我的 MILP 问题基于简单但大量的约束和变量。
- 大多数决策变量是“半”类型的（例如生产数量、运输数量等）
- S( wijk ) 是整数类型（一行的移位数）
- 数据：delta、theta、alpha、lambda、N( ijw )、Mmin( ijk )、Mmax( ijk )、V0( ik )、D wijk
问题公式在小规模上达到了最佳解决方案，但对于较大规模，它只是在某个“间隙”处“停滞”并且不会向前发展
一种。小规模问题规模：少于 15 周（计划范围）
b. 更大规模问题的规模：>= 15 周
问题输入法：.lp 文件（因此在命令提示符下使用 lp.py 脚本解决）
gurobi 版本：6.0（学术许可）
关于我可以做些什么来获得较大案例的最佳解决方案的任何建议？
以下是 15 周和 124 种产品的示例输出日志。
C:\gurobi600\win64\python27\bin>gurobi lp.py model124
Optimize a model with 40146 rows, 61820 columns and 160660 nonzeros
Coefficient statistics:
Matrix range [1e+00, 1e+04]
Objective range [3e-01, 3e+01]
Bounds range [0e+00, 0e+00]
RHS range [8e+00, 5e+04]
Presolve removed 25296 rows and 23436 columns
Presolve time: 0.15s
Presolved: 14850 rows, 38384 columns, 87748 nonzeros
Variable types: 34754 continuous, 3630 integer (0 binary)
Root relaxation: objective 4.221641e+08, 20576 iterations, 0.27 seconds
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 4.2216e+08 0 1394 - 4.2216e+08 - - 0s
H 0 0 4.344708e+08 4.2216e+08 2.83% - 1s
H 0 0 4.269043e+08 4.2216e+08 1.11% - 1s
0 0 4.2246e+08 0 1296 4.2690e+08 4.2246e+08 1.04% - 1s
0 0 4.2255e+08 0 1199 4.2690e+08 4.2255e+08 1.02% - 1s
0 0 4.2260e+08 0 1141 4.2690e+08 4.2260e+08 1.01% - 1s
0 0 4.2260e+08 0 1140 4.2690e+08 4.2260e+08 1.01% - 1s
0 0 4.2260e+08 0 1139 4.2690e+08 4.2260e+08 1.01% - 1s
0 0 4.2260e+08 0 1135 4.2690e+08 4.2260e+08 1.01% - 2s
0 0 4.2260e+08 0 1395 4.2690e+08 4.2260e+08 1.01% - 2s
H 0 0 4.267905e+08 4.2260e+08 0.98% - 3s
0 0 4.2260e+08 0 1147 4.2679e+08 4.2260e+08 0.98% - 3s
H 0 0 4.261854e+08 4.2260e+08 0.84% - 3s
0 0 4.2263e+08 0 1117 4.2619e+08 4.2263e+08 0.84% - 3s
0 0 4.2263e+08 0 1116 4.2619e+08 4.2263e+08 0.84% - 3s
0 0 4.2263e+08 0 1116 4.2619e+08 4.2263e+08 0.84% - 3s
0 0 4.2263e+08 0 1114 4.2619e+08 4.2263e+08 0.84% - 3s
0 2 4.2263e+08 0 1114 4.2619e+08 4.2263e+08 0.84% - 4s
18 17 4.2263e+08 9 1105 4.2619e+08 4.2263e+08 0.84% 21.8 5s
H 27 27 4.261065e+08 4.2263e+08 0.82% 16.3 5s
H 56 57 4.260888e+08 4.2263e+08 0.81% 11.7 5s
H 57 59 4.260728e+08 4.2263e+08 0.81% 11.6 5s
H 176 176 4.257390e+08 4.2263e+08 0.73% 10.1 6s
H 363 366 4.257251e+08 4.2263e+08 0.73% 9.9 9s
451 450 4.2271e+08 153 1009 4.2573e+08 4.2263e+08 0.73% 9.6 10s
H 474 476 4.254454e+08 4.2263e+08 0.66% 9.4 10s
H 815 816 4.253518e+08 4.2263e+08 0.64% 9.5 13s
984 985 4.2281e+08 336 880 4.2535e+08 4.2263e+08 0.64% 9.5 15s
H 1000 999 4.253516e+08 4.2263e+08 0.64% 9.4 15s
H 1086 1085 4.253373e+08 4.2263e+08 0.64% 9.4 16s
H 1482 1473 4.253030e+08 4.2263e+08 0.63% 9.2 19s
1505 1505 4.2297e+08 536 730 4.2530e+08 4.2263e+08 0.63% 9.1 20s
H 1552 1546 4.252662e+08 4.2263e+08 0.62% 9.0 20s
H 1577 1580 4.252426e+08 4.2263e+08 0.62% 9.0 21s
H 1622 1610 4.252100e+08 4.2263e+08 0.61% 8.9 21s
H 1746 1743 4.251278e+08 4.2263e+08 0.59% 8.7 22s
H 1779 1782 4.250611e+08 4.2263e+08 0.57% 8.6 23s
H 1828 1820 4.250061e+08 4.2263e+08 0.56% 8.5 23s
H 1878 1868 4.250016e+08 4.2263e+08 0.56% 8.4 23s
H 1931 1917 4.249827e+08 4.2263e+08 0.55% 8.3 24s
H 1978 1954 4.248879e+08 4.2263e+08 0.53% 8.3 24s
H 2003 2003 4.247702e+08 4.2263e+08 0.50% 8.2 39s
H 2004 2003 4.243849e+08 4.2263e+08 0.41% 8.2 39s
2007 2008 4.2331e+08 713 604 4.2438e+08 4.2263e+08 0.41% 8.2 40s
H 2450 2450 4.242743e+08 4.2263e+08 0.39% 7.4 45s
H 2505 2478 4.242170e+08 4.2263e+08 0.38% 7.3 47s
2614 2614 4.2371e+08 921 450 4.2422e+08 4.2263e+08 0.38% 7.1 50s
H 2898 2900 4.242040e+08 4.2263e+08 0.37% 6.9 54s
2899 2897 4.2385e+08 1011 397 4.2420e+08 4.2263e+08 0.37% 6.9 55s
3652 3643 4.2416e+08 1247 242 4.2420e+08 4.2263e+08 0.37% 6.5 60s
3980 3911 4.2265e+08 12 1080 4.2420e+08 4.2265e+08 0.37% 11.6 65s
4402 4192 4.2298e+08 119 1002 4.2420e+08 4.2265e+08 0.37% 11.3 71s
4739 4415 4.2313e+08 206 936 4.2420e+08 4.2265e+08 0.37% 11.2 75s
5194 4723 4.2327e+08 327 863 4.2420e+08 4.2265e+08 0.37% 11.0 81s
5600 4990 4.2335e+08 430 800 4.2420e+08 4.2265e+08 0.37% 10.9 85s
6055 5294 4.2347e+08 544 722 4.2420e+08 4.2265e+08 0.37% 10.7 91s
6526 5610 4.2357e+08 662 647 4.2420e+08 4.2265e+08 0.37% 10.6 96s
6840 5818 4.2364e+08 743 579 4.2420e+08 4.2265e+08 0.37% 10.5 100s
7381 6177 4.2376e+08 880 481 4.2420e+08 4.2265e+08 0.37% 10.4 106s
7745 6422 4.2383e+08 970 414 4.2420e+08 4.2265e+08 0.37% 10.3 110s
7955 6560 4.2386e+08 1024 370 4.2420e+08 4.2265e+08 0.37% 10.3 119s
8079 6642 4.2388e+08 1055 342 4.2420e+08 4.2265e+08 0.37% 10.3 121s
8574 6974 4.2399e+08 1180 242 4.2420e+08 4.2265e+08 0.37% 10.1 126s
9087 7317 4.2413e+08 1313 174 4.2420e+08 4.2265e+08 0.37% 9.9 131s
H 9675 6763 4.240515e+08 4.2265e+08 0.33% 9.7 139s
9677 6760 cutoff 1472 4.2405e+08 4.2265e+08 0.33% 9.7 142s
H 9913 6697 4.240485e+08 4.2266e+08 0.33% 9.7 148s
H 9914 6503 4.240433e+08 4.2266e+08 0.33% 9.7 148s
9915 6510 4.2282e+08 70 1044 4.2404e+08 4.2266e+08 0.33% 9.7 151s
10194 6691 4.2295e+08 137 1002 4.2404e+08 4.2266e+08 0.33% 9.6 157s
10196 6695 4.2295e+08 137 1003 4.2404e+08 4.2266e+08 0.33% 9.6 160s
10843 7125 4.2327e+08 297 881 4.2404e+08 4.2266e+08 0.33% 9.6 167s
11170 7343 4.2335e+08 376 835 4.2404e+08 4.2266e+08 0.33% 9.5 171s
H11485 7331 4.240303e+08 4.2266e+08 0.32% 9.5 176s
11651 7447 4.2345e+08 455 798 4.2403e+08 4.2266e+08 0.32% 9.5 180s
12009 7680 4.2356e+08 548 735 4.2403e+08 4.2266e+08 0.32% 9.4 186s
H12010 7497 4.240210e+08 4.2266e+08 0.32% 9.4 186s
12011 7500 4.2356e+08 548 734 4.2402e+08 4.2266e+08 0.32% 9.4 190s
12748 7991 4.2376e+08 737 605 4.2402e+08 4.2266e+08 0.32% 9.3 198s
13135 8275 4.2382e+08 831 528 4.2402e+08 4.2266e+08 0.32% 9.3 203s
13534 8670 4.2389e+08 928 450 4.2402e+08 4.2266e+08 0.32% 9.2 207s
13912 9012 4.2395e+08 1024 404 4.2402e+08 4.2266e+08 0.32% 9.2 212s
H14310 9370 4.240165e+08 4.2266e+08 0.32% 9.2 218s
14323 9388 4.2401e+08 1125 319 4.2402e+08 4.2266e+08 0.32% 9.2 220s
14858 9900 4.2290e+08 124 1006 4.2402e+08 4.2266e+08 0.32% 9.2 251s
14900 9944 4.2291e+08 129 999 4.2402e+08 4.2266e+08 0.32% 9.2 256s
15362 10409 4.2306e+08 201 942 4.2402e+08 4.2266e+08 0.32% 9.2 261s
15822 10886 4.2317e+08 283 883 4.2402e+08 4.2266e+08 0.32% 9.1 265s
16264 11314 4.2327e+08 339 857 4.2402e+08 4.2266e+08 0.32% 9.1 270s
16698 11771 4.2333e+08 400 822 4.2402e+08 4.2266e+08 0.32% 9.1 275s
17470 12516 4.2352e+08 493 1135 4.2402e+08 4.2266e+08 0.32% 9.1 297s
17475 12519 4.2345e+08 288 774 4.2402e+08 4.2345e+08 0.13% 9.1 300s
17482 12524 4.2374e+08 710 771 4.2402e+08 4.2346e+08 0.13% 9.1 305s
17490 12531 4.2352e+08 493 764 4.2402e+08 4.2346e+08 0.13% 10.5 310s
17492 12532 4.2346e+08 232 764 4.2402e+08 4.2346e+08 0.13% 10.5 315s
17494 12536 4.2346e+08 32 763 4.2402e+08 4.2346e+08 0.13% 11.8 322s
17495 12536 4.2347e+08 32 763 4.2402e+08 4.2346e+08 0.13% 11.8 328s
17496 12537 4.2346e+08 33 764 4.2402e+08 4.2346e+08 0.13% 11.8 333s
17505 12548 4.2348e+08 36 767 4.2402e+08 4.2347e+08 0.13% 11.8 339s
17641 12631 4.2354e+08 70 751 4.2402e+08 4.2347e+08 0.13% 11.9 343s
17729 12695 4.2357e+08 91 748 4.2402e+08 4.2347e+08 0.13% 11.9 349s
17917 12822 4.2360e+08 138 714 4.2402e+08 4.2347e+08 0.13% 11.9 355s
18182 12993 4.2364e+08 209 658 4.2402e+08 4.2347e+08 0.13% 12.0 361s
18476 13194 4.2369e+08 282 598 4.2402e+08 4.2347e+08 0.13% 12.0 368s
18807 13409 4.2372e+08 363 543 4.2402e+08 4.2347e+08 0.13% 12.0 374s
19048 13572 4.2374e+08 423 492 4.2402e+08 4.2347e+08 0.13% 12.0 381s
19363 13780 4.2377e+08 501 429 4.2402e+08 4.2347e+08 0.13% 12.1 388s
19736 14033 4.2380e+08 591 381 4.2402e+08 4.2347e+08 0.13% 12.2 395s
H20136 13669 4.239906e+08 4.2347e+08 0.12% 12.2 411s
H20137 13073 4.239710e+08 4.2347e+08 0.12% 12.2 411s
20138 13074 4.2384e+08 693 315 4.2397e+08 4.2347e+08 0.12% 12.2 419s
20562 13357 4.2388e+08 797 261 4.2397e+08 4.2347e+08 0.12% 12.3 427s
21013 13646 4.2391e+08 910 202 4.2397e+08 4.2347e+08 0.12% 12.3 435s
21354 13826 4.2393e+08 979 161 4.2397e+08 4.2347e+08 0.12% 12.4 443s
21809 14087 4.2356e+08 84 735 4.2397e+08 4.2348e+08 0.12% 12.4 451s
22272 14394 4.2365e+08 198 657 4.2397e+08 4.2348e+08 0.12% 12.5 460s
22753 14713 4.2373e+08 320 601 4.2397e+08 4.2348e+08 0.12% 12.5 469s
23262 15052 4.2379e+08 448 514 4.2397e+08 4.2348e+08 0.12% 12.6 478s
23795 15410 4.2384e+08 581 420 4.2397e+08 4.2348e+08 0.12% 12.6 486s
24253 15713 4.2387e+08 692 348 4.2397e+08 4.2348e+08 0.12% 12.6 496s
24858 16100 4.2393e+08 843 226 4.2397e+08 4.2348e+08 0.12% 12.6 506s
H25485 15349 4.239534e+08 4.2348e+08 0.11% 12.7 533s
25583 15320 cutoff 1051 4.2395e+08 4.2348e+08 0.11% 12.7 542s
26023 15611 4.2362e+08 167 697 4.2395e+08 4.2348e+08 0.11% 12.7 552s
26717 16066 4.2372e+08 327 600 4.2395e+08 4.2348e+08 0.11% 12.6 563s
27500 16601 4.2381e+08 523 455 4.2395e+08 4.2348e+08 0.11% 12.6 575s
28256 17085 4.2387e+08 667 383 4.2395e+08 4.2348e+08 0.11% 12.5 580s
28421 17212 4.2388e+08 689 368 4.2395e+08 4.2348e+08 0.11% 12.5 591s
29251 17740 4.2394e+08 879 240 4.2395e+08 4.2348e+08 0.11% 12.4 600s
29930 18145 4.2357e+08 73 739 4.2395e+08 4.2348e+08 0.11% 12.3 610s
30646 18617 4.2369e+08 227 667 4.2395e+08 4.2348e+08 0.11% 12.3 619s
31336 19071 4.2377e+08 325 607 4.2395e+08 4.2348e+08 0.11% 12.2 628s
31924 19439 4.2382e+08 426 535 4.2395e+08 4.2348e+08 0.11% 12.2 640s
32206 19622 4.2385e+08 469 503 4.2395e+08 4.2348e+08 0.11% 12.2 648s
32792 20001 4.2389e+08 566 443 4.2395e+08 4.2348e+08 0.11% 12.2 656s
33348 20366 4.2394e+08 700 371 4.2395e+08 4.2348e+08 0.11% 12.2 680s
33350 20371 4.2394e+08 698 372 4.2395e+08 4.2348e+08 0.11% 12.2 688s
33876 20696 4.2359e+08 119 724 4.2395e+08 4.2348e+08 0.11% 12.2 697s
34374 21029 4.2367e+08 247 652 4.2395e+08 4.2348e+08 0.11% 12.2 705s
34375 21029 4.2367e+08 248 652 4.2395e+08 4.2348e+08 0.11% 12.2 716s
34896 21387 4.2374e+08 355 588 4.2395e+08 4.2348e+08 0.11% 12.2 723s
35412 21734 4.2378e+08 429 537 4.2395e+08 4.2348e+08 0.11% 12.2 730s
35963 22081 4.2383e+08 536 462 4.2395e+08 4.2348e+08 0.11% 12.2 737s
35964 22081 4.2384e+08 537 462 4.2395e+08 4.2348e+08 0.11% 12.2 742s