1 Base data

nodes = ['Finland', 'Sweden', 'Norway', 'Denmark', 'Germany']
commodities = ['ATMCashMachines', 'BranchOffices']

arcs, capacity = gp.multidict({
    ('Finland', 'Norway'):   500,
    ('Finland', 'Denmark'):  580,
    ('Finland', 'Germany'):  620,
    ('Sweden',  'Norway'):   720,
    ('Sweden',  'Denmark'):  820,
    ('Sweden',  'Germany'):  920})

2 Operation cost for triplets commodity-source-destination

cost = {
    ('ATMCashMachines', 'Finland', 'Norway'):   50,
    ('ATMCashMachines', 'Finland', 'Denmark'):  20,
    ('ATMCashMachines', 'Finland', 'Germany'):  10,
    ('ATMCashMachines', 'Sweden',  'Norway'):   40,
    ('ATMCashMachines', 'Sweden',  'Denmark'):  40,
    ('ATMCashMachines', 'Sweden',  'Germany'):  30,
    ('BranchOffices',   'Finland', 'Norway'):   20,
    ('BranchOffices',   'Finland', 'Denmark'):  40,
    ('BranchOffices',   'Finland', 'Germany'):  80,
    ('BranchOffices',   'Sweden',  'Norway'):   60,
    ('BranchOffices',   'Sweden',  'Denmark'):  30,
    ('BranchOffices',   'Sweden',  'Germany'):  30}

3 Demand pairs of commodity-country

inflow = {
    ('ATMCashMachines', 'Finland'):   50,
    ('ATMCashMachines', 'Sweden'):    60,
    ('ATMCashMachines', 'Norway'):   -50,
    ('ATMCashMachines', 'Denmark'):  -50,
    ('ATMCashMachines', 'Germany'):  -10,
    ('BranchOffices',   'Finland'):   60,
    ('BranchOffices',   'Sweden'):    40,
    ('BranchOffices',   'Norway'):   -40,
    ('BranchOffices',   'Denmark'):  -30,
    ('BranchOffices',   'Germany'):  -30}

4 Create optimization model

m = gp.Model('netflow')

Using license file C:\Users\Heatfront\gurobi.lic
Academic license - for non-commercial use only

5 Create variables

flow = m.addVars(commodities, arcs, obj=cost, name="flow")

6 Arc-capacity constraints

m.addConstrs(
    (flow.sum('*', i, j) <= capacity[i, j] for i, j in arcs), "cap")

{('Finland', 'Norway'): <gurobi.Constr *Awaiting Model Update*>, ('Finland', 'Denmark'): <gurobi.Constr *Awaiting Model Update*>, ('Finland', 'Germany'): <gurobi.Constr *Awaiting Model Update*>, ('Sweden', 'Norway'): <gurobi.Constr *Awaiting Model Update*>, ('Sweden', 'Denmark'): <gurobi.Constr *Awaiting Model Update*>, ('Sweden', 'Germany'): <gurobi.Constr *Awaiting Model Update*>}

7 Model optimization

m.addConstrs(
    (flow.sum(h, '*', j) + inflow[h, j] == flow.sum(h, j, '*')
        for h in commodities for j in nodes), "node")

{('ATMCashMachines', 'Finland'): <gurobi.Constr *Awaiting Model Update*>, ('ATMCashMachines', 'Sweden'): <gurobi.Constr *Awaiting Model Update*>, ('ATMCashMachines', 'Norway'): <gurobi.Constr *Awaiting Model Update*>, ('ATMCashMachines', 'Denmark'): <gurobi.Constr *Awaiting Model Update*>, ('ATMCashMachines', 'Germany'): <gurobi.Constr *Awaiting Model Update*>, ('BranchOffices', 'Finland'): <gurobi.Constr *Awaiting Model Update*>, ('BranchOffices', 'Sweden'): <gurobi.Constr *Awaiting Model Update*>, ('BranchOffices', 'Norway'): <gurobi.Constr *Awaiting Model Update*>, ('BranchOffices', 'Denmark'): <gurobi.Constr *Awaiting Model Update*>, ('BranchOffices', 'Germany'): <gurobi.Constr *Awaiting Model Update*>}

m.optimize()

Gurobi Optimizer version 9.0.0 build v9.0.0rc2 (win64)
Optimize a model with 16 rows, 12 columns and 36 nonzeros
Model fingerprint: 0xf3ddfcd8
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+01, 8e+01]
  Bounds range     [0e+00, 0e+00]
  RHS range        [1e+01, 9e+02]
Presolve removed 15 rows and 9 columns
Presolve time: 0.01s
Presolved: 1 rows, 3 columns, 3 nonzeros

Iteration    Objective       Primal Inf.    Dual Inf.      Time
       0    5.7000000e+03   2.500000e+00   0.000000e+00      0s
       1    6.1000000e+03   0.000000e+00   0.000000e+00      0s

Solved in 1 iterations and 0.02 seconds
Optimal objective  6.100000000e+03

8 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]))

Optimal flows for ATMCashMachines:
Finland -> Denmark: 50
Sweden -> Norway: 50
Sweden -> Germany: 10

Optimal flows for BranchOffices:
Finland -> Norway: 40
Finland -> Denmark: 20
Sweden -> Denmark: 10
Sweden -> Germany: 30

9 Results Tabluation