Gurobi solution for the first transportation problem in An Illustrated Guide to Linear Programming.

trans_problem_1.py

from gurobipy import *

try:

    factories = ['FactoryOne','FactoryTwo']

    stores = ['StoreOne','StoreTwo','StoreThree']

    cost = {
        ('FactoryOne','StoreOne'): 8,
        ('FactoryOne','StoreTwo'): 6,
        ('FactoryOne','StoreThree'): 10,
        ('FactoryTwo','StoreOne'): 9,
        ('FactoryTwo','StoreTwo'): 5,
        ('FactoryTwo','StoreThree'): 7
    }

    supply = {
        ('FactoryOne'): 11,
        ('FactoryTwo'): 14
    }

    demand = {
        ('StoreOne'): 10,
        ('StoreTwo'): 8,
        ('StoreThree'): 7
    }

    # Create a new model
    m = Model("transport_problem_1")

    # Create variables
    flow = {}
    for f in factories:
        for s in stores:
            flow[f,s] = m.addVar(obj=cost[f,s], name='flow_%s_%s' % (f, s))

    # Integrate new variables
    m.update()

    # Add supply constraints
    for f in factories:
        m.addConstr(quicksum(flow[f,s] for s in stores) == supply[f], 'supply_%s' % (f))
    
    # Add demand constraints
    for s in stores:
        m.addConstr(quicksum(flow[f,s] for f in factories) == demand[s], 'demand_%s' % (s))

    # Optimize the model. The default ModelSense is to is to minimize the objective, which is what we want.
    m.optimize()

    # Print solution
    if m.status == GRB.status.OPTIMAL:
        print '\nOptimal flows :'
        for f in factories:
            for s in stores:
                print f, '->', s, ':', flow[f,s].x

except GurobiError:
    print 'Error reported'