mathematical-optimizationmodelinglinear-programminggurobi
Gurobi fails to reach optimum solution for a larger case of the same MILP formulation
My MILP problem is based on simple but large number of constraints and variables.
- Most of the decision variables are of 'semi' type (example production quantity , transportation quantity etc)
- S(wijk) is of integer type ( number of shifts on a line)
- Data : delta , theta , alpha , lambda , N(ijw), Mmin(ijk), Mmax(ijk), V0(ik), Dwijk
The problem formulation reaches an optimum solution for a small scale but for larger scales it just 'stalls' at certain 'gap' and doesn't move forward
a. small scale problem size : less than 15 weeks (planning horizon)
b. larger scale problems' size : >= 15 weeks
problem input method : .lp file ( hence solved using lp.py script on command prompt)
gurobi version : 6.0 ( academic license)
Any suggestions on what I can do to obtain optimum solutions for the larger cases ?
following is an example output log for a case of 15 weeks and 124 products .
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 742sSolution
Gurobi isn't stalling. It has found a solution within 0.11% of optimal and is continuing to try to improve the bound to 0.01%. If you want to stop it sooner, you should change the parameter MIPGap.
To actually make Gurobi faster, you can try changing other parameters with the Tuning Tool. You best bet is to tighten your model formulation, but that's very problem dependent, and you haven't posted your actual formulation.
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