00 | 55.00 | 55.00 | 65.00 | 65.00 | 55.00 |
2 | 60 | 30.00 | 30.00 | 30.00 | 30.00 | 30.00 | 30.00 | 30.00 | 36.67 | 36.67 | 30.00 |
3 | 71 | 39.44 | 39.44 | 39.44 | 39.44 | 39.44 | 39.44 | 39.44 | 22.54 | 22.54 | 39.44 |
4 | 91 | 17.58 | 17.58 | 17.58 | 17.58 | 17.58 | 17.58 | 17.58 | 26.37 | 26.37 | 17.58 |
5 | 135 | 11.85 | 22.22 | 22.22 | 22.22 | 11.85 | 11.85 | 25.19 | 22.22 | 17.78 | 11.85 |
6 | 102 | 41.18 | 41.18 | 41.18 | 41.18 | 41.18 | 41.18 | 41.18 | 66.67 | 66.67 | 41.18 |
7 | 73 | 106.85 | 106.85 | 106.85 | 106.85 | 106.85 | 106.85 | 106.85 | 52.05 | 52.05 | 106.85 |
8 | 80 | 80.00 | 80.00 | 80.00 | 80.00 | 80.00 | 80.00 | 80.00 | 87.50 | 87.50 | 80.00 |
9 | 54 | 148.15 | 166.67 | 166.67 | 166.67 | 148.15 | 148.15 | 248.15 | 148.15 | 148.15 | 148.15 |
10 | 59 | 57.63 | 57.63 | 57.63 | 57.63 | 57.63 | 57.63 | 57.63 | 57.63 | 57.63 | 57.63 |
11 | 68 | 185.29 | 185.29 | 185.29 | 185.29 | 185.29 | 185.29 | 185.29 | 185.29 | 185.29 | 185.29 |
12 | 116 | 51.72 | 51.72 | 51.72 | 51.72 | 51.72 | 51.72 | 87.93 | 101.72 | 101.72 | 51.72 |
13 | 84 | 66.67 | 66.67 | 66.67 | 66.67 | 66.67 | 66.67 | 66.67 | 78.57 | 78.57 | 66.67 |
14 | 52 | 151.92 | 151.92 | 151.92 | 151.92 | 151.92 | 151.92 | 151.92 | 151.92 | 151.92 | 151.92 |
15 | 37 | 297.30 | 297.30 | 297.30 | 297.30 | 297.30 | 297.30 | 297.30 | 297.30 | 297.30 | 297.30 |
Problem instances | RPD of each of the proposed variants of GHA-DDR in comparison with optimal TE/L | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
GHA-DDR11 | GHA-DDR12 | GHA-DDR13 | GHA-DDR14 | GHA-DDR15 | GHA-DDR16 | GHA-DDR17 | GHA-DDR18 | GHA-DDR19 | GHA-DDR20 | |
1 | 55.00 | 55.00 | 55.00 | 20.00 | 50.00 | 50.00 | 50.00 | 50.00 | 50.00 | 100.00 |
2 | 30.00 | 30.00 | 30.00 | 33.33 | 25.00 | 21.67 | 21.67 | 21.67 | 21.67 | 21.67 |
3 | 39.44 | 39.44 | 39.44 | 16.90 | 19.72 | 16.90 | 16.90 | 16.90 | 16.90 | 33.80 |
4 | 17.58 | 17.58 | 17.58 | 21.98 | 16.48 | 20.88 | 20.88 | 20.88 | 20.88 | 47.25 |
5 | 11.85 | 11.85 | 11.85 | 11.85 | 4.44 | 4.44 | 4.44 | 4.44 | 4.44 | 22.22 |
6 | 41.18 | 41.18 | 41.18 | 7.84 | 21.57 | 21.57 | 21.57 | 21.57 | 21.57 | 41.18 |
7 | 106.85 | 106.85 | 106.85 | 52.05 | 63.01 | 63.01 | 63.01 | 63.01 | 63.01 | 63.01 |
8 | 80.00 | 80.00 | 80.00 | 0.00 | 62.50 | 62.50 | 62.50 | 62.50 | 62.50 | 62.50 |
9 | 148.15 | 148.15 | 148.15 | 118.52 | 122.22 | 159.26 | 122.22 | 159.26 | 159.26 | 111.11 |
10 | 57.63 | 57.63 | 57.63 | 57.63 | 57.63 | 57.63 | 57.63 | 57.63 | 57.63 | 84.75 |
11 | 185.29 | 185.29 | 185.29 | 61.76 | 79.41 | 79.41 | 138.24 | 79.41 | 79.41 | 111.76 |
12 | 51.72 | 51.72 | 51.72 | 24.14 | 24.14 | 24.14 | 24.14 | 24.14 | 24.14 | 24.14 |
13 | 66.67 | 66.67 | 66.67 | 59.52 | 57.14 | 57.14 | 57.14 | 57.14 | 57.14 | 57.14 |
14 | 151.92 | 151.92 | 151.92 | 75.00 | 75.00 | 75.00 | 75.00 | 75.00 | 75.00 | 75.00 |
15 | 297.30 | 297.30 | 297.30 | 21.62 | 21.62 | 21.62 | 21.62 | 21.62 | 21.62 | 21.62 |
Appendix 5: Performance analysis of each of the twenty proposed variants of GHA-DDR in comparison with optimal Lmax based on RPD
Problem instances | Optimal Lmax | RPD of each of the proposed variants of GHA-DDR in comparison with optimal Lmax | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
GHA-DDR1 | GHA-DDR2 | GHA-DDR3 | GHA-DDR4 | GHA-DDR5 | GHA-DDR6 | GHA-DDR7 | GHA-DDR8 | GHA-DDR9 | GHA-DDR10 | ||
1 | 21 | 23.81 | 23.81 | 23.81 | 23.81 | 23.81 | 23.81 | 23.81 | 0.00 | 0.00 | 23.81 |
2 | 21 | 23.81 | 23.81 | 23.81 | 23.81 | 23.81 | 23.81 | 23.81 | 0.00 | 0.00 | 23.81 |
3 | 21 | 23.81 | 23.81 | 23.81 | 23.81 | 23.81 | 23.81 | 23.81 | 0.00 | 0.00 | 23.81 |
4 | 26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 7.69 | 7.69 | 0.00 |
5 | 37 | 13.51 | 13.51 | 13.51 | 13.51 | 13.51 | 13.51 | 13.51 | 35.14 | 0.00 | 13.51 |
6 | 20 | 30.00 | 30.00 | 30.00 | 30.00 | 30.00 | 30.00 | 30.00 | 105.00 | 105.00 | 30.00 |
7 | 24 | 16.67 | 16.67 | 16.67 | 16.67 | 16.67 | 16.67 | 16.67 | 16.67 | 16.67 | 16.67 |
8 | 25 | 20.00 | 20.00 | 20.00 | 20.00 | 20.00 | 20.00 | 20.00 | 56.00 | 56.00 | 20.00 |
9 | 14 | 7.14 | 7.14 | 7.14 | 7.14 | 7.14 | 7.14 | 42.86 | 7.14 | 7.14 | 7.14 |
10 | 16 | 6.25 | 6.25 | 6.25 | 6.25 | 6.25 | 6.25 | 6.25 | 6.25 | 6.25 | 6.25 |
11 | 13 | 23.08 | 23.08 | 23.08 | 23.08 | 23.08 | 23.08 | 23.08 | 23.08 | 23.08 | 23.08 |
12 | 30 | 30.00 | 30.00 | 30.00 | 30.00 | 30.00 | 30.00 | 73.33 | 83.33 | 83.33 | 30.00 |
13 | 8 | 62.50 | 62.50 | 62.50 | 62.50 | 62.50 | 62.50 | 62.50 | 187.50 | 187.50 | 62.50 |
14 | 15 | 20.00 | 20.00 | 20.00 | 20.00 | 20.00 | 20.00 | 20.00 | 20.00 | 20.00 | 20.00 |
15 | 9 | 22.22 | 22.22 | 22.22 | 22.22 | 22.22 | 22.22 | 22.22 | 22.22 | 22.22 | 22.22 |
Problem instances | RPD of each of the proposed variants of GHA-DDR in comparison with optimal Lmax | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
GHA-DDR11 | GHA-DDR12 | GHA-DDR13 | GHA-DDR14 | GHA-DDR15 | GHA-DDR16 | GHA-DDR17 | GHA-DDR18 | GHA-DDR19 | GHA-DDR20 | |
1 | 23.81 | 23.81 | 23.81 | 23.81 | 28.57 | 28.57 | 28.57 | 28.57 | 28.57 | 71.43 |
2 | 23.81 | 23.81 | 23.81 | 0.00 | 28.57 | 28.57 | 28.57 | 28.57 | 28.57 | 28.57 |
3 | 23.81 | 23.81 | 23.81 | 0.00 | 4.76 | 4.76 | 4.76 | 4.76 | 4.76 | 28.57 |
4 | 0.00 | 0.00 | 0.00 | 7.69 | 3.85 | 3.85 | 3.85 | 3.85 | 3.85 | 46.15 |
5 | 13.51 | 13.51 | 13.51 | 13.51 | 2.70 | 2.70 | 2.70 | 2.70 | 2.70 | 2.70 |
6 | 30.00 | 30.00 | 30.00 | 15.00 | 80.00 | 80.00 | 80.00 | 80.00 | 80.00 | 80.00 |
7 | 16.67 | 16.67 | 16.67 | 16.67 | 16.67 | 16.67 | 16.67 | 16.67 | 16.67 | 16.67 |
8 | 20.00 | 20.00 | 20.00 | 20.00 | 60.00 | 60.00 | 60.00 | 60.00 | 60.00 | 60.00 |
9 | 7.14 | 7.14 | 7.14 | 271.43 | 7.14 | 50.00 | 7.14 | 50.00 | 50.00 | 157.14 |
10 | 6.25 | 6.25 | 6.25 | 6.25 | 6.25 | 6.25 | 6.25 | 6.25 | 6.25 | 68.75 |
11 | 23.08 | 23.08 | 23.08 | 130.77 | 15.38 | 15.38 | 53.85 | 15.38 | 15.38 | 38.46 |
12 | 30.00 | 30.00 | 30.00 | 36.67 | 36.67 | 36.67 | 36.67 | 36.67 | 36.67 | 36.67 |
13 | 62.50 | 62.50 | 62.50 | 400.00 | 150.00 | 150.00 | 150.00 | 150.00 | 150.00 | 150.00 |
14 | 20.00 | 20.00 | 20.00 | 20.00 | 20.00 | 20.00 | 20.00 | 20.00 | 20.00 | 20.00 |
15 | 22.22 | 22.22 | 22.22 | 11.11 | 11.11 | 11.11 | 11.11 | 11.11 | 11.11 | 11.11 |
Appendix 6: Performance analysis of each of the twenty proposed variants of GHA-DDR in comparison with estimated optimal TWT based on ARPD score
S. No. | Problem configuration | ARPD score of each of the proposed variants of GHA-DDR in comparison with estimated optimal TWT | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
GHA-DDR1 | GHA-DDR2 | GHA-DDR3 | GHA-DDR4 | GHA-DDR5 | GHA-DDR6 | GHA-DDR7 | GHA-DDR8 | GHA-DDR9 | GHA-DDR10 | ||
1 | J1.A1, D1 | 53.12 | 54.65 | 54.65 | 54.65 | 53.12 | 53.79 | 44.38 | 55.86 | 63.17 | 53.79 |
2 | J1.A1, D2 | 59.46 | 82.96 | 82.96 | 82.96 | 59.46 | 58.71 | 66.49 | 92.89 | 103.81 | 58.71 |
3 | J1, A1, D3 | 152.71 | 219.08 | 219.08 | 219.08 | 152.71 | 152.71 | 164.72 | 150.20 | 155.90 | 152.71 |
4 | J1, A2, D1 | 89.49 | 94.30 | 94.30 | 94.30 | 89.49 | 90.30 | 82.00 | 144.90 | 152.33 | 90.30 |
5 | J1, A2, D2 | 247.90 | 220.21 | 220.21 | 220.21 | 247.90 | 247.09 | 128.69 | 221.13 | 278.96 | 247.09 |
6 | J1, A2, D3 | 105.09 | 180.45 | 180.45 | 180.45 | 105.09 | 105.09 | 127.11 | 120.86 | 134.45 | 105.09 |
7 | J1, A3, D1 | 57.56 | 56.08 | 56.08 | 56.08 | 57.56 | 57.56 | 46.00 | 155.74 | 156.72 | 57.56 |
8 | J1, A3, D2 | 90.87 | 117.22 | 117.22 | 117.22 | 90.87 | 93.70 | 97.60 | 142.79 | 181.55 | 93.70 |
9 | J1, A3, D3 | 120.41 | 173.58 | 173.58 | 173.58 | 120.41 | 120.41 | 165.21 | 246.28 | 280.79 | 120.41 |
10 | J2.A1, D1 | 118.03 | 111.15 | 111.15 | 111.15 | 118.03 | 109.42 | 78.65 | 124.10 | 126.07 | 109.42 |
11 | J2.A1, D2 | 74.90 | 120.01 | 120.01 | 120.01 | 74.90 | 73.17 | 88.36 | 100.55 | 109.14 | 73.17 |
12 | J2, A1, D3 | 91.65 | 173.39 | 173.39 | 173.39 | 91.65 | 92.94 | 121.19 | 115.31 | 129.06 | 92.94 |
13 | J2, A2, D1 | 134.21 | 138.21 | 138.21 | 138.21 | 134.21 | 138.44 | 107.61 | 130.43 | 131.02 | 138.44 |
14 | J2, A2, D2 | 155.44 | 163.02 | 163.02 | 163.02 | 155.44 | 149.74 | 122.05 | 191.10 | 205.17 | 149.74 |
15 | J2, A2, D3 | 185.21 | 229.86 | 229.86 | 229.86 | 185.21 | 180.35 | 177.63 | 211.60 | 226.70 | 180.35 |
16 | J2, A3, D1 | 140.55 | 141.87 | 141.87 | 141.87 | 140.55 | 141.45 | 109.27 | 194.19 | 194.97 | 141.45 |
17 | J2, A3, D2 | 157.98 | 183.43 | 183.43 | 183.43 | 157.98 | 182.57 | 122.41 | 183.93 | 188.70 | 182.57 |
18 | J2, A3, D3 | 196.67 | 234.83 | 234.83 | 234.83 | 196.67 | 198.48 | 171.85 | 230.16 | 238.08 | 198.48 |
19 | J3, A1, D1 | 75.81 | 80.04 | 80.04 | 80.04 | 75.81 | 79.39 | 41.07 | 66.93 | 68.46 | 79.39 |
20 | J3, A1, D2 | 93.98 | 90.45 | 90.45 | 90.45 | 93.98 | 90.71 | 43.75 | 70.63 | 74.39 | 90.61 |
21 | J3, A1, D3 | 98.03 | 110.72 | 110.72 | 110.72 | 98.03 | 92.42 | 61.02 | 72.44 | 82.17 | 92.42 |
22 | J3, A2, D1 | 106.93 | 106.88 | 106.88 | 106.88 | 106.93 | 104.62 | 51.46 | 80.49 | 80.69 | 104.62 |
23 | J3, A2, D2 | 97.54 | 109.79 | 109.79 | 109.79 | 97.54 | 107.39 | 56.90 | 82.11 | 83.97 | 107.39 |
24 | J3, A2, D3 | 129.11 | 144.65 | 144.65 | 144.65 | 129.11 | 124.09 | 86.72 | 107.12 | 105.67 | 124.09 |
25 | J3, A3, D1 | 99.34 | 107.88 | 107.88 | 107.88 | 99.34 | 105.02 | 62.84 | 91.01 | 92.36 | 105.02 |
26 | J3, A3, D2 | 118.92 | 120.47 | 120.47 | 120.47 | 118.92 | 122.00 | 65.65 | 93.02 | 97.02 | 122.00 |
27 | J3, A3, D3 | 133.23 | 132.27 | 132.27 | 132.27 | 133.23 | 124.85 | 76.90 | 94.22 | 104.62 | 124.85 |
S. No. | ARPD score of each of the proposed variants of GHA-DDR in comparison with estimated optimal TWT | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
GHA-DDR11 | GHA-DDR12 | GHA-DDR13 | GHA-DDR14 | GHA-DDR15 | GHA-DDR16 | GHA-DDR17 | GHA-DDR18 | GHA-DDR19 | GHA-DDR20 | |
1 | 53.12 | 53.79 | 53.12 | 165.02 | 0.26 | 3.70 | 4.38 | 2.06 | 2.06 | 2.55 |
2 | 59.46 | 58.71 | 59.46 | 268.97 | 9.54 | 4.24 | 6.50 | 3.86 | 3.93 | 20.82 |
3 | 152.71 | 152.71 | 152.71 | 765.51 | 3.14 | 47.60 | 47.41 | 46.43 | 46.43 | 65.32 |
4 | 89.49 | 90.30 | 89.49 | 182.12 | 5.59 | 2.53 | 2.62 | 1.78 | 1.78 | 5.80 |
5 | 247.90 | 247.09 | 247.90 | 533.80 | 37.76 | 1.22 | 20.56 | 0.59 | 0.89 | 33.53 |
6 | 105.09 | 105.09 | 105.09 | 499.80 | 18.01 | 5.44 | 12.19 | 1.52 | 1.52 | 27.67 |
7 | 57.56 | 57.56 | 57.56 | 199.47 | 3.69 | 6.29 | 8.34 | 5.43 | 4.92 | 8.93 |
8 | 90.87 | 93.70 | 90.87 | 172.65 | 8.84 | 2.83 | 8.12 | 2.03 | 2.03 | 18.28 |
9 | 120.41 | 120.41 | 120.41 | 496.82 | 6.61 | 4.53 | 10.99 | 4.57 | 4.57 | 24.85 |
10 | 118.03 | 109.55 | 118.03 | 109.22 | 2.26 | 3.74 | 2.68 | 2.20 | 1.89 | 6.27 |
11 | 74.90 | 73.17 | 74.90 | 101.96 | 6.67 | 5.52 | 7.21 | 2.69 | 1.40 | 16.32 |
12 | 91.65 | 92.94 | 91.65 | 145.22 | 8.22 | 10.42 | 11.96 | 9.55 | 6.02 | 2.20 |
13 | 134.21 | 138.44 | 134.21 | 127.14 | 3.11 | 6.82 | 5.03 | 1.04 | 1.28 | 11.71 |
14 | 155.44 | 149.74 | 155.44 | 152.84 | 22.60 | 8.88 | 18.53 | 2.94 | 1.31 | 23.31 |
15 | 185.21 | 180.35 | 185.21 | 202.49 | 18.10 | 8.57 | 21.11 | 4.65 | 1.50 | 16.25 |
16 | 140.55 | 141.45 | 140.55 | 183.36 | 19.77 | 9.65 | 11.66 | 0.57 | 0.93 | 15.53 |
17 | 157.98 | 182.57 | 157.98 | 165.69 | 24.65 | 7.23 | 20.92 | 2.59 | 0.85 | 47.37 |
18 | 196.67 | 198.48 | 196.67 | 211.44 | 47.41 | 6.39 | 39.17 | 3.80 | 3.36 | 47.04 |
19 | 75.81 | 80.31 | 75.81 | 58.08 | 3.94 | 1.61 | 3.56 | 0.13 | 1.00 | 7.87 |
20 | 93.98 | 90.64 | 93.98 | 60.76 | 1.68 | 4.25 | 2.24 | 0.23 | 2.62 | 9.16 |
21 | 98.03 | 95.31 | 98.03 | 58.15 | 0.99 | 4.31 | 2.91 | 1.37 | 1.22 | 9.53 |
22 | 106.93 | 103.67 | 106.93 | 74.43 | 4.19 | 2.73 | 0.26 | 0.13 | 1.37 | 6.12 |
23 | 97.54 | 107.39 | 97.54 | 74.04 | 5.57 | 6.92 | 4.41 | 0.87 | 0.96 | 12.16 |
24 | 129.11 | 124.09 | 129.11 | 75.75 | 10.54 | 7.26 | 11.89 | 0.28 | 1.85 | 28.51 |
25 | 99.34 | 104.39 | 99.34 | 76.33 | 3.26 | 4.85 | 1.98 | 0.77 | 1.43 | 6.15 |
26 | 118.92 | 122.00 | 118.92 | 90.27 | 5.90 | 7.24 | 3.05 | 0.34 | 0.82 | 19.52 |
27 | 133.23 | 124.85 | 133.23 | 89.45 | 17.01 | 14.11 | 6.76 | 1.40 | 2.85 | 18.04 |
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Vimala Rani, M., Mathirajan, M. Performance evaluation of due-date based dispatching rules in dynamic scheduling of diffusion furnace. OPSEARCH 57, 462–512 (2020). https://doi.org/10.1007/s12597-019-00434-8
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DOI: https://doi.org/10.1007/s12597-019-00434-8