Originally posted by: SystemAdmin

Hello,

I have a MIP problem with the following problem statistics:

Variables            : 3299695  [Fix: 313,  Box: 153,  Binary: 3299229] Objective nonzeros   : 3275586 Linear constraints   : 4895476  [Less: 3299542,  Greater: 1580490,  Equal: 15444] Nonzeros           : 25839153 RHS nonzeros       : 4879945   Variables            : Min LB: 0.000000         Max UB: 18.11000 Objective nonzeros   : Min   : 0.02490204       Max   : 240.0000 Linear constraints   : Nonzeros           : Min   : 0.4000000        Max   : 240.0000 RHS nonzeros       : Min   : 1.000000         Max   : 267.6752

I generate some columns using column generation and delete all the non-generated binary columns and empty constraints. Then I try to solve this reduced MIP with following statistics:

Variables            :    5063  [Fix: 313,  Box: 153,  Binary: 4597] Objective nonzeros   :    4156 Linear constraints   : 4882695  [Less: 3299460,  Greater: 1580490,  Equal: 2745] Nonzeros           : 9641733 RHS nonzeros       : 4879863   Variables            : Min LB: 0.000000         Max UB: 18.11000 Objective nonzeros   : Min   : 0.02490204       Max   : 240.0000 Linear constraints   : Nonzeros           : Min   : 0.4000000        Max   : 240.0000 RHS nonzeros       : Min   : 1.000000         Max   : 267.6752

When I solve the reduced problem, the tree size increases abnormally. The solve starts off normally:

Tried aggregator 2 times. MIP Presolve eliminated 4877137 rows and 380 columns. MIP Presolve modified 7542 coefficients. Aggregator did 1918 substitutions. Reduced MIP has 3640 rows, 2765 columns, and 15567 nonzeros. Reduced MIP has 2620 binaries, 0 generals, 0 SOSs, and 0 indicators. Presolve time = 10.13 sec. (2805.11 ticks) Found incumbent of value 35.623122 after 10.86 sec. (2943.73 ticks) Probing time = 0.01 sec. (1.40 ticks) Cover probing fixed 0 vars, tightened 1 bounds. Tried aggregator 2 times. MIP Presolve eliminated 156 rows and 6 columns. MIP Presolve modified 4306 coefficients. Aggregator did 7 substitutions. Reduced MIP has 3477 rows, 2752 columns, and 15203 nonzeros. Reduced MIP has 2611 binaries, 0 generals, 0 SOSs, and 0 indicators. Presolve time = 0.40 sec. (43.08 ticks) Probing time = 0.01 sec. (1.39 ticks) Clique table members: 6883. MIP emphasis: balance optimality and feasibility. MIP search method: dynamic search. Parallel mode: deterministic, using up to 8 threads. Root relaxation solution time = 1.51 sec. (414.42 ticks)   Nodes                                         Cuts/  Node  Left     Objective  IInf  Best Integer    Best Bound    ItCnt     Gap   *     0+    0                           35.6231   -36720.8023       15     --- 0     0   -36623.7416   801       35.6231   -36623.7416       15     --- *     0+    0                       -11245.9422   -36623.7416     1285  225.66% 0     0   -36620.9747   829   -11245.9422     Cuts: 123     1285  225.64% 0     0   -36618.4937   827   -11245.9422     Cuts: 178     2173  225.62% 0     0   -36615.6556 836   -11245.9422      Cuts: 93     3087  225.59% *     0+    0                       -11724.3932   -36615.6556     3087  212.30% *     0+    0                       -16032.7473   -36615.6556     3087  128.38% 0     0   -36615.4987   844   -16032.7473      Cuts: 44     3289  128.38% 0     0   -36615.4167   839   -16032.7473       Cuts: 9     3394  128.38% *     0+    0                       -25362.4054   -36615.4167     3394   44.37% 0     0   -36615.3467   845   -25362.4054       Cuts: 8     3503   44.37% *     0+    0                       -25841.2766   -36615.3467     3503   41.69% 0     2   -36615.3467   845   -25841.2766   -36615.3467     3503   41.69% Elapsed time = 24.34 sec. (6744.21 ticks, tree = 0.01 MB, solutions = 6) 2     4   -36613.8944   832   -25841.2766   -36615.3467     5026   41.69% 6     8   -36611.2896   814   -25841.2766   -36614.1888     8204   41.69% 10    12   -36598.6682   801   -25841.2766   -36613.2437    12053   41.69% 17    19   -36584.5597   794   -25841.2766   -36613.2437    21316   41.69% 23    25   -36596.1511   787   -25841.2766   -36613.2437    25045   41.69% 24    26   -36548.6223   788   -25841.2766   -36613.2437    26296   41.69% 42    44   -36522.4146   800   -25841.2766   -36613.2437    38530   41.69% 64    66   -36576.3688   786   -25841.2766   -36613.2437    49797   41.69% 73    75   -36574.6452   806   -25841.2766   -36613.2437    53974   41.69% *    98+   98                       -26310.9783   -36613.2437    63284   39.16% *   145+  145                       -26793.3587   -36613.2437    78655   36.65% *   176+  176                       -28234.0483   -36613.2437    92943   29.68% *   176+  176                       -30388.7308   -36613.2437    92943   20.48% 176   178   -35814.3195   731   -30388.7308   -36613.2437    92943   20.48% Elapsed time = 37.14 sec. (11644.39 ticks, tree = 0.52 MB, solutions = 6) 342   342   -35342.1475   712   -30388.7308   -36613.2437   171720   20.48% *   349+ 347                       -31582.5209   -36613.2437   174294   15.93% 536   515   -35483.1157   709   -31582.5209   -36613.2437   236251   15.93% 612   589   -35903.2536   759   -31582.5209   -36613.2437   266021   15.93% 845   815   -36545.3878   817   -31582.5209   -36613.2437   333318   15.93% 909   874   -36247.5932   787   -31582.5209   -36613.2437   357729   15.93% 1053   996   -36252.1797   761   -31582.5209   -36610.7541   427064   15.92% *  1161+ 1102                       -31822.3611   -36610.7541   474852   15.05% 1204  1111   -35276.2778   655   -31822.3611   -36610.7541   489673   15.05% 1247  1154   -36372.0657   822   -31822.3611   -36610.7541   513230   15.05% 1435  1334   -34870.8601   610   -31822.3611   -36610.7541   591725   15.05% 1569  1466   -33378.6390   504   -31822.3611   -36610.7541   634760   15.05% Elapsed time = 75.80 sec. (21753.52 ticks, tree = 2.83 MB, solutions = 15) 1685  1580   -35104.1008   744   -31822.3611   -36610.7541   668101   15.05% 1833  1701   -36613.7163   886   -31822.3611   -36608.4686   714737   15.04% 1835  1703   -36604.9956   853   -31822.3611   -36608.4686   716296   15.04% 1837  1705   -36477.7713   830   -31822.3611   -36608.4686   718887   15.04% 1840  1705   -36533.3094   807   -31822.3611   -36608.4686   722211   15.04% 1848  1710   -36299.5137   810   -31822.3611   -36608.4686   738649   15.04% *  1857+ 1150                       -31822.5247   -36608.4686   748717   15.04% 1858  1153   -36534.3374   857   -31822.5247   -36608.4686   748875   15.04% 1878  1164   -36267.8945   809   -31822.5247   -36598.2794   762890   15.01% 1927  1189   -36330.6836   807   -31822.5247   -36597.5417   784044   15.01% 1994  1230   -36111.9916   781   -31822.5247   -36597.5417   811896   15.01% Elapsed time = 121.35 sec. (37362.45 ticks, tree = 5.01 MB, solutions = 16) 2064  1267   -35364.2139   728   -31822.5247   -36597.5417   833553   15.01% 2155  1322   -35361.0618   716   -31822.5247   -36597.5417   860629   15.01% 2361  1447   -34878.2844   702   -31822.5247   -36597.5417   900216   15.01% 2402  1476   -35763.8594   748   -31822.5247   -36597.5417   913071   15.01% 2571  1573   -35861.0971   765   -31822.5247   -36597.5417   943647   15.01% 2857  1735   -35500.0106   713   -31822.5247   -36597.5417   982010   15.01% 2954  1781   -34834.6933   682   -31822.5247   -36597.5417   995271   15.01% 3218  1928   -35410.1369   766   -31822.5247   -36597.5417  1033796   15.01% 3587  2105   -36378.4410   820   -31822.5247   -36597.5417  1080839   15.01% 3631  2115   -36160.7430   781   -31822.5247   -36597.5417  1091798   15.01% Elapsed time = 160.22 sec. (47533.13 ticks, tree = 53.16 MB, solutions = 16) 3685  2148   -32546.2667   511   -31822.5247   -36597.5417  1111061   15.01% 3770  2197   -36278.6068   800   -31822.5247   -36597.5417  1127935   15.01% 4050  2346   -35496.8312   753   -31822.5247   -36597.5417  1178389   15.01% 4146  2397   -35495.1345   736   -31822.5247   -36597.5417  1195118   15.01% 4258  2453   -34797.5087   618   -31822.5247   -36597.5417  1211414   15.01% 4524  2611   -35984.9918   834   -31822.5247   -36597.5417  1248295   15.01% 4588  2675   -35888.1472   792   -31822.5247   -36597.5417  1259242   15.01% 4878  2932   -35473.7748   769   -31822.5247   -36597.5417  1303439   15.01% 5043  3075   -35540.6087   749   -31822.5247   -36597.5417  1330447   15.01% 5359  3375   -36373.3599   846   -31822.5247   -36568.3598  1375769   14.91% Elapsed time = 195.46 sec. (57728.68 ticks, tree = 102.54 MB, solutions = 16) 5446  3462   -36148.1134   805   -31822.5247   -36568.3598  1389923   14.91% 5511  3527   -35814.3433   799   -31822.5247   -36568.3598  1400230   14.91% 6096  4095   -34816.3351   721   -31822.5247   -36568.3598  1465892   14.91% 6145  4140   -35384.8689   757   -31822.5247   -36568.3598  1477447   14.91% 6175  4170   -35467.3941   809   -31822.5247   -36568.3598  1483808   14.91% 6316  4306   -36395.7415   854   -31822.5247   -36568.3598  1508109   14.91% 6451  4441   -36296.4541   839   -31822.5247   -36568.3598  1527845   14.91% 6579  4569   -35878.2588   830   -31822.5247   -36568.3598  1543156   14.91% 7369  5341   -34183.7603   660   -31822.5247   -36568.3598  1643353   14.91% 7456  5424   -35964.8387   799   -31822.5247   -36568.3598  1656473   14.91% Elapsed time = 224.44 sec. (69069.84 ticks, tree = 165.27 MB, solutions = 16) Nodefile size = 32.89 MB (28.20 MB after compression) 7520  5483   -35515.3556   776   -31822.5247   -36568.3598  1668625   14.91% 7672  5635   -34777.1380   704   -31822.5247   -36568.3598  1693197   14.91% 8149  6088   -35703.7916   771   -31822.5247   -36395.6075  1768247   14.37% 8253  6192   -35366.3803   771   -31822.5247   -36395.6075  1792858   14.37% 8397  6334   -34040.5775   648   -31822.5247   -36395.6075  1819707   14.37% 8597  6534   -33723.7381   667   -31822.5247   -36395.6075  1849227   14.37% 8885  6814   -32959.8267   613   -31822.5247   -36395.6075  1884835   14.37% 9188  7100   -35553.2236   781   -31822.5247   -36382.7402  1931100   14.33% 9236  7148   -35218.5290   754   -31822.5247   -36382.7402  1940472   14.33% 9300  7208   -35031.7344   737   -31822.5247   -36382.7402  1951786   14.33% Elapsed time = 251.66 sec. (79160.83 ticks, tree = 206.45 MB, solutions = 16) Nodefile size = 72.61 MB (62.52 MB after compression) 9412  7314   -34605.0006   709   -31822.5247   -36382.7402  1972744   14.33% 9540  7442   -33762.1572   594   -31822.5247   -36382.7402  1991960   14.33% 9899  7801   -33518.3550   581   -31822.5247   -36382.7402  2036002   14.33% 10208  8082   -35726.0484   774   -31822.5247   -36382.7402  2069921   14.33% 10475  8337   -35407.5454   744   -31822.5247   -36382.7402  2113784   14.33% 10711  8573   -34291.0367   677   -31822.5247   -36382.7402  2144385   14.33% 10885  8743   -34210.3600   754   -31822.5247   -36382.7402  2166232   14.33% 11439  9287   -36308.2531   791   -31822.5247   -36377.4958  2228111   14.31% 11599  9437   -35536.1930   760   -31822.5247   -36377.4958  2253195   14.31% 11815  9642   -34668.3705   691   -31822.5247   -36377.4958  2285161   14.31% Elapsed time = 281.69 sec. (89007.88 ticks, tree = 289.33 MB, solutions = 16) Nodefile size = 152.39 MB (132.61 MB after compression) 12088  9911   -33956.2932   775   -31822.5247   -36377.4958  2323369   14.31% 12360 10179   -33257.6234   734   -31822.5247   -36377.4958  2361207   14.31% 12728 10543   -32333.7920   691   -31822.5247   -36377.4958  2401639   14.31% 13016 10809   -33704.2080   662   -31822.5247   -36377.4958  2441373   14.31% 13102 10893   -35727.2671   738   -31822.5247   -36375.8445  2459442   14.31% 13198 10989   -34646.5401   645   -31822.5247   -36375.8445  2475533   14.31% 13422 11209   -33190.5583   549   -31822.5247   -36375.8445  2504086   14.31% 13665 11442   -32540.6737   476   -31822.5247   -36375.8445  2538469   14.31% 13857 11628   -36347.0246   808   -31822.5247   -36375.8445  2560965   14.31% 14312 12059   -33013.8415   636   -31822.5247   -36375.3369  2616306   14.31% Elapsed time = 316.92 sec. (99262.46 ticks, tree = 407.29 MB, solutions = 16) Nodefile size = 272.45 MB (239.29 MB after compression) 14468 12215   -34870.3165   668   -31822.5247   -36375.3369  2638627   14.31% 14540 12281   -34410.5095   679   -31822.5247   -36375.3369  2651239   14.31% 14692 12429   -33813.9601   651   -31822.5247   -36375.3369  2678355   14.31% 14821 12558   -34843.2070   673   -31822.5247   -36375.3369  2701589   14.31% 15032 12762   -34926.2657   741   -31822.5247   -36375.3369  2733239   14.31% 15192 12916   -34436.4014   712   -31822.5247   -36375.3369  2764489   14.31% 15750 13445   -35845.5867   763   -31822.5247   -36374.3647  2855014   14.30% 15893 13570   -35128.9732   726   -31822.5247   -36374.3647  2878349   14.30% 16054 13729   -34497.8289   728   -31822.5247   -36374.3647  2904557   14.30%

After few hours, the nodefile size is as high as 97GB.

Also, should the solve time reduce considerably as I am solving only with a fraction of the original variables, though the generated columns has a high chance of being in the optimal solution.

What could be the issue?

Regards,
Vivek.
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: SystemAdmin

Also instead of deleting the columns/rows, I changed the upper bounds to 0.0 and still saw the same behavior.
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#DecisionOptimization

Originally posted by: T_O

Your reduced problem is still difficult to solve.

If the node file size is a problem for you, you might try to set the node selection strategy to DFS (set mip strat var 3). You might also try to change other parameters: generate more cuts, do more aggressive probing, ...

Best regards,
Thomas
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: T_O

By the way, i have to correct my above post:

"set mip strat var 3" changes the branching rule to strong branching, which might also help you to reduce the tree size.
To enable DFS do "set mip strat node 0".

Best regards,
Thomas
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: SystemAdmin

Hi Thomas,

Thanks. I did use the DFS before. Now strong branching also seems to help. What interesting is that in strong branching, node size does not monotonically increases. Sometimes it decreases too.

I think the reason for my slow convergence is that I don't have all the necessary columns to complete 100% customer assignment.

If I add more columns to the same problem, turn on advanced basis (currently it's off), resolve the problem, would it be faster? Would I be able to reuse the tree information from the previous run?

Regards,
Vivek.
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: SystemAdmin

Just to update. Adding more columns and perturbing my objective helped in the converging fast, along with strong branching.

Also, with CPX_PARAM_ADVIND on, the next MIP run was using the basis (through MIP starts) from the previous run. So I am able to save on time there too.

Thanks for all the help!

Regards,
Vivek.
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: SystemAdmin

You eliminated a lot of columns but not very many rows. Eliminating columns (especially binary variables) helps, but how much can vary a lot. For instance, if the variables typically are nonbasic (zero) in the node LP solutions, eliminating them probably is not a huge boon. Meanwhile, you may have increased the density of the constraint matrix. (I'm too lazy to actually check.)

Your best bound moves a bit slowly, and you are not pruning very many of the nodes encountered. In addition to Thomas's suggestions, you might try changing the MIPEmphasis parameter to emphasize moving the bound and see if that helps.

Paul

Mathematicians are like Frenchmen: whenever you say something to them, they translate it into their own language, and at once it is something entirely different. (Goethe)
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#DecisionOptimization

Originally posted by: SystemAdmin

Thanks Thomas and Paul.

Using DFS definitely helps in the reduction of the tree size.

The nature of my problem is such that the bound attained in the root's LP relaxation stays the same and the objective of the optimal integer solution usually ends up same as this best bound. It's a network flow problem.

I tried one another approach.

I deleted all non-generated variables and invalid constraints but the problem is still very difficult to solve.

Variables            :   21299  [Fix: 313,  Box: 153,  Binary: 20833] Objective nonzeros   :   18254 Linear constraints   :   38662  [Less: 20935,  Greater: 9340,  Equal: 8387] Nonzeros           :  152668 RHS nonzeros       :   30188   Variables : Min LB: 0.000000         Max UB: 18.11000 Objective nonzeros   : Min   : 0.02490204       Max   : 240.0000 Linear constraints   : Nonzeros           : Min   : 0.4000000        Max   : 240.0000 RHS nonzeros       : Min   : 1.000000         Max   : 267.6752

Iteration summary:

Tried aggregator 2 times. MIP Presolve eliminated 17595 rows and 1703 columns. MIP Presolve modified 35089 coefficients. Aggregator did 3784 substitutions. Reduced MIP has 17283 rows, 15812 columns, and 83107 nonzeros. Reduced MIP has 15659 binaries, 0 generals, 0 SOSs, and 0 indicators. Presolve time = 0.65 sec. (162.19 ticks) Found incumbent of value 26.098265 after 1.47 sec. (306.61 ticks) Probing time = 0.23 sec. (14.70 ticks) Cover probing fixed 0 vars, tightened 5 bounds. Tried aggregator 2 times. MIP Presolve eliminated 38 rows and 8 columns. MIP Presolve modified 20938 coefficients. Aggregator did 1 substitutions. Reduced MIP has 17244 rows, 15803 columns, and 82997 nonzeros. Reduced MIP has 15650 binaries, 0 generals, 0 SOSs, and 0 indicators. Presolve time = 0.48 sec. (162.52 ticks) Probing time = 0.14 sec. (5.94 ticks) Clique table members: 42285. MIP emphasis: balance optimality and feasibility. MIP search method: dynamic search. Parallel mode: deterministic, using up to 8 threads. Parallel mode: deterministic, using up to 5 threads 

for concurrent optimization. Tried aggregator 1 time. No LP presolve or aggregator reductions. Presolve time = 0.02 sec. (10.67 ticks) Initializing dual steep norms . . .   Barrier solved model.   Root relaxation solution time = 4.18 sec. (1758.43 ticks)   Nodes                                         Cuts/  Node  Left     Objective  IInf  Best Integer    Best Bound    ItCnt     Gap   *     0+    0                           26.0983   -36720.0000       14     --- Found incumbent of value 26.098265 after 8.38 sec. (2320.18 ticks) 0     0   -36630.0195  1506       26.0983   -36630.0195       14     --- *     0+    0                       -19392.9078   -36630.0195      571   88.88% Found incumbent of value -19392.907794 after 16.90 sec. (6791.54 ticks) 0     0   -36630.0195  1484   -19392.9078      Cuts: 66      571   88.88% 0     0   -36630.0195  1789   -19392.9078      Cuts: 59     7653   88.88% 0     0   -36630.0195  1925   -19392.9078     Cuts: 155    14463   88.88% *     0+    0                       -20110.9281   -36630.0195    14463   82.14% Found incumbent of value -20110.928086 after 52.64 sec. (25026.44 ticks) 0     2   -36630.0195  1925   -20110.9281   -36630.0195    14463   82.14% Elapsed time = 74.67 sec. (39660.81 ticks, tree = 0.01 MB, solutions = 3) 1     3   -36630.0195  1888   -20110.9281   -36630.0195    29054   82.14% 3     5   -36630.0195  2001   -20110.9281   -36630.0195    39172   82.14% 4     6   -36630.0195  1966   -20110.9281   -36630.0195    48218   82.14% 5     7   -36630.0195  1764   -20110.9281   -36630.0195    56565   82.14% Impl Bds: 63 7     9   -36630.0195  1965   -20110.9281   -36630.0195    65618   82.14% 8    10   -36630.0195  1943   -20110.9281   -36630.0195    75435   82.14% 9    11   -36630.0195  1713   -20110.9281   -36630.0195    93527   82.14% Impl Bds: 25 11    13   -36630.0195  1854   -20110.9281   -36630.0195   124094   82.14% 12    14   -36630.0195  1922   -20110.9281   -36630.0195   130344   82.14% 13    15   -36630.0195  1928   -20110.9281   -36630.0195   135450   82.14% Elapsed time = 260.69 sec. (104932.88 ticks, tree = 0.01 MB, solutions = 3) 15    17   -36630.0195  1710   -20110.9281   -36630.0195   136270   82.14% Impl Bds: 20 16    18   -36630.0195  1815   -20110.9281   -36630.0195   136681   82.14% 17    19   -36630.0195  1905   -20110.9281   -36630.0195   147618   82.14% 19    21   -36630.0195  1709   -20110.9281   -36630.0195   169154   82.14% 20    22   -36630.0195  1902   -20110.9281   -36630.0195   180289   82.14% 31    33   -36629.7739  1558   -20110.9281   -36630.0195   223464   82.14% Impl Bds: 186 32    34   -36630.0195  1921   -20110.9281   -36630.0195   240242   82.14% 33    35   -36630.0195  1968   -20110.9281   -36630.0195   260284   82.14% 35    37   -36630.0195  1919   -20110.9281   -36630.0195   294135   82.14% 37    39   -36630.0195  1992   -20110.9281   -36630.0195   338891   82.14% Elapsed time = 377.82 sec. (150869.61 ticks, tree = 0.02 MB, solutions = 3) 41    43   -36630.0195  1823   -20110.9281   -36630.0195   400126   82.14% 43    45   -36630.0195  1873   -20110.9281   -36630.0195   413604   82.14% 54    56   -36629.7655  1551   -20110.9281   -36630.0195   467982   82.14% 60    62   -36630.0195  1990   -20110.9281   -36630.0195   510765   82.14% 64    66   -36630.0195  1919   -20110.9281   -36630.0195   538548   82.14% 67    69   -36629.8928  2185   -20110.9281   -36630.0195   554305   82.14% 76    78   -36630.0195  2107   -20110.9281   -36630.0195   611320   82.14% 91    93   -36630.0147  1890   -20110.9281   -36630.0195   696743   82.14% 96    98   -36629.9681  1641   -20110.9281   -36630.0195   718530   82.14% 101   103   -36629.9779  1773   -20110.9281   -36630.0195   746955   82.14% Elapsed time = 447.70 sec. (178513.40 ticks, tree = 0.10 MB, solutions = 3)   <snip>   Elapsed time = 44813.91 sec. (17817593.57 ticks, tree = 76238.69 MB, solutions = 39) Nodefile size = 76072.38 MB (55346.57 MB after compression) 427859 414006   -36627.3959   976   -36149.0413   -36630.0195 1.81e+08    1.33% 428502 414639   -36620.6847   846   -36149.0413   -36630.0195 1.81e+08    1.33% 428892 415026   -36571.2689   827   -36149.0413   -36630.0195 1.81e+08    1.33% Impl Bds: 5 429020 415150   -36382.4256   743   -36149.0413   -36630.0195 1.81e+08    1.33% 429060 415186        cutoff         -36149.0413   -36630.0195 1.81e+08    1.33% 429865 415977   -36628.2048  1166   -36149.0413   -36630.0195 1.82e+08    1.33% Impl Bds: 3 429929 416041   -36627.8014   981   -36149.0413   -36630.0195 1.82e+08    1.33% 430121 416232   -36625.5453   854   -36149.0413   -36630.0195 1.82e+08    1.33% 431062 417153   -36386.7951   998   -36149.0413   -36630.0195 1.83e+08    1.33% Impl Bds: 1 431177 417264   -36629.4958  1166   -36149.0413   -36630.0195 1.83e+08    1.33% Elapsed time = 45246.89 sec. (17993918.23 ticks, tree = 76981.62 MB, solutions = 39) Nodefile size = 76816.05 MB (55909.38 MB after compression) 431233 417318   -36629.3884  1007   -36149.0413   -36630.0195 1.83e+08    1.33% 431795 417872   -36629.7407  1149   -36149.0413   -36630.0195 1.83e+08    1.33% 432119 418192   -36629.1843   970   -36149.0413   -36630.0195 1.83e+08    1.33% Cuts: 2 432453 418522   -36629.3080   921   -36149.0413   -36630.0195 1.83e+08    1.33% 432525 418593   -36390.6475   933   -36149.0413   -36630.0195 1.83e+08    1.33% 433644 419688   -36629.6649   825   -36149.0413   -36630.0195 1.84e+08    1.33% Impl Bds: 1 433685 419729   -36389.8012   855   -36149.0413   -36630.0195 1.84e+08    1.33% 433704 419748   -36629.6866   901   -36149.0413   -36630.0195 1.84e+08    1.33% 434683 420724   -36629.4525   781   -36149.0413   -36630.0195 1.84e+08    1.33% 434949 420986   -36629.7382  1173   -36149.0413   -36630.0195 1.84e+08    1.33% Elapsed time = 45679.60 sec. (18165970.21 ticks, tree = 77525.61 MB, solutions = 39) Nodefile size = 77350.20 MB (56304.70 MB after compression)

My best integer solution I have got so far has made 151/153 customer assignments. If it makes two more assignments, then the optimal solution is found.

Regards,
Vivek.
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#DecisionOptimization