# Best known solution and lower bound for each instance

 Best Known Solution for 2BP|O|F (the items are Oriented and cutting is Free) CLASS 1 N = 20 N = 40 N = 60 N = 80 N = 100 Instance Lb* Ub* Lb* Ub* Lb* Ub* Lb* Ub* Lb* Ub* 1 8 8 10 10 22 23 24 25 28 28 2 5 5 12 12 18 19 26 26 31 31 3 9 9 17 17 21 21 27 27 29 29 4 6 6 14 14 22 22 27 27 30 30 5 6 6 15 15 19 19 26 26 32 32 6 9 9 14 14 17 17 28 28 37 37 7 6 6 11 11 15 16 31 31 28 28 8 6 6 19 19 21 21 29 29 33 33 9 8 8 11 11 18 18 30 30 31 31 10 8 8 11 11 24 24 26 26 38 38 71 71 134 134 197 200 274 275 317 317 CLASS 2 N = 20 N = 40 N = 60 N = 80 N = 100 Instance Lb* Ub* Lb* Ub* Lb* Ub* Lb* Ub* Lb* Ub* 1 1 1 1 1 3 3 3 3 4 4 2 1 1 2 2 2 2 3 3 4 4 3 1 1 2 2 3 3 3 3 3 3 4 1 1 2 2 3 3 3 3 4 4 5 1 1 2 2 2 2 3 3 4 4 6 1 1 2 2 2 2 3 3 4 4 7 1 1 2 2 2 2 3 3 4 4 8 1 1 2 2 3 3 3 3 4 4 9 1 1 2 2 2 2 4 4 4 4 10 1 1 2 2 3 3 3 3 4 4 10 10 19 19 25 25 31 31 39 39 CLASS 3 N = 20 N = 40 N = 60 N = 80 N = 100 Instance Lb* Ub* Lb* Ub* Lb* Ub* Lb* Ub* Lb* Ub* 1 6 6 6 6 16 16 17 17 19 19 2 3 3 8 8 12 13 18 18 22 22 3 6 6 11 11 13 14 17 18 18 19 4 4 4 10 10 14 15 18 18 20 20 5 4 4 12 12 12 12 16 17 22 22 6 7 7 10 10 12 12 20 20 27 27 7 5 5 8 8 11 11 20 20 20 20 8 4 4 13 13 15 15 22 22 23 23 9 5 5 7 8 13 13 21 21 21 22 10 7 7 7 8 18 18 18 18 29 29 51 51 92 94 136 139 187 189 221 223 CLASS 4 N = 20 N = 40 N = 60 N = 80 N = 100 Instance Lb* Ub* Lb* Ub* Lb* Ub* Lb* Ub* Lb* Ub* 1 1 1 1 1 3 3 3 3 3 3 2 1 1 2 2 2 2 3 3 4 4 3 1 1 2 2 2 3 3 3 3 3 4 1 1 2 2 2 3 3 3 4 4 5 1 1 2 2 2 2 3 3 4 4 6 1 1 2 2 2 2 3 3 4 4 7 1 1 2 2 2 2 3 4 3 4 8 1 1 2 2 3 3 3 3 4 4 9 1 1 2 2 2 2 3 4 4 4 10 1 1 2 2 3 3 3 3 4 4 10 10 19 19 23 25 30 32 37 38 CLASS 5 N = 20 N = 40 N = 60 N = 80 N = 100 Instance Lb* Ub* Lb* Ub* Lb* Ub* Lb* Ub* Lb* Ub* 1 8 8 8 8 20 20 22 22 23 24 2 5 5 10 10 17 17 22 23 28 29 3 7 7 15 15 19 19 24 25 24 24 4 5 5 13 13 20 20 25 25 26 26 5 5 5 14 14 15 15 22 23 28 28 6 9 9 12 12 15 16 25 26 34 34 7 6 6 10 10 14 14 27 27 25 25 8 5 5 17 17 19 19 26 26 29 29 9 7 7 10 10 16 16 26 27 27 27 10 8 8 10 10 24 24 22 23 35 35 65 65 119 119 179 180 241 247 279 281 CLASS 6 N = 20 N = 40 N = 60 N = 80 N = 100 Instance Lb* Ub* Lb* Ub* Lb* Ub* Lb* Ub* Lb* Ub* 1 1 1 1 1 2 2 3 3 3 3 2 1 1 1 2 2 2 3 3 3 4 3 1 1 2 2 2 2 3 3 3 3 4 1 1 2 2 2 2 3 3 3 3 5 1 1 2 2 2 2 3 3 3 3 6 1 1 1 2 2 2 3 3 4 4 7 1 1 2 2 2 2 3 3 3 3 8 1 1 2 2 2 2 3 3 3 4 9 1 1 1 1 2 2 3 3 3 3 10 1 1 1 1 3 3 3 3 4 4 10 10 15 17 21 21 30 30 32 34 CLASS 7 N = 20 N = 40 N = 60 N = 80 N = 100 Instance Lb* Ub* Lb* Ub* Lb* Ub* Lb* Ub* Lb* Ub* 1 5 5 10 10 17 17 20 21 27 27 2 5 5 12 12 14 14 25 25 27 27 3 5 5 9 10 17 17 20 21 24 25 4 7 7 14 14 15 15 21 22 26 27 5 6 6 10 10 14 15 23 24 25 25 6 6 6 11 11 15 15 22 23 28 28 7 4 4 11 12 15 15 24 25 27 27 8 7 7 11 11 17 17 22 23 29 29 9 6 6 8 8 14 14 23 24 25 25 10 4 4 13 13 18 19 24 24 31 31 55 55 109 111 156 158 224 232 269 271 CLASS 8 N = 20 N = 40 N = 60 N = 80 N = 100 Instance Lb* Ub* Lb* Ub* Lb* Ub* Lb* Ub* Lb* Ub* 1 6 6 11 12 17 17 22 22 26 27 2 7 7 13 13 17 17 24 24 27 27 3 5 5 11 11 16 17 20 21 24 24 4 7 7 12 12 15 15 20 20 30 31 5 6 6 9 9 14 14 26 26 29 29 6 6 6 12 12 15 15 22 22 26 27 7 5 5 11 11 14 14 22 22 25 26 8 5 5 11 11 17 17 22 22 28 29 9 7 7 9 9 16 17 21 21 27 27 10 4 4 13 13 18 18 24 24 32 32 58 58 112 113 159 161 223 224 274 279 CLASS 9 N = 20 N = 40 N = 60 N = 80 N = 100 Instance Lb* Ub* Lb* Ub* Lb* Ub* Lb* Ub* Lb* Ub* 1 19 19 25 25 46 46 59 59 71 71 2 13 13 32 32 45 45 58 58 64 64 3 14 14 29 29 46 46 57 57 68 68 4 16 16 31 31 44 44 53 53 78 78 5 16 16 27 27 41 41 62 62 65 65 6 14 14 29 29 37 37 62 62 71 71 7 9 9 24 24 41 41 59 59 66 66 8 14 14 26 26 47 47 58 58 74 74 9 15 15 21 21 45 45 49 49 66 66 10 13 13 34 34 45 45 60 60 72 72 143 143 278 278 437 437 577 577 695 695 CLASS 10 N = 20 N = 40 N = 60 N = 80 N = 100 Instance Lb* Ub* Lb* Ub* Lb* Ub* Lb* Ub* Lb* Ub* 1 6 6 8 8 11 12 12 13 14 15 2 3 3 8 8 12 12 10 11 15 16 3 4 4 9 9 11 11 11 11 15 16 4 5 5 6 6 7 8 13 14 17 18 5 4 4 6 6 8 8 14 14 17 18 6 4 4 6 6 13 13 13 13 13 13 7 5 5 7 7 10 10 14 14 13 14 8 3 3 7 7 10 10 10 10 18 18 9 5 5 8 8 8 9 12 13 16 16 10 3 3 9 9 8 8 14 15 15 15 42 42 74 74 98 101 123 128 153 159