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Results

Once we've added the model constraints, we call optimize and then output the optimal solution:


# Compute optimal solution
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    solution = m.getAttr('x', flow)
    for h in commodities:
        print('\nOptimal flows for %s:' % h)
        for i, j in arcs:
            if solution[h, i, j] > 0:
                print('%s -> %s: %g' % (i, j, solution[h, i, j]))

If you run the example gurobi.sh netflow.py, you should see the following output:

Using license file /opt/gurobi/gurobi.lic
Set parameter LogFile to value gurobi.log

Gurobi Optimizer version 9.0.0 build v9.0.0rc0 (linux64)

Optimize a model with 16 rows, 12 columns and 36 nonzeros
Model fingerprint: 0xf10778ba
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+01, 8e+01]
  Bounds range     [0e+00, 0e+00]
  RHS range        [1e+01, 1e+02]
Presolve removed 16 rows and 12 columns
Presolve time: 0.00s
Presolve: All rows and columns removed
Iteration    Objective       Primal Inf.    Dual Inf.      Time
       0    5.5000000e+03   0.000000e+00   2.000000e+01      0s
Extra one simplex iteration after uncrush
       1    5.5000000e+03   0.000000e+00   0.000000e+00      0s

Solved in 1 iterations and 0.00 seconds
Optimal objective  5.500000000e+03

Optimal flows for Pencils:
Detroit -> Boston: 50
Denver -> New York: 50
Denver -> Seattle: 10

Optimal flows for Pens:
Detroit -> Boston: 30
Detroit -> New York: 30
Denver -> Boston: 10
Denver -> Seattle: 30