Set parameter TokenServer to value "gurobi.cc.ic.ac.uk"

********************************
*** COLUMN GENERATION SCHEME ***
********************************

*** OUTER ITERATION 0 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.211088 seconds.
    local lower bound updated to 0.191353
    local upper bound updated to 0.330867

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.0659764 seconds.
    local lower bound updated to 0.330867
    local upper bound updated to 0.330867
The Primal step takes 0.2797 (S)
lower bound updated to 0.330867

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.397264
    local lower bound updated to 0.397264
The Dual step takes 0.0236444 (S)
upper bound updated to 0.397264
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.324403 seconds.
    local lower bound updated to 0.235324
    local upper bound updated to 0.331418

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.248574 seconds.
    local lower bound updated to 0.330802
    local upper bound updated to 0.330867

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.101121 seconds.
    local lower bound updated to 0.330867
    local upper bound updated to 0.330867
The Primal step takes 0.679293 (S)
lower bound updated to 0.330867

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.37874
    local lower bound updated to 0.366229

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.37874
    local lower bound updated to 0.368692

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.370413
    local lower bound updated to 0.369104

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.369104
    local lower bound updated to 0.369104
The Dual step takes 0.401261 (S)
upper bound updated to 0.369104
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.642656 seconds.
    local lower bound updated to 0.276131
    local upper bound updated to 0.350698

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.239908 seconds.
    local lower bound updated to 0.314606
    local upper bound updated to 0.34247

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.370775 seconds.
    local lower bound updated to 0.336935
    local upper bound updated to 0.342312

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 0.467913 seconds.
    local lower bound updated to 0.340152
    local upper bound updated to 0.341861

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 0.61365 seconds.
    local lower bound updated to 0.340152
    local upper bound updated to 0.340731

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 0.419655 seconds.
    local lower bound updated to 0.340152
    local upper bound updated to 0.340499

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 0.545884 seconds.
    local lower bound updated to 0.340499
    local upper bound updated to 0.340499
The Primal step takes 3.31949 (S)
lower bound updated to 0.340499

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.394254
    local lower bound updated to 0.349848

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.370369
    local lower bound updated to 0.359335

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.370369
    local lower bound updated to 0.363687

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.370369
    local lower bound updated to 0.363892

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.367999
    local lower bound updated to 0.364012

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.364012
    local lower bound updated to 0.364012
The Dual step takes 1.24231 (S)
upper bound updated to 0.364012
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.895305 seconds.
    local lower bound updated to 0.287034
    local upper bound updated to 0.359176

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.597404 seconds.
    local lower bound updated to 0.312031
    local upper bound updated to 0.357577

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 1.54183 seconds.
    local lower bound updated to 0.347311
    local upper bound updated to 0.354689

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 1.65654 seconds.
    local lower bound updated to 0.350862
    local upper bound updated to 0.352758

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 1.21297 seconds.
    local lower bound updated to 0.350862
    local upper bound updated to 0.352239

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 2.00174 seconds.
    local lower bound updated to 0.351031
    local upper bound updated to 0.35208

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 2.06595 seconds.
    local lower bound updated to 0.351031
    local upper bound updated to 0.352037

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 1.76771 seconds.
    local lower bound updated to 0.351552
    local upper bound updated to 0.352032

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 2.11327 seconds.
    local lower bound updated to 0.351552
    local upper bound updated to 0.352029

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 2.13666 seconds.
    local lower bound updated to 0.351889
    local upper bound updated to 0.352028

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 1.93517 seconds.
    local lower bound updated to 0.351908
    local upper bound updated to 0.352003

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 2.47076 seconds.
    local lower bound updated to 0.351908
    local upper bound updated to 0.352002

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 2.3612 seconds.
    local lower bound updated to 0.352002
    local upper bound updated to 0.352002
The Primal step takes 22.8121 (S)
lower bound updated to 0.352002

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.379515
    local lower bound updated to 0.352002

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.369565
    local lower bound updated to 0.354197

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.369565
    local lower bound updated to 0.355034

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.362578
    local lower bound updated to 0.355716

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.359468
    local lower bound updated to 0.355809

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.358488
    local lower bound updated to 0.355926

    ++ RESTRICTED DUAL ITERATION 7 ++
    local upper bound updated to 0.357868
    local lower bound updated to 0.355942

    ++ RESTRICTED DUAL ITERATION 8 ++
    local upper bound updated to 0.357533
    local lower bound updated to 0.356062

    ++ RESTRICTED DUAL ITERATION 9 ++
    local upper bound updated to 0.356062
    local lower bound updated to 0.356062
The Dual step takes 8.17853 (S)
upper bound updated to 0.356062
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 2.07932 seconds.
    local lower bound updated to 0.301151
    local upper bound updated to 0.356062

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 2.35472 seconds.
    local lower bound updated to 0.344374
    local upper bound updated to 0.355595

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 3.86437 seconds.
    local lower bound updated to 0.349286
    local upper bound updated to 0.355306

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 4.54299 seconds.
    local lower bound updated to 0.350099
    local upper bound updated to 0.353427

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 3.53465 seconds.
    local lower bound updated to 0.352451
    local upper bound updated to 0.353396

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 3.43895 seconds.
    local lower bound updated to 0.352637
    local upper bound updated to 0.353327

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 4.2175 seconds.
    local lower bound updated to 0.352637
    local upper bound updated to 0.353319

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 3.68484 seconds.
    local lower bound updated to 0.353275
    local upper bound updated to 0.353317

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 4.20144 seconds.
    local lower bound updated to 0.353317
    local upper bound updated to 0.353317
The Primal step takes 31.9789 (S)
lower bound updated to 0.353317

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.373854
    local lower bound updated to 0.353317

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.357108
    local lower bound updated to 0.35346

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.354605
    local lower bound updated to 0.35369

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.35369
    local lower bound updated to 0.35369
The Dual step takes 5.81071 (S)
upper bound updated to 0.35369
*** OUTER ITERATION 5 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 3.3445 seconds.
    local lower bound updated to 0.30392
    local upper bound updated to 0.35369

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 3.08316 seconds.
    local lower bound updated to 0.353069
    local upper bound updated to 0.353639

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 4.32186 seconds.
    local lower bound updated to 0.353454
    local upper bound updated to 0.353597

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 3.89618 seconds.
    local lower bound updated to 0.353454
    local upper bound updated to 0.35359

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 4.32978 seconds.
    local lower bound updated to 0.353507
    local upper bound updated to 0.353581

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 4.12126 seconds.
    local lower bound updated to 0.353581
    local upper bound updated to 0.353581
The Primal step takes 23.1419 (S)
lower bound updated to 0.353581

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.370935
    local lower bound updated to 0.353581

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.354464
    local lower bound updated to 0.353589

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.353589
    local lower bound updated to 0.353589
The Dual step takes 5.70004 (S)
upper bound updated to 0.353589
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 3.56981 seconds.
    local lower bound updated to 0.304967
    local upper bound updated to 0.353589

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 3.23224 seconds.
    local lower bound updated to 0.353589
    local upper bound updated to 0.353589
The time obtain the optimal randomized assortment is 110.386 (S)
Now, the randomization optimization has been finished. We are checking the lower bound ....
Set parameter OutputFlag to value 1
Set parameter LogFile to value "/rds/general/user/zw1819/home/RAO/RAO_MC/FinalRun/RecFMResult/logFile_13_4_60.000000_61914.log"
The computation time limit for a lower bound is 85888
The model output flag is 1
Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)
Thread count: 24 physical cores, 48 logical processors, using up to 4 threads
Optimize a model with 2850 rows, 2514 columns and 8923 nonzeros
Model fingerprint: 0x8a8743f4
Variable types: 2465 continuous, 49 integer (49 binary)
Coefficient statistics:
  Matrix range     [6e-04, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e-01, 1e+00]
Presolve removed 906 rows and 1686 columns
Presolve time: 0.03s
Presolved: 1944 rows, 828 columns, 7297 nonzeros
Variable types: 780 continuous, 48 integer (48 binary)
Found heuristic solution: objective 0.5789459
Found heuristic solution: objective 0.4985662

Root relaxation: objective 1.780156e-01, 252 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0    0.17802    0   28    0.49857    0.17802  64.3%     -    0s
H    0     0                       0.3824001    0.17802  53.4%     -    0s
H    0     0                       0.3685180    0.17802  51.7%     -    0s
     0     0    0.24223    0   26    0.36852    0.24223  34.3%     -    0s
H    0     0                       0.3575415    0.24223  32.3%     -    0s
     0     0    0.27431    0   25    0.35754    0.27431  23.3%     -    0s
H    0     0                       0.3552791    0.27431  22.8%     -    0s
     0     0    0.27465    0   25    0.35528    0.27465  22.7%     -    0s
     0     0    0.28719    0   25    0.35528    0.28719  19.2%     -    0s
     0     0    0.28942    0   25    0.35528    0.28942  18.5%     -    0s
     0     0    0.29196    0   22    0.35528    0.29196  17.8%     -    0s
     0     0    0.29207    0   22    0.35528    0.29207  17.8%     -    0s
H    0     0                       0.3537445    0.29207  17.4%     -    0s
     0     0    0.29217    0   22    0.35374    0.29217  17.4%     -    0s
H    0     0                       0.3535893    0.29217  17.4%     -    1s
     0     2    0.29217    0   22    0.35359    0.29217  17.4%     -    1s
H  230   104                       0.3535893    0.32129  9.13%  25.5    1s
H 1048   159                       0.3535893    0.34577  2.21%  21.6    2s

Cutting planes:
  Gomory: 2
  Implied bound: 328
  MIR: 79
  Flow cover: 214
  RLT: 40
  Relax-and-lift: 100

Explored 2145 nodes (41935 simplex iterations) in 4.63 seconds (2.75 work units)
Thread count was 4 (of 48 available processors)

Solution count 9: 0.353589 0.353589 0.353745 ... 0.578946

Optimal solution found (tolerance 1.00e-04)
Best objective 3.535893128327e-01, best bound 3.535893128327e-01, gap 0.0000%
The objective bound is 0.353589 while the objective upper bound is 0.353589

============================================

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   2.96 (ave)

============================================
