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 0.156146 seconds.
    local lower bound updated to 0.457993
    local upper bound updated to 0.742287

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.106564 seconds.
    local lower bound updated to 0.692802
    local upper bound updated to 0.692802
The Primal step takes 0.264693 (S)
lower bound updated to 0.692802

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.780973
    local lower bound updated to 0.752191

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.752191
    local lower bound updated to 0.752191
The Dual step takes 0.022478 (S)
upper bound updated to 0.752191
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.237721 seconds.
    local lower bound updated to 0.552912
    local upper bound updated to 0.73728

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.0525823 seconds.
    local lower bound updated to 0.685521
    local upper bound updated to 0.716771

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.21701 seconds.
    local lower bound updated to 0.715559
    local upper bound updated to 0.715888

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 0.1856 seconds.
    local lower bound updated to 0.715778
    local upper bound updated to 0.715858

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 0.176509 seconds.
    local lower bound updated to 0.715858
    local upper bound updated to 0.715858
The Primal step takes 0.877542 (S)
lower bound updated to 0.715858

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.777072
    local lower bound updated to 0.743923

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.743923
    local lower bound updated to 0.743923
The Dual step takes 0.0754698 (S)
upper bound updated to 0.743923
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.277668 seconds.
    local lower bound updated to 0.576491
    local upper bound updated to 0.718345

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.208061 seconds.
    local lower bound updated to 0.7101
    local upper bound updated to 0.715958

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.203045 seconds.
    local lower bound updated to 0.715636
    local upper bound updated to 0.715858

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 0.227673 seconds.
    local lower bound updated to 0.715858
    local upper bound updated to 0.715858
The Primal step takes 0.922781 (S)
lower bound updated to 0.715858

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.758445
    local lower bound updated to 0.729153

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.736099
    local lower bound updated to 0.729376

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.729376
    local lower bound updated to 0.729376
The Dual step takes 0.160047 (S)
upper bound updated to 0.729376
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.34193 seconds.
    local lower bound updated to 0.618384
    local upper bound updated to 0.72805

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.194342 seconds.
    local lower bound updated to 0.721674
    local upper bound updated to 0.726193

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.20086 seconds.
    local lower bound updated to 0.722205
    local upper bound updated to 0.72515

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 0.231399 seconds.
    local lower bound updated to 0.72285
    local upper bound updated to 0.724849

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 0.264865 seconds.
    local lower bound updated to 0.72285
    local upper bound updated to 0.724522

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 0.292042 seconds.
    local lower bound updated to 0.724089
    local upper bound updated to 0.724496

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 0.362298 seconds.
    local lower bound updated to 0.724089
    local upper bound updated to 0.724356

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 0.230333 seconds.
    local lower bound updated to 0.724356
    local upper bound updated to 0.724356
The Primal step takes 2.13722 (S)
lower bound updated to 0.724356

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.741763
    local lower bound updated to 0.724782

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.724782
    local lower bound updated to 0.724782
The Dual step takes 0.141106 (S)
upper bound updated to 0.724782
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.376178 seconds.
    local lower bound updated to 0.629741
    local upper bound updated to 0.724782

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.260569 seconds.
    local lower bound updated to 0.724782
    local upper bound updated to 0.724782
The Primal step takes 0.642741 (S)
lower bound updated to 0.724782

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.740826
    local lower bound updated to 0.724782

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.724782
    local lower bound updated to 0.724782
The Dual step takes 0.167388 (S)
upper bound updated to 0.724782
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.371368 seconds.
    local lower bound updated to 0.629741
    local upper bound updated to 0.724782

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.274121 seconds.
    local lower bound updated to 0.724782
    local upper bound updated to 0.724782
The time obtain the optimal randomized assortment is 6.06356 (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_11_4_60.000000_67112.log"
The computation time limit for a lower bound is 85992
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 720 rows, 700 columns and 2181 nonzeros
Model fingerprint: 0x4e735911
Variable types: 659 continuous, 41 integer (41 binary)
Coefficient statistics:
  Matrix range     [1e-03, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [7e-01, 1e+00]
Presolve removed 291 rows and 491 columns
Presolve time: 0.01s
Presolved: 429 rows, 209 columns, 1587 nonzeros
Variable types: 170 continuous, 39 integer (39 binary)
Found heuristic solution: objective 0.7773851

Root relaxation: objective 5.948893e-01, 65 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    0.59489    0   10    0.77739    0.59489  23.5%     -    0s
H    0     0                       0.7650064    0.59489  22.2%     -    0s
H    0     0                       0.7454276    0.63791  14.4%     -    0s
     0     0    0.63831    0   15    0.74543    0.63831  14.4%     -    0s
     0     0    0.63831    0   15    0.74543    0.63831  14.4%     -    0s
H    0     0                       0.7448549    0.63831  14.3%     -    0s
H    0     0                       0.7437614    0.64700  13.0%     -    0s
     0     0    0.64700    0   12    0.74376    0.64700  13.0%     -    0s
H    0     0                       0.7355295    0.64700  12.0%     -    0s
     0     0    0.64743    0   12    0.73553    0.64743  12.0%     -    0s
H    0     0                       0.7352012    0.64743  11.9%     -    0s
H    0     0                       0.7329745    0.64743  11.7%     -    0s
     0     0    0.65915    0   14    0.73297    0.65915  10.1%     -    0s
     0     0    0.66119    0   14    0.73297    0.66119  9.79%     -    0s
     0     0    0.66940    0   14    0.73297    0.66940  8.67%     -    0s
     0     0    0.67279    0   14    0.73297    0.67279  8.21%     -    0s
     0     0    0.67279    0   15    0.73297    0.67279  8.21%     -    0s
H    0     0                       0.7247822    0.67279  7.17%     -    0s
     0     2    0.67279    0   15    0.72478    0.67279  7.17%     -    0s

Cutting planes:
  Gomory: 1
  Implied bound: 26
  MIR: 12
  Flow cover: 30
  Relax-and-lift: 16

Explored 75 nodes (1465 simplex iterations) in 0.31 seconds (0.10 work units)
Thread count was 4 (of 48 available processors)

Solution count 9: 0.724782 0.732975 0.735201 ... 0.777385

Optimal solution found (tolerance 1.00e-04)
Best objective 7.247822213505e-01, best bound 7.247822213505e-01, gap 0.0000%
The objective bound is 0.724782 while the objective upper bound is 0.724782

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   2.85 (ave)

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