Bin Packing Homepage at Jena University


Prof. Dr. Armin Scholl

Dr. Robert Klein

Chair of Business Administration and Decision Analysis
Friedrich-Schiller-University Jena

Chair of Operations Research
Darmstadt University of Technology


Data set 1 for BPP-1

* The data can be downloaded by clicking here. The data files have extensions ".bpp".

Notation

parametermeaning
nnumber of items
wjweight (size) of item j (j=1,...,n)
cbin capacity
m*minimal number of bins

Parameter setting

parametervalues
n50, 100, 200, 500
c100, 120, 150
wjfrom [1,100], [20,100], [30,100] for j=1,...,n

The weights are chosen as integer values from the given intervals using uniformly distributed random numbers. For each of the 36 instance classes defined by the settings above, 20 instances are generated resulting in a total of 720 instances. In contrast to Martello and Toth (1990), we omit instances with wj from [50,100], because these instances are very simple and are solved by applying the simple reduction procedure MTRP. In order to avoid such simple cases for each bin capacity, we instead use the third interval given above.

Name conventions:

The instances are given names "NxCyWz_v.BPP" where
  • x=1 (for n=50), x=2 (n=100), x=3 (n=200), x=4 (n=500)
  • y=1 (for c=100), y=2 (c=120), y=3 (c=150)
  • z=1 (for wj from [1,100]), z=2 ([20,100]), z=4 ([30,100])
  • v=A..T for the 20 instances of each class

Instances and minimal number of bins

Namem*Namem*Namem*
N1C1W1_A 25 N1C1W1_B 31 N1C1W1_C 20
N1C1W1_D 28 N1C1W1_E 26 N1C1W1_F 27
N1C1W1_G 25 N1C1W1_H 31 N1C1W1_I 25
N1C1W1_J 26 N1C1W1_K 26 N1C1W1_L 33
N1C1W1_M 30 N1C1W1_N 25 N1C1W1_O 32
N1C1W1_P 26 N1C1W1_Q 28 N1C1W1_R 25
N1C1W1_S 28 N1C1W1_T 28 N1C1W2_A 29
N1C1W2_B 30 N1C1W2_C 33 N1C1W2_D 31
N1C1W2_E 36 N1C1W2_F 30 N1C1W2_G 30
N1C1W2_H 33 N1C1W2_I 35 N1C1W2_J 34
N1C1W2_K 35 N1C1W2_L 31 N1C1W2_M 30
N1C1W2_N 33 N1C1W2_O 29 N1C1W2_P 33
N1C1W2_Q 36 N1C1W2_R 34 N1C1W2_S 37
N1C1W2_T 38 N1C1W4_A 35 N1C1W4_B 40
N1C1W4_C 36 N1C1W4_D 38 N1C1W4_E 38
N1C1W4_F 32 N1C1W4_G 37 N1C1W4_H 40
N1C1W4_I 35 N1C1W4_J 37 N1C1W4_K 41
N1C1W4_L 35 N1C1W4_M 41 N1C1W4_N 39
N1C1W4_O 34 N1C1W4_P 38 N1C1W4_Q 34
N1C1W4_R 38 N1C1W4_S 36 N1C1W4_T 42
N1C2W1_A 21 N1C2W1_B 26 N1C2W1_C 23
N1C2W1_D 21 N1C2W1_E 17 N1C2W1_F 22
N1C2W1_G 21 N1C2W1_H 23 N1C2W1_I 27
N1C2W1_J 27 N1C2W1_K 24 N1C2W1_L 25
N1C2W1_M 26 N1C2W1_N 21 N1C2W1_O 15
N1C2W1_P 21 N1C2W1_Q 24 N1C2W1_R 23
N1C2W1_S 22 N1C2W1_T 22 N1C2W2_A 24
N1C2W2_B 27 N1C2W2_C 29 N1C2W2_D 24
N1C2W2_E 33 N1C2W2_F 26 N1C2W2_G 29
N1C2W2_H 23 N1C2W2_I 25 N1C2W2_J 25
N1C2W2_K 29 N1C2W2_L 30 N1C2W2_M 30
N1C2W2_N 26 N1C2W2_O 29 N1C2W2_P 23
N1C2W2_Q 30 N1C2W2_R 25 N1C2W2_S 24
N1C2W2_T 26 N1C2W4_A 29 N1C2W4_B 32
N1C2W4_C 30 N1C2W4_D 28 N1C2W4_E 30
N1C2W4_F 32 N1C2W4_G 30 N1C2W4_H 30
N1C2W4_I 35 N1C2W4_J 30 N1C2W4_K 32
N1C2W4_L 31 N1C2W4_M 31 N1C2W4_N 32
N1C2W4_O 30 N1C2W4_P 28 N1C2W4_Q 33
N1C2W4_R 35 N1C2W4_S 38 N1C2W4_T 29
N1C3W1_A 16 N1C3W1_B 16 N1C3W1_C 17
N1C3W1_D 19 N1C3W1_E 16 N1C3W1_F 20
N1C3W1_G 15 N1C3W1_H 19 N1C3W1_I 17
N1C3W1_J 16 N1C3W1_K 17 N1C3W1_L 17
N1C3W1_M 17 N1C3W1_N 20 N1C3W1_O 16
N1C3W1_P 19 N1C3W1_Q 20 N1C3W1_R 21
N1C3W1_S 16 N1C3W1_T 18 N1C3W2_A 19
N1C3W2_B 20 N1C3W2_C 22 N1C3W2_D 20
N1C3W2_E 21 N1C3W2_F 23 N1C3W2_G 23
N1C3W2_H 23 N1C3W2_I 19 N1C3W2_J 22
N1C3W2_K 21 N1C3W2_L 21 N1C3W2_M 21
N1C3W2_N 22 N1C3W2_O 21 N1C3W2_P 18
N1C3W2_Q 19 N1C3W2_R 19 N1C3W2_S 21
N1C3W2_T 22 N1C3W4_A 21 N1C3W4_B 22
N1C3W4_C 24 N1C3W4_D 21 N1C3W4_E 23
N1C3W4_F 21 N1C3W4_G 23 N1C3W4_H 23
N1C3W4_I 23 N1C3W4_J 22 N1C3W4_K 24
N1C3W4_L 20 N1C3W4_M 21 N1C3W4_N 21
N1C3W4_O 22 N1C3W4_P 25 N1C3W4_Q 25
N1C3W4_R 22 N1C3W4_S 22 N1C3W4_T 24
N2C1W1_A 48 N2C1W1_B 49 N2C1W1_C 46
N2C1W1_D 50 N2C1W1_E 58 N2C1W1_F 50
N2C1W1_G 60 N2C1W1_H 52 N2C1W1_I 62
N2C1W1_J 59 N2C1W1_K 55 N2C1W1_L 55
N2C1W1_M 46 N2C1W1_N 48 N2C1W1_O 48
N2C1W1_P 54 N2C1W1_Q 46 N2C1W1_R 56
N2C1W1_S 45 N2C1W1_T 52 N2C1W2_A 64
N2C1W2_B 61 N2C1W2_C 68 N2C1W2_D 74
N2C1W2_E 65 N2C1W2_F 65 N2C1W2_G 73
N2C1W2_H 70 N2C1W2_I 67 N2C1W2_J 67
N2C1W2_K 72 N2C1W2_L 62 N2C1W2_M 65
N2C1W2_N 64 N2C1W2_O 64 N2C1W2_P 68
N2C1W2_Q 65 N2C1W2_R 67 N2C1W2_S 66
N2C1W2_T 66 N2C1W4_A 73 N2C1W4_B 71
N2C1W4_C 77 N2C1W4_D 82 N2C1W4_E 73
N2C1W4_F 77 N2C1W4_G 71 N2C1W4_H 75
N2C1W4_I 73 N2C1W4_J 74 N2C1W4_K 70
N2C1W4_L 75 N2C1W4_M 72 N2C1W4_N 71
N2C1W4_O 80 N2C1W4_P 67 N2C1W4_Q 75
N2C1W4_R 70 N2C1W4_S 80 N2C1W4_T 70
N2C2W1_A 42 N2C2W1_B 50 N2C2W1_C 40
N2C2W1_D 42 N2C2W1_E 40 N2C2W1_F 49
N2C2W1_G 45 N2C2W1_H 46 N2C2W1_I 45
N2C2W1_J 42 N2C2W1_K 41 N2C2W1_L 49
N2C2W1_M 44 N2C2W1_N 43 N2C2W1_O 50
N2C2W1_P 46 N2C2W1_Q 49 N2C2W1_R 41
N2C2W1_S 43 N2C2W1_T 39 N2C2W2_A 52
N2C2W2_B 56 N2C2W2_C 53 N2C2W2_D 51
N2C2W2_E 54 N2C2W2_F 48 N2C2W2_G 53
N2C2W2_H 53 N2C2W2_I 49 N2C2W2_J 56
N2C2W2_K 50 N2C2W2_L 52 N2C2W2_M 54
N2C2W2_N 51 N2C2W2_O 50 N2C2W2_P 50
N2C2W2_Q 54 N2C2W2_R 51 N2C2W2_S 58
N2C2W2_T 56 N2C2W4_A 57 N2C2W4_B 60
N2C2W4_C 65 N2C2W4_D 61 N2C2W4_E 60
N2C2W4_F 57 N2C2W4_G 61 N2C2W4_H 61
N2C2W4_I 58 N2C2W4_J 60 N2C2W4_K 59
N2C2W4_L 57 N2C2W4_M 60 N2C2W4_N 63
N2C2W4_O 62 N2C2W4_P 60 N2C2W4_Q 62
N2C2W4_R 56 N2C2W4_S 55 N2C2W4_T 57
N2C3W1_A 35 N2C3W1_B 35 N2C3W1_C 35
N2C3W1_D 37 N2C3W1_E 34 N2C3W1_F 35
N2C3W1_G 33 N2C3W1_H 35 N2C3W1_I 34
N2C3W1_J 33 N2C3W1_K 36 N2C3W1_L 35
N2C3W1_M 31 N2C3W1_N 32 N2C3W1_O 35
N2C3W1_P 35 N2C3W1_Q 34 N2C3W1_R 33
N2C3W1_S 36 N2C3W1_T 35 N2C3W2_A 41
N2C3W2_B 43 N2C3W2_C 41 N2C3W2_D 41
N2C3W2_E 39 N2C3W2_F 39 N2C3W2_G 41
N2C3W2_H 38 N2C3W2_I 44 N2C3W2_J 43
N2C3W2_K 42 N2C3W2_L 41 N2C3W2_M 43
N2C3W2_N 41 N2C3W2_O 45 N2C3W2_P 41
N2C3W2_Q 41 N2C3W2_R 40 N2C3W2_S 43
N2C3W2_T 43 N2C3W4_A 43 N2C3W4_B 45
N2C3W4_C 42 N2C3W4_D 44 N2C3W4_E 47
N2C3W4_F 45 N2C3W4_G 44 N2C3W4_H 44
N2C3W4_I 44 N2C3W4_J 43 N2C3W4_K 47
N2C3W4_L 45 N2C3W4_M 44 N2C3W4_N 45
N2C3W4_O 45 N2C3W4_P 45 N2C3W4_Q 46
N2C3W4_R 42 N2C3W4_S 42 N2C3W4_T 46
N3C1W1_A 105 N3C1W1_B 114 N3C1W1_C 99
N3C1W1_D 108 N3C1W1_E 98 N3C1W1_F 113
N3C1W1_G 111 N3C1W1_H 104 N3C1W1_I 100
N3C1W1_J 108 N3C1W1_K 102 N3C1W1_L 97
N3C1W1_M 106 N3C1W1_N 93 N3C1W1_O 98
N3C1W1_P 108 N3C1W1_Q 98 N3C1W1_R 99
N3C1W1_S 100 N3C1W1_T 102 N3C1W2_A 125
N3C1W2_B 126 N3C1W2_C 125 N3C1W2_D 139
N3C1W2_E 132 N3C1W2_F 123 N3C1W2_G 132
N3C1W2_H 129 N3C1W2_I 126 N3C1W2_J 126
N3C1W2_K 120 N3C1W2_L 136 N3C1W2_M 136
N3C1W2_N 136 N3C1W2_O 127 N3C1W2_P 126
N3C1W2_Q 135 N3C1W2_R 123 N3C1W2_S 130
N3C1W2_T 136 N3C1W4_A 149 N3C1W4_B 149
N3C1W4_C 146 N3C1W4_D 148 N3C1W4_E 142
N3C1W4_F 140 N3C1W4_G 148 N3C1W4_H 141
N3C1W4_I 140 N3C1W4_J 142 N3C1W4_K 147
N3C1W4_L 148 N3C1W4_M 149 N3C1W4_N 148
N3C1W4_O 143 N3C1W4_P 143 N3C1W4_Q 146
N3C1W4_R 145 N3C1W4_S 145 N3C1W4_T 146
N3C2W1_A 91 N3C2W1_B 82 N3C2W1_C 84
N3C2W1_D 85 N3C2W1_E 87 N3C2W1_F 88
N3C2W1_G 87 N3C2W1_H 87 N3C2W1_I 87
N3C2W1_J 87 N3C2W1_K 77 N3C2W1_L 91
N3C2W1_M 85 N3C2W1_N 91 N3C2W1_O 82
N3C2W1_P 88 N3C2W1_Q 82 N3C2W1_R 82
N3C2W1_S 89 N3C2W1_T 83 N3C2W2_A 107
N3C2W2_B 105 N3C2W2_C 104 N3C2W2_D 107
N3C2W2_E 116 N3C2W2_F 106 N3C2W2_G 102
N3C2W2_H 117 N3C2W2_I 102 N3C2W2_J 107
N3C2W2_K 110 N3C2W2_L 105 N3C2W2_M 108
N3C2W2_N 105 N3C2W2_O 107 N3C2W2_P 107
N3C2W2_Q 105 N3C2W2_R 110 N3C2W2_S 107
N3C2W2_T 107 N3C2W4_A 113 N3C2W4_B 112
N3C2W4_C 132 N3C2W4_D 114 N3C2W4_E 110
N3C2W4_F 115 N3C2W4_G 122 N3C2W4_H 113
N3C2W4_I 115 N3C2W4_J 120 N3C2W4_K 117
N3C2W4_L 116 N3C2W4_M 120 N3C2W4_N 117
N3C2W4_O 113 N3C2W4_P 122 N3C2W4_Q 118
N3C2W4_R 123 N3C2W4_S 118 N3C2W4_T 119
N3C3W1_A 66 N3C3W1_B 71 N3C3W1_C 69
N3C3W1_D 63 N3C3W1_E 68 N3C3W1_F 69
N3C3W1_G 65 N3C3W1_H 69 N3C3W1_I 68
N3C3W1_J 65 N3C3W1_K 63 N3C3W1_L 68
N3C3W1_M 71 N3C3W1_N 69 N3C3W1_O 66
N3C3W1_P 72 N3C3W1_Q 73 N3C3W1_R 66
N3C3W1_S 68 N3C3W1_T 70 N3C3W2_A 84
N3C3W2_B 81 N3C3W2_C 82 N3C3W2_D 79
N3C3W2_E 79 N3C3W2_F 81 N3C3W2_G 81
N3C3W2_H 82 N3C3W2_I 79 N3C3W2_J 83
N3C3W2_K 83 N3C3W2_L 82 N3C3W2_M 83
N3C3W2_N 77 N3C3W2_O 82 N3C3W2_P 80
N3C3W2_Q 76 N3C3W2_R 79 N3C3W2_S 80
N3C3W2_T 79 N3C3W4_A 89 N3C3W4_B 88
N3C3W4_C 88 N3C3W4_D 87 N3C3W4_E 85
N3C3W4_F 84 N3C3W4_G 94 N3C3W4_H 84
N3C3W4_I 92 N3C3W4_J 88 N3C3W4_K 89
N3C3W4_L 90 N3C3W4_M 88 N3C3W4_N 87
N3C3W4_O 87 N3C3W4_P 86 N3C3W4_Q 87
N3C3W4_R 87 N3C3W4_S 84 N3C3W4_T 85
N4C1W1_A 240 N4C1W1_B 262 N4C1W1_C 241
N4C1W1_D 246 N4C1W1_E 272 N4C1W1_F 265
N4C1W1_G 259 N4C1W1_H 251 N4C1W1_I 262
N4C1W1_J 288 N4C1W1_K 253 N4C1W1_L 258
N4C1W1_M 246 N4C1W1_N 256 N4C1W1_O 258
N4C1W1_P 271 N4C1W1_Q 277 N4C1W1_R 254
N4C1W1_S 261 N4C1W1_T 256 N4C1W2_A 317
N4C1W2_B 328 N4C1W2_C 319 N4C1W2_D 327
N4C1W2_E 310 N4C1W2_F 321 N4C1W2_G 307
N4C1W2_H 315 N4C1W2_I 304 N4C1W2_J 311
N4C1W2_K 311 N4C1W2_L 316 N4C1W2_M 330
N4C1W2_N 311 N4C1W2_O 319 N4C1W2_P 317
N4C1W2_Q 319 N4C1W2_R 319 N4C1W2_S 312
N4C1W2_T 323 N4C1W4_A 368 N4C1W4_B 349
N4C1W4_C 365 N4C1W4_D 359 N4C1W4_E 373
N4C1W4_F 369 N4C1W4_G 362 N4C1W4_H 359
N4C1W4_I 359 N4C1W4_J 368 N4C1W4_K 371
N4C1W4_L 355 N4C1W4_M 360 N4C1W4_N 363
N4C1W4_O 351 N4C1W4_P 363 N4C1W4_Q 359
N4C1W4_R 370 N4C1W4_S 359 N4C1W4_T 355
N4C2W1_A 210 N4C2W1_B 213 N4C2W1_C 213
N4C2W1_D 200 N4C2W1_E 215 N4C2W1_F 203
N4C2W1_G 211 N4C2W1_H 215 N4C2W1_I 209
N4C2W1_J 202 N4C2W1_K 210 N4C2W1_L 209
N4C2W1_M 217 N4C2W1_N 210 N4C2W1_O 212
N4C2W1_P 212 N4C2W1_Q 210 N4C2W1_R 212
N4C2W1_S 210 N4C2W1_T 212 N4C2W2_A 253
N4C2W2_B 254 N4C2W2_C 249 N4C2W2_D 258
N4C2W2_E 257 N4C2W2_F 272 N4C2W2_G 252
N4C2W2_H 255 N4C2W2_I 262 N4C2W2_J 256
N4C2W2_K 259 N4C2W2_L 263 N4C2W2_M 261
N4C2W2_N 264 N4C2W2_O 253 N4C2W2_P 266
N4C2W2_Q 257 N4C2W2_R 256 N4C2W2_S 273
N4C2W2_T 256 N4C2W4_A 293 N4C2W4_B 281
N4C2W4_C 295 N4C2W4_D 295 N4C2W4_E 287
N4C2W4_F 304 N4C2W4_G 291 N4C2W4_H 296
N4C2W4_I 287 N4C2W4_J 300 N4C2W4_K 289
N4C2W4_L 297 N4C2W4_M 287 N4C2W4_N 299
N4C2W4_O 293 N4C2W4_P 301 N4C2W4_Q 293
N4C2W4_R 300 N4C2W4_S 293 N4C2W4_T 287
N4C3W1_A 164 N4C3W1_B 165 N4C3W1_C 166
N4C3W1_D 158 N4C3W1_E 165 N4C3W1_F 164
N4C3W1_G 169 N4C3W1_H 170 N4C3W1_I 167
N4C3W1_J 169 N4C3W1_K 164 N4C3W1_L 163
N4C3W1_M 167 N4C3W1_N 176 N4C3W1_O 169
N4C3W1_P 167 N4C3W1_Q 176 N4C3W1_R 167
N4C3W1_S 168 N4C3W1_T 173 N4C3W2_A 203
N4C3W2_B 203 N4C3W2_C 201 N4C3W2_D 201
N4C3W2_E 200 N4C3W2_F 209 N4C3W2_G 201
N4C3W2_H 201 N4C3W2_I 198 N4C3W2_J 204
N4C3W2_K 204 N4C3W2_L 201 N4C3W2_M 198
N4C3W2_N 198 N4C3W2_O 209 N4C3W2_P 202
N4C3W2_Q 199 N4C3W2_R 194 N4C3W2_S 196
N4C3W2_T 195 N4C3W4_A 216 N4C3W4_B 215
N4C3W4_C 218 N4C3W4_D 215 N4C3W4_E 219
N4C3W4_F 222 N4C3W4_G 222 N4C3W4_H 219
N4C3W4_I 224 N4C3W4_J 213 N4C3W4_K 215
N4C3W4_L 219 N4C3W4_M 216 N4C3W4_N 225
N4C3W4_O 226 N4C3W4_P 219 N4C3W4_Q 222
N4C3W4_R 214 N4C3W4_S 216 N4C3W4_T 216

Acknowledgment

Originally, 16 instances remained open, i.e., the optimal solutions were not known. In the meantime these instances have been solved by methods of:
  • Schwerin, P. and G. Wäscher: The bin-packing problem: A problem generator and some numerical experiments with FFD packing and MTP. International Transactions in Operational Research 4 (1997), pp. 377-389.
  • Fleszar, K. and K. Hindi: New heuristics for one-dimensional bin packing. Computers & Operations Research 29 (2002), 821-839.
  • Alvim, A.C.F., C.C. Ribeiro, F. Glover, and D.J. Aloise: A hybrid improvement heuristic for the one-dimensional bin packing problem. Working Paper, Catholic University of Rio de Janeiro, Brazil, 2002.
  • Schoenfield, J.E.: Fast, exact solution of open bin packing problems without linear programming. Working Paper, 2002.

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Last updated: 09/01/03 by Armin Scholl