Advances in Operations Research

Research Article

An Exact Method for the 2D Guillotine Strip Packing Problem

Table 4

Results obtained by dichotomic and branch-and-bound algorithms on random instances.
ProblemBound Dichotomic B&B
Class LB UB T(sec) T (sec)
10 10 35.50 36 35.50 10 0.01 35.50 10 112.32
15 45.90 49.10 46.90 10 221.60 46.70 9 999.67
20 63.50 66.70 65 10 1112.25 65.70 6 2151.81
25 82.10 84.80 84 10 1758.08 85 3 1854.33
Avg 56.86 59.15 57.88 10.00 772.99 58.23 7 1279.53
30 10 10.20 11.30 10.70 10 0.01 10.70 10 301.21
15 16.40 19.40 17.10 10 137.78 18.30 5 1267.74
20 19.60 21.70 20.80 10 612.82 20.90 3 2921.28
25 26.90 29.40 28.20 10 955.14 29.30 3 2663.98
Avg 18.28 20.45 19.20 10.00 426.44 19.80 5.25 1788.55
40 10 31.90 34.90 33.80 10 0.07 34.40 10 516.54
15 147 153.60 147.50 10 171.80 149.30 5 1592.42
20 169 176.20 172.80 10 810.37 175.40 4 3004.14
25 220.20 232.60 227.20 8 1008.53 232 2 1518.21
Avg 142.03 149.33 145.33 9.50 497.69 147.78 5.25 1657.83
100 10 37 41.70 40.80 10 1.01 40.80 10 960.26
15 49.40 59.90 54.50 10 465.60 55.50 4 968.76
20 60.80 67.60 63.60 10 854.63 68.20 4 1975.87
25 84.60 98.80 90.60 6 937.73 97.20 4 2980.43
Avg 57.95 67.00 62.38 9.00 564.74 65.43 3600 5.50 2381.27
100 10 320.92 330 321.40 10 1.98 321.40 10 111.04
15 403.50 434.40 419.50 10 319.54 421.50 5 812.22
20 569.90 593.00 581.10 8 1213.28 583 5 722.19
25 624.17 694.67 665 1 3489.31 689.17 0 3600
Avg 478.37 513.02 496.75 7.25 1256.03 503.77 5 1311.36
300 10 108.10 122.70 118.30 10 0.17 118.30 10 429.45
15 121.20 144.10 128.60 10 231.44 136.70 2 2512.21
20 168.03 195.80 179.20 9 2012.20 193.50 1 3600
25 220 261.60 248 1 3512.89 250.10 1 2851.1
Avg 154.33 181.05 168.53 7.50 1439.17 174.65 3.50 2348.19
100 10 337.30 338.70 338.40 10 3.56 338.40 10 5
15 532 532.20 532.10 10 2.20 542.30 10 3.6
20 731.30 738.10 738.10 10 466.15 738.10 10 332.8
25 707.70 715.20 714.60 6 1735.13 710.80 7 1342.76
Avg 577.08 581.05 580.80 9.00 551.76 582.40 9.25 421.04
100 10 247.10 285.50 267.60 10 2.94 263.90 10 752.9
15 396.32 435.10 421.80 10 1153.48 433.10 6 2821.2
20 507.50 571.75 559 7 3086.11 561.50 2 3600
25 635.17 771 693.67 6 3475.83 701.70 1 1880.4
Avg 446.52 485.52 485.52 8.25 1929.59 490.05 4.75 2263.63
100 10 543.70 544.50 543.70 10 0.54 543.70 10 30.7
15 871.20 871.20 871.20 10 0.10 871.20 10 59.8
20 1155.50 1159.80 1155.50 10 0.01 1159.70 9 432.3
25 1476.90 1479 1477 10 0.26 1479 8 754.1
Avg 1011.83 1013.65 1011.85 10.00 0.23 1013.40 9.25 319.23
100 10 163.40 174.90 170.60 10 0.12 170.5 10 343.2
15 253.01 268.90 258.50 10 243.07 265.10 4 2500.3
20 345.60 378.40 365.10 10 1637.05 375 4 2871.2
25 388.22 416 408.89 5 2581.66 419.67 1 3600
Avg 287.56 309.55 300.77 8.75 1115.47 307.57 4.75 2328.68