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Some characterizations of robust solution sets for uncertain convex optimization problems with locally Lipschitz inequality constraints
An efficient heuristic algorithm for two-dimensional rectangular packing problem with central rectangle
National Engineering Research Center for E-learning, Central China Normal University, Wuhan 430079, China |
This paper presents a heuristic algorithm for solving a specific NP-hard 2D rectangular packing problem in which a rectangle called central rectangle is required to be placed in the center of the final layout, and the aspect ratio of the container is also required to be in a given range. The key component of the proposed algorithm is a greedy constructive procedure, according to which, the rectangles are packed into the container one by one and each rectangle is packed into the container by an angle-occupying placement with maximum fit degree. The proposed algorithm is evaluated on two groups of 35 well-known benchmark instances. Computational results disclose that the proposed algorithm outperforms the previous algorithm for the packing problem. For the first group of test instances, solutions with average filling rate 99.31% can be obtained; for the real-world layout problem in the second group, the filling rate of the solution is 94.75%.
References:
[1] |
A. Lodi, S. Martello and M. Monaci,
Two-dimensional packing problems: A survey, European Journal of Operational Research, 141 (2002), 241-252.
doi: 10.1016/S0377-2217(02)00123-6. |
[2] |
K. A. Dowsland and W. B. Dowsland,
Packing problems, European Journal of Operational Research, 56 (1992), 2-14.
|
[3] |
H. F. Lee and E. C. Sewell,
The strip-packing problem for a boat manufacturing firm, IIE Transactions, 31 (1999), 639-651.
doi: 10.1080/07408179908969865. |
[4] |
D. S. Hochbaum and W. Maass,
Approximation schemes for covering and packing problems in image processing and VLSI, Journal of the Association for Computing Machinery, 32 (1985), 130-136.
doi: 10.1145/2455.214106. |
[5] |
B. S. Baker, Jr. E. G. Coffman and R. L. Rivest,
Orthogonal packing in two dimensions, SIAM Journal on Computing, 9 (1980), 846-855.
doi: 10.1137/0209064. |
[6] |
B. Chazelle,
The bottom-left bin packing heuristic: An efficient implementation, IEEE Transactions on Computers, 32 (1983), 697-707.
doi: 10.1109/tc.1983.1676307. |
[7] |
S. Jakobs,
On genetic algorithms for the packing of polygons, European Journal of Operational Research, 88 (1996), 165-181.
doi: 10.1016/0377-2217(94)00166-9. |
[8] |
D. Q. Liu and H. F. Teng,
An improved BL-algorithm for genetic algorithm of the orthogonal packing of rectangles, European Journal of Operational Research, 112 (1999), 413-420.
doi: 10.1016/S0377-2217(97)00437-2. |
[9] |
E. Hopper and B. Turton,
An empirical investigation of meta-heuristic and heuristic algorithms for a 2D packing problem, European Journal of Operational Research, 128 (2001), 34-57.
doi: 10.1016/S0377-2217(99)00357-4. |
[10] |
Y. L. Wu, W. Q. Huang, S. C. Lau, C. K. Wong and G. H. Young,
An effective quasi-human based heuristic for solving the rectangle packing problem, European Journal of Operational Research, 141 (2002), 341-358.
doi: 10.1016/S0377-2217(02)00129-7. |
[11] |
W. Q. Huang and D. B. Chen,
An efficient heuristic algorithm for rectangle-packing problem, Simulation Modelling Practice and Theory, 15 (2007), 1356-1365.
|
[12] |
D. F. Zhang, Y. Kang and A. S. Deng,
A new heuristic recursive algorithm for the strip rectangular packing problem, Computers & Operations Research, 33 (2006), 2209-2217.
|
[13] |
L. J. Wei, D. F. Zhang and Q. S. Chen,
A least wasted first heuristic algorithm for the rectangular packing problem, Computers & Operations Research, 36 (2009), 1608-1614.
doi: 10.1016/j.cor.2008.03.004. |
[14] |
R. Alvarez-Valdes, F. Parreño and J. M. Tamarit,
Reactive GRASP for the strip-packing problem, Computers & Operations Research, 35 (2008), 1065-1083.
doi: 10.1016/j.cor.2006.07.004. |
[15] |
K. He, W. Q. Huang and Y. Jin,
An efficient deterministic heuristic for two-dimensional rectangular packing, Computers & Operations Research, 39 (2012), 1355-1363.
doi: 10.1016/j.cor.2011.08.005. |
[16] |
W. S. Xiao, L. Wu, X. Tian and J. L. Wang, Applying a new adaptive genetic algorithm to study the layout of drilling equipment in semisubmersible drilling platforms, Mathematical Problems in Engineering, 2015 (2015), Article ID 146902, 9 pages.
doi: 10.1155/2015/146902. |
[17] |
L. Wu, L. Zhang, W.S. Xiao, Q. Liu, C. Mu and Y.W. Yang,
A novel heuristic algorithm for two-dimensional rectangle packing area minimization problem with central rectangle, Computers & Industrial Engineering, 102 (2016), 208-218.
doi: 10.1016/j.cie.2016.10.011. |
[18] |
E. K. Burke, G. Kendall and G. Whitwell,
A new placement heuristic for the orthogonal stock-cutting problem, Operations Research, 52 (2004), 655-671.
doi: 10.1287/opre.1040.0109. |
show all references
References:
[1] |
A. Lodi, S. Martello and M. Monaci,
Two-dimensional packing problems: A survey, European Journal of Operational Research, 141 (2002), 241-252.
doi: 10.1016/S0377-2217(02)00123-6. |
[2] |
K. A. Dowsland and W. B. Dowsland,
Packing problems, European Journal of Operational Research, 56 (1992), 2-14.
|
[3] |
H. F. Lee and E. C. Sewell,
The strip-packing problem for a boat manufacturing firm, IIE Transactions, 31 (1999), 639-651.
doi: 10.1080/07408179908969865. |
[4] |
D. S. Hochbaum and W. Maass,
Approximation schemes for covering and packing problems in image processing and VLSI, Journal of the Association for Computing Machinery, 32 (1985), 130-136.
doi: 10.1145/2455.214106. |
[5] |
B. S. Baker, Jr. E. G. Coffman and R. L. Rivest,
Orthogonal packing in two dimensions, SIAM Journal on Computing, 9 (1980), 846-855.
doi: 10.1137/0209064. |
[6] |
B. Chazelle,
The bottom-left bin packing heuristic: An efficient implementation, IEEE Transactions on Computers, 32 (1983), 697-707.
doi: 10.1109/tc.1983.1676307. |
[7] |
S. Jakobs,
On genetic algorithms for the packing of polygons, European Journal of Operational Research, 88 (1996), 165-181.
doi: 10.1016/0377-2217(94)00166-9. |
[8] |
D. Q. Liu and H. F. Teng,
An improved BL-algorithm for genetic algorithm of the orthogonal packing of rectangles, European Journal of Operational Research, 112 (1999), 413-420.
doi: 10.1016/S0377-2217(97)00437-2. |
[9] |
E. Hopper and B. Turton,
An empirical investigation of meta-heuristic and heuristic algorithms for a 2D packing problem, European Journal of Operational Research, 128 (2001), 34-57.
doi: 10.1016/S0377-2217(99)00357-4. |
[10] |
Y. L. Wu, W. Q. Huang, S. C. Lau, C. K. Wong and G. H. Young,
An effective quasi-human based heuristic for solving the rectangle packing problem, European Journal of Operational Research, 141 (2002), 341-358.
doi: 10.1016/S0377-2217(02)00129-7. |
[11] |
W. Q. Huang and D. B. Chen,
An efficient heuristic algorithm for rectangle-packing problem, Simulation Modelling Practice and Theory, 15 (2007), 1356-1365.
|
[12] |
D. F. Zhang, Y. Kang and A. S. Deng,
A new heuristic recursive algorithm for the strip rectangular packing problem, Computers & Operations Research, 33 (2006), 2209-2217.
|
[13] |
L. J. Wei, D. F. Zhang and Q. S. Chen,
A least wasted first heuristic algorithm for the rectangular packing problem, Computers & Operations Research, 36 (2009), 1608-1614.
doi: 10.1016/j.cor.2008.03.004. |
[14] |
R. Alvarez-Valdes, F. Parreño and J. M. Tamarit,
Reactive GRASP for the strip-packing problem, Computers & Operations Research, 35 (2008), 1065-1083.
doi: 10.1016/j.cor.2006.07.004. |
[15] |
K. He, W. Q. Huang and Y. Jin,
An efficient deterministic heuristic for two-dimensional rectangular packing, Computers & Operations Research, 39 (2012), 1355-1363.
doi: 10.1016/j.cor.2011.08.005. |
[16] |
W. S. Xiao, L. Wu, X. Tian and J. L. Wang, Applying a new adaptive genetic algorithm to study the layout of drilling equipment in semisubmersible drilling platforms, Mathematical Problems in Engineering, 2015 (2015), Article ID 146902, 9 pages.
doi: 10.1155/2015/146902. |
[17] |
L. Wu, L. Zhang, W.S. Xiao, Q. Liu, C. Mu and Y.W. Yang,
A novel heuristic algorithm for two-dimensional rectangle packing area minimization problem with central rectangle, Computers & Industrial Engineering, 102 (2016), 208-218.
doi: 10.1016/j.cie.2016.10.011. |
[18] |
E. K. Burke, G. Kendall and G. Whitwell,
A new placement heuristic for the orthogonal stock-cutting problem, Operations Research, 52 (2004), 655-671.
doi: 10.1287/opre.1040.0109. |







Parameter | Description | Value |
Nar | Lower bound of the aspect ratio of the container | 0.5 |
Nar | Upper bound of the aspect ratio of the container | 2 |
Lower bound of the between centrality of CR in vertical direction | 1 | |
Upper bound of the between centrality of CR in vertical direction | 2 | |
Lower bound of the between centrality of CR in horizontal direction | 1 | |
Upper bound of the between centrality of CR in horizontal direction | 2 |
Parameter | Description | Value |
Nar | Lower bound of the aspect ratio of the container | 0.5 |
Nar | Upper bound of the aspect ratio of the container | 2 |
Lower bound of the between centrality of CR in vertical direction | 1 | |
Upper bound of the between centrality of CR in vertical direction | 2 | |
Lower bound of the between centrality of CR in horizontal direction | 1 | |
Upper bound of the between centrality of CR in horizontal direction | 2 |
Instance | Filling rate (%) under different values of parameter | |||||||||||||||
0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 1.0 | 1.1 | 1.2 | 1.3 | 1.4 | 1.5 | 1.6 | |
N1 | 81.63 | 81.63 | 83.33 | 77.37 | 83.33 | 78.43 | 77.75 | 77.37 | 74.59 | 74.59 | 73.46 | 73.46 | 74.59 | 74.59 | 73.46 | 52.59 |
N2 | 100 | 100 | 98.81 | 98.04 | 100 | 98.81 | 98.81 | 98.04 | 98.04 | 98.04 | 98.04 | 98.04 | 98.81 | 98.81 | 98.04 | 98.04 |
N3 | 99.67 | 99.67 | 99.47 | 99.67 | 99.21 | 99.21 | 99.21 | 98.75 | 98.81 | 98.81 | 98.88 | 98.04 | 99.21 | 98.04 | 98.04 | 90.74 |
N4 | 98.98 | 98.77 | 99.01 | 98.46 | 98.49 | 98.77 | 98.98 | 97.86 | 98.51 | 98.28 | 98.05 | 98.77 | 96.75 | 97.09 | 98.31 | 89.19 |
N5 | 99.21 | 99.21 | 99.21 | 99.21 | 98.18 | 98.24 | 98.12 | 98.39 | 98.19 | 97.98 | 97.65 | 97.98 | 98.27 | 97.23 | 97.92 | 97.22 |
N6 | 100 | 100 | 99.70 | 99.56 | 99.50 | 99.56 | 99.70 | 99.21 | 99.30 | 99.21 | 99.36 | 99.36 | 99.36 | 99.70 | 99.50 | 99.21 |
N7 | 100 | 99.95 | 100 | 99.95 | 99.55 | 99.95 | 99.50 | 99.50 | 99.55 | 99.30 | 99.90 | 99.95 | 99.55 | 99.30 | 99.38 | 99.30 |
N8 | 99.90 | 99.90 | 99.91 | 99.90 | 99.76 | 99.70 | 99.76 | 99.90 | 99.37 | 99.71 | 99.55 | 99.69 | 99.57 | 99.76 | 99.71 | 99.36 |
N9 | 99.75 | 99.75 | 99.73 | 99.73 | 99.73 | 99.68 | 99.73 | 99.68 | 99.68 | 99.68 | 99.68 | 99.68 | 99.68 | 99.68 | 99.68 | 99.68 |
N10 | 100 | 100 | 99.96 | 100 | 99.93 | 99.96 | 99.93 | 99.89 | 99.74 | 99.91 | 99.89 | 99.74 | 99.93 | 99.91 | 99.88 | 99.71 |
Average | 97.91 | 97.89 | 97.91 | 97.19 | 97.77 | 97.23 | 97.15 | 96.86 | 96.58 | 96.55 | 96.06 | 96.47 | 96.57 | 96.41 | 96.39 | 92.50 |
Instance | Filling rate (%) under different values of parameter | |||||||||||||||
0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 1.0 | 1.1 | 1.2 | 1.3 | 1.4 | 1.5 | 1.6 | |
N1 | 81.63 | 81.63 | 83.33 | 77.37 | 83.33 | 78.43 | 77.75 | 77.37 | 74.59 | 74.59 | 73.46 | 73.46 | 74.59 | 74.59 | 73.46 | 52.59 |
N2 | 100 | 100 | 98.81 | 98.04 | 100 | 98.81 | 98.81 | 98.04 | 98.04 | 98.04 | 98.04 | 98.04 | 98.81 | 98.81 | 98.04 | 98.04 |
N3 | 99.67 | 99.67 | 99.47 | 99.67 | 99.21 | 99.21 | 99.21 | 98.75 | 98.81 | 98.81 | 98.88 | 98.04 | 99.21 | 98.04 | 98.04 | 90.74 |
N4 | 98.98 | 98.77 | 99.01 | 98.46 | 98.49 | 98.77 | 98.98 | 97.86 | 98.51 | 98.28 | 98.05 | 98.77 | 96.75 | 97.09 | 98.31 | 89.19 |
N5 | 99.21 | 99.21 | 99.21 | 99.21 | 98.18 | 98.24 | 98.12 | 98.39 | 98.19 | 97.98 | 97.65 | 97.98 | 98.27 | 97.23 | 97.92 | 97.22 |
N6 | 100 | 100 | 99.70 | 99.56 | 99.50 | 99.56 | 99.70 | 99.21 | 99.30 | 99.21 | 99.36 | 99.36 | 99.36 | 99.70 | 99.50 | 99.21 |
N7 | 100 | 99.95 | 100 | 99.95 | 99.55 | 99.95 | 99.50 | 99.50 | 99.55 | 99.30 | 99.90 | 99.95 | 99.55 | 99.30 | 99.38 | 99.30 |
N8 | 99.90 | 99.90 | 99.91 | 99.90 | 99.76 | 99.70 | 99.76 | 99.90 | 99.37 | 99.71 | 99.55 | 99.69 | 99.57 | 99.76 | 99.71 | 99.36 |
N9 | 99.75 | 99.75 | 99.73 | 99.73 | 99.73 | 99.68 | 99.73 | 99.68 | 99.68 | 99.68 | 99.68 | 99.68 | 99.68 | 99.68 | 99.68 | 99.68 |
N10 | 100 | 100 | 99.96 | 100 | 99.93 | 99.96 | 99.93 | 99.89 | 99.74 | 99.91 | 99.89 | 99.74 | 99.93 | 99.91 | 99.88 | 99.71 |
Average | 97.91 | 97.89 | 97.91 | 97.19 | 97.77 | 97.23 | 97.15 | 96.86 | 96.58 | 96.55 | 96.06 | 96.47 | 96.57 | 96.41 | 96.39 | 92.50 |
Instance | HACR | HA_AOP | ||||||||||||||
Fillrate (%) | Nar | Time (s) | Fillrate (%) | Nar | Time (s) | |||||||||||
N1 | 10 | 48 | 37 | 90.09 | 1.297 | 1.400 | 1.056 | 15.37 | 48 | 40 | 83.33 | 1.200 | 2.000 | 1.000 | 0.45 | |
N2 | 20 | 36 | 45 | 92.59 | 0.800 | 1.250 | 1.500 | 77.48 | 30 | 50 | 100 | 0.6 | 2.000 | 1.500 | 0.13 | |
N3 | 30 | 32 | 50 | 93.75 | 0.640 | 1.133 | 1.174 | 162.07 | 28 | 54 | 99.21 | 0.519 | 1.000 | 1.000 | 0.70 | |
N4 | 40 | 89 | 76 | 94.62 | 1.171 | 1.119 | 1.533 | 294.51 | 70 | 93 | 98.49 | 0.753 | 1.500 | 2.000 | 17.10 | |
N5 | 50 | 92 | 114 | 95.35 | 0.807 | 1.244 | 1.073 | 452.74 | 98 | 104 | 98.18 | 0.942 | 1.500 | 1.000 | 66.40 | |
N6 | 60 | 74 | 71 | 95.17 | 1.042 | 1.467 | 1.536 | 747.08 | 75 | 67 | 99.50 | 1.119 | 2.000 | 2.000 | 20.76 | |
N7 | 70 | 85 | 98 | 96.04 | 0.867 | 1.237 | 1.333 | 1061.3 | 90 | 89 | 99.55 | 1.011 | 1.500 | 1.500 | 62.07 | |
N8 | 80 | 96 | 86 | 96.90 | 1.116 | 1.400 | 1.263 | 1406.7 | 99 | 81 | 99.76 | 1.222 | 2.000 | 1.000 | 54.29 | |
N9 | 100 | 81 | 85 | 97.47 | 0.853 | 1.025 | 1.159 | 1913.8 | 94 | 80 | 99.73 | 1.175 | 1.000 | 2.000 | 59.98 | |
N10 | 200 | 78 | 138 | 97.55 | 0.565 | 1.026 | 1.379 | 6075.4 | 121 | 87 | 99.93 | 1.391 | 2.000 | 1.500 | 334.58 | |
N11 | 300 | 89 | 120 | 98.31 | 0.742 | 1.094 | 1.124 | 12489 | 105 | 100 | 100 | 1.050 | 2.000 | 2.000 | 572.07 | |
N12 | 500 | 155 | 195 | 99.26 | 0.795 | 1.067 | 1.000 | 20435 | 154 | 196 | 99.39 | 0.786 | 1.000 | 2.000 | 93376.28 | |
N13 | 3152 | 822 | 750 | 99.66 | 1.096 | 1.055 | 1.344 | 1.16 | 1024 | 600 | 100 | 1.707 | 2.000 | 2.000 | 187.80 | |
C11 | 16 | 18 | 24 | 92.59 | 0.750 | 1.250 | 1.400 | 54.45 | 20 | 20 | 100 | 1.000 | 1.000 | 1.500 | 0.07 | |
C12 | 17 | 16 | 27 | 92.59 | 0.593 | 1.286 | 1.077 | 60.88 | 20 | 20 | 100 | 1.000 | 1.000 | 1.500 | 0.05 | |
C13 | 16 | 21 | 21 | 90.70 | 1.000 | 1.625 | 1.625 | 52.16 | 25 | 16 | 100 | 1.563 | 1.000 | 1.000 | 0.01 | |
C21 | 25 | 28 | 23 | 93.17 | 1.217 | 1.000 | 1.300 | 98.76 | 30 | 20 | 100 | 1.500 | 2.000 | 1.000 | 0.02 | |
C22 | 25 | 24 | 27 | 92.30 | 0.889 | 1.400 | 1.455 | 94.05 | 20 | 30 | 100 | 0.667 | 2.000 | 1.000 | 0.04 | |
C23 | 25 | 28 | 23 | 93.17 | 1.217 | 1.333 | 1.556 | 103.44 | 30 | 20 | 100 | 1.500 | 2.000 | 1.500 | 0.02 | |
C31 | 28 | 38 | 50 | 94.74 | 0.760 | 1.111 | 1.083 | 154.62 | 30 | 60 | 100 | 0.500 | 2.000 | 1.500 | 0.86 | |
C32 | 29 | 52 | 37 | 93.56 | 1.405 | 1.364 | 1.176 | 149.78 | 44 | 41 | 99.78 | 1.073 | 1.500 | 2.000 | 2.11 | |
C33 | 28 | 40 | 48 | 93.75 | 0.833 | 1.500 | 1.400 | 160.22 | 40 | 45 | 100 | 0.889 | 1.000 | 2.000 | 0.74 | |
C41 | 49 | 54 | 70 | 95.24 | 0.771 | 1.700 | 1.333 | 427.69 | 82 | 44 | 99.78 | 1.864 | 2.000 | 2.000 | 11.28 | |
C42 | 49 | 73 | 52 | 94.84 | 1.404 | 1.433 | 1.364 | 432.15 | 72 | 50 | 100 | 1.440 | 2.000 | 1.500 | 2.65 | |
C43 | 49 | 60 | 63 | 95.24 | 0.952 | 1.308 | 1.100 | 430.27 | 50 | 72 | 100 | 0.694 | 2.000 | 1.000 | 4.05 | |
C51 | 72 | 80 | 70 | 96.43 | 1.143 | 1.353 | 1.188 | 1216.3 | 100 | 54 | 100 | 1.852 | 1.500 | 1.000 | 1.80 | |
C52 | 73 | 73 | 77 | 96.07 | 0.948 | 1.433 | 1.265 | 1300.4 | 100 | 54 | 100 | 1.852 | 2.000 | 2.000 | 0.21 | |
C53 | 72 | 78 | 72 | 96.15 | 1.083 | 1.137 | 1.215 | 1278.2 | 90 | 60 | 100 | 1.500 | 1.000 | 2.000 | 5.06 | |
C61 | 97 | 101 | 99 | 96.01 | 1.020 | 1.172 | 1.020 | 1714.5 | 120 | 80 | 100 | 1.500 | 1.000 | 2.000 | 13.99 | |
C62 | 97 | 108 | 92 | 96.62 | 1.174 | 1.571 | 1.300 | 1807.6 | 128 | 75 | 100 | 1.707 | 2.000 | 2.000 | 2.65 | |
C63 | 97 | 100 | 100 | 96.00 | 1.000 | 1.273 | 1.174 | 1786.3 | 85 | 113 | 99.95 | 0.752 | 1.000 | 1.500 | 83.70 | |
C71 | 196 | 197 | 200 | 97.46 | 0.985 | 1.402 | 1.128 | 6246.2 | 183 | 210 | 99.92 | 0.871 | 1.500 | 2.000 | 3668.73 | |
C72 | 197 | 180 | 219 | 97.41 | 0.822 | 1.308 | 1.190 | 6012.7 | 256 | 150 | 100 | 1.707 | 2.000 | 1.000 | 1.23 | |
C73 | 196 | 238 | 166 | 97.20 | 1.434 | 1.380 | 1.243 | 6175.6 | 194 | 198 | 99.97 | 0.980 | 2.000 | 1.000 | 4621.96 | |
Average | 95.24 | 5614.32 | 99.31 | 3045.99 |
Instance | HACR | HA_AOP | ||||||||||||||
Fillrate (%) | Nar | Time (s) | Fillrate (%) | Nar | Time (s) | |||||||||||
N1 | 10 | 48 | 37 | 90.09 | 1.297 | 1.400 | 1.056 | 15.37 | 48 | 40 | 83.33 | 1.200 | 2.000 | 1.000 | 0.45 | |
N2 | 20 | 36 | 45 | 92.59 | 0.800 | 1.250 | 1.500 | 77.48 | 30 | 50 | 100 | 0.6 | 2.000 | 1.500 | 0.13 | |
N3 | 30 | 32 | 50 | 93.75 | 0.640 | 1.133 | 1.174 | 162.07 | 28 | 54 | 99.21 | 0.519 | 1.000 | 1.000 | 0.70 | |
N4 | 40 | 89 | 76 | 94.62 | 1.171 | 1.119 | 1.533 | 294.51 | 70 | 93 | 98.49 | 0.753 | 1.500 | 2.000 | 17.10 | |
N5 | 50 | 92 | 114 | 95.35 | 0.807 | 1.244 | 1.073 | 452.74 | 98 | 104 | 98.18 | 0.942 | 1.500 | 1.000 | 66.40 | |
N6 | 60 | 74 | 71 | 95.17 | 1.042 | 1.467 | 1.536 | 747.08 | 75 | 67 | 99.50 | 1.119 | 2.000 | 2.000 | 20.76 | |
N7 | 70 | 85 | 98 | 96.04 | 0.867 | 1.237 | 1.333 | 1061.3 | 90 | 89 | 99.55 | 1.011 | 1.500 | 1.500 | 62.07 | |
N8 | 80 | 96 | 86 | 96.90 | 1.116 | 1.400 | 1.263 | 1406.7 | 99 | 81 | 99.76 | 1.222 | 2.000 | 1.000 | 54.29 | |
N9 | 100 | 81 | 85 | 97.47 | 0.853 | 1.025 | 1.159 | 1913.8 | 94 | 80 | 99.73 | 1.175 | 1.000 | 2.000 | 59.98 | |
N10 | 200 | 78 | 138 | 97.55 | 0.565 | 1.026 | 1.379 | 6075.4 | 121 | 87 | 99.93 | 1.391 | 2.000 | 1.500 | 334.58 | |
N11 | 300 | 89 | 120 | 98.31 | 0.742 | 1.094 | 1.124 | 12489 | 105 | 100 | 100 | 1.050 | 2.000 | 2.000 | 572.07 | |
N12 | 500 | 155 | 195 | 99.26 | 0.795 | 1.067 | 1.000 | 20435 | 154 | 196 | 99.39 | 0.786 | 1.000 | 2.000 | 93376.28 | |
N13 | 3152 | 822 | 750 | 99.66 | 1.096 | 1.055 | 1.344 | 1.16 | 1024 | 600 | 100 | 1.707 | 2.000 | 2.000 | 187.80 | |
C11 | 16 | 18 | 24 | 92.59 | 0.750 | 1.250 | 1.400 | 54.45 | 20 | 20 | 100 | 1.000 | 1.000 | 1.500 | 0.07 | |
C12 | 17 | 16 | 27 | 92.59 | 0.593 | 1.286 | 1.077 | 60.88 | 20 | 20 | 100 | 1.000 | 1.000 | 1.500 | 0.05 | |
C13 | 16 | 21 | 21 | 90.70 | 1.000 | 1.625 | 1.625 | 52.16 | 25 | 16 | 100 | 1.563 | 1.000 | 1.000 | 0.01 | |
C21 | 25 | 28 | 23 | 93.17 | 1.217 | 1.000 | 1.300 | 98.76 | 30 | 20 | 100 | 1.500 | 2.000 | 1.000 | 0.02 | |
C22 | 25 | 24 | 27 | 92.30 | 0.889 | 1.400 | 1.455 | 94.05 | 20 | 30 | 100 | 0.667 | 2.000 | 1.000 | 0.04 | |
C23 | 25 | 28 | 23 | 93.17 | 1.217 | 1.333 | 1.556 | 103.44 | 30 | 20 | 100 | 1.500 | 2.000 | 1.500 | 0.02 | |
C31 | 28 | 38 | 50 | 94.74 | 0.760 | 1.111 | 1.083 | 154.62 | 30 | 60 | 100 | 0.500 | 2.000 | 1.500 | 0.86 | |
C32 | 29 | 52 | 37 | 93.56 | 1.405 | 1.364 | 1.176 | 149.78 | 44 | 41 | 99.78 | 1.073 | 1.500 | 2.000 | 2.11 | |
C33 | 28 | 40 | 48 | 93.75 | 0.833 | 1.500 | 1.400 | 160.22 | 40 | 45 | 100 | 0.889 | 1.000 | 2.000 | 0.74 | |
C41 | 49 | 54 | 70 | 95.24 | 0.771 | 1.700 | 1.333 | 427.69 | 82 | 44 | 99.78 | 1.864 | 2.000 | 2.000 | 11.28 | |
C42 | 49 | 73 | 52 | 94.84 | 1.404 | 1.433 | 1.364 | 432.15 | 72 | 50 | 100 | 1.440 | 2.000 | 1.500 | 2.65 | |
C43 | 49 | 60 | 63 | 95.24 | 0.952 | 1.308 | 1.100 | 430.27 | 50 | 72 | 100 | 0.694 | 2.000 | 1.000 | 4.05 | |
C51 | 72 | 80 | 70 | 96.43 | 1.143 | 1.353 | 1.188 | 1216.3 | 100 | 54 | 100 | 1.852 | 1.500 | 1.000 | 1.80 | |
C52 | 73 | 73 | 77 | 96.07 | 0.948 | 1.433 | 1.265 | 1300.4 | 100 | 54 | 100 | 1.852 | 2.000 | 2.000 | 0.21 | |
C53 | 72 | 78 | 72 | 96.15 | 1.083 | 1.137 | 1.215 | 1278.2 | 90 | 60 | 100 | 1.500 | 1.000 | 2.000 | 5.06 | |
C61 | 97 | 101 | 99 | 96.01 | 1.020 | 1.172 | 1.020 | 1714.5 | 120 | 80 | 100 | 1.500 | 1.000 | 2.000 | 13.99 | |
C62 | 97 | 108 | 92 | 96.62 | 1.174 | 1.571 | 1.300 | 1807.6 | 128 | 75 | 100 | 1.707 | 2.000 | 2.000 | 2.65 | |
C63 | 97 | 100 | 100 | 96.00 | 1.000 | 1.273 | 1.174 | 1786.3 | 85 | 113 | 99.95 | 0.752 | 1.000 | 1.500 | 83.70 | |
C71 | 196 | 197 | 200 | 97.46 | 0.985 | 1.402 | 1.128 | 6246.2 | 183 | 210 | 99.92 | 0.871 | 1.500 | 2.000 | 3668.73 | |
C72 | 197 | 180 | 219 | 97.41 | 0.822 | 1.308 | 1.190 | 6012.7 | 256 | 150 | 100 | 1.707 | 2.000 | 1.000 | 1.23 | |
C73 | 196 | 238 | 166 | 97.20 | 1.434 | 1.380 | 1.243 | 6175.6 | 194 | 198 | 99.97 | 0.980 | 2.000 | 1.000 | 4621.96 | |
Average | 95.24 | 5614.32 | 99.31 | 3045.99 |
No. | Layout module | Length (m) | Width (m) | Height (m) |
1 | Drilling floor | 33.00 | 24 | 10.00 |
2 | Drilling collar storage area | 9.60 | 2.00 | 1.10 |
3 | Drilling pipe area No.1 | 9.60 | 8.50 | 1.70 |
4 | Drilling pipe area No.2 | 9.60 | 8.50 | 1.70 |
5 | 30in drive pipe area | 12.50 | 2.70 | 2.70 |
6 | 20in drive pipe area | 12.50 | 3.50 | 3.50 |
7 | 13-3/8in drive pipe area | 12.50 | 4.00 | 4.00 |
8 | 9-5/8in drive pipe area | 12.00 | 7.00 | 6.00 |
9 | 7in drive pipe area | 10.50 | 5.00 | 4.20 |
10 | Flatwise marine riser area | 23.00 | 13.00 | 7.00 |
11 | Vertical marine riser area | 32.00 | 10.00 | 23.00 |
12 | Pipe conveyor area | 24.00 | 4.00 | 10.00 |
13 | Bop area | 28.50 | 10.00 | 3.80 |
14 | Christmas tree area | 20.00 | 9.50 | 3.80 |
15 | Mud purification area | 18.00 | 16.50 | 2.00 |
16 | Living quarters | 38.00 | 11.00 | 11.00 |
No. | Layout module | Length (m) | Width (m) | Height (m) |
1 | Drilling floor | 33.00 | 24 | 10.00 |
2 | Drilling collar storage area | 9.60 | 2.00 | 1.10 |
3 | Drilling pipe area No.1 | 9.60 | 8.50 | 1.70 |
4 | Drilling pipe area No.2 | 9.60 | 8.50 | 1.70 |
5 | 30in drive pipe area | 12.50 | 2.70 | 2.70 |
6 | 20in drive pipe area | 12.50 | 3.50 | 3.50 |
7 | 13-3/8in drive pipe area | 12.50 | 4.00 | 4.00 |
8 | 9-5/8in drive pipe area | 12.00 | 7.00 | 6.00 |
9 | 7in drive pipe area | 10.50 | 5.00 | 4.20 |
10 | Flatwise marine riser area | 23.00 | 13.00 | 7.00 |
11 | Vertical marine riser area | 32.00 | 10.00 | 23.00 |
12 | Pipe conveyor area | 24.00 | 4.00 | 10.00 |
13 | Bop area | 28.50 | 10.00 | 3.80 |
14 | Christmas tree area | 20.00 | 9.50 | 3.80 |
15 | Mud purification area | 18.00 | 16.50 | 2.00 |
16 | Living quarters | 38.00 | 11.00 | 11.00 |
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