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

trans_problem_2.py

from gurobipy import *

try:

    cities = ['OklahomaCity','Macon','Columbus']

    bases = ['MacDill','March','DavisMonthan','McConnell','Pinecastle']

    distance = {
        ('OklahomaCity','MacDill'): 938,
        ('OklahomaCity','March'): 1030,
        ('OklahomaCity','DavisMonthan'): 824,
        ('OklahomaCity','McConnell'): 136,
        ('OklahomaCity','Pinecastle'): 995,
        ('Macon','MacDill'): 346,
        ('Macon','March'): 1818,
        ('Macon','DavisMonthan'): 1416,
        ('Macon','McConnell'): 806,
        ('Macon','Pinecastle'): 296,
        ('Columbus','MacDill'): 905,
        ('Columbus','March'): 1795,
        ('Columbus','DavisMonthan'): 1590,
        ('Columbus','McConnell'): 716,
        ('Columbus','Pinecastle'): 854
    }

    supply = {
        ('OklahomaCity'): 8,
        ('Macon'): 5,
        ('Columbus'): 8
    }

    demand = {
        ('MacDill'): 3,
        ('March'): 5,
        ('DavisMonthan'): 5,
        ('McConnell'): 5,
        ('Pinecastle'): 3
    }

    # Create a new model
    m = Model("transport_problem_2")

    # Create variables
    flow = {}
    for c in cities:
        for b in bases:
            flow[c,b] = m.addVar(obj=distance[c,b], name='flow_%s_%s' % (c, b))

    # Integrate new variables
    m.update()

    # Add supply constraints
    for c in cities:
        m.addConstr(quicksum(flow[c,b] for b in bases) == supply[c], 'supply_%s' % (c))
    
    # Add demand constraints
    for b in bases:
        m.addConstr(quicksum(flow[c,b] for c in cities) == demand[b], 'demand_%s' % (b))

    # 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 c in cities:
            for b in bases:
                print c, '->', b, ':', flow[c,b].x

except GurobiError:
    print 'Error reported'