"""
transp.py: a model for the transportation problem

Model for solving a transportation problem:
minimize the total transportation cost for satisfying demand at
customers, from capacitated facilities.

Data:
    I - set of customers
    J - set of facilities
    c[i,j] - unit transportation cost on arc (i,j)
    d[i] - demand at node i
    M[j] - capacity
    
Copyright (c) by Joao Pedro PEDROSO and Mikio KUBO, 2012
"""

from gurobipy import *

I,d = multidict({1:80, 2:270, 3:250 , 4:160, 5:180}) # demand
J,M = multidict({1:500, 2:500, 3:500})               # capacity
c = {(1,1):4,    (1,2):6,    (1,3):9,  # cost
     (2,1):5,    (2,2):4,    (2,3):7,
     (3,1):6,    (3,2):3,    (3,3):4,
     (4,1):8,    (4,2):5,    (4,3):3,
     (5,1):10,   (5,2):8,    (5,3):4,
     }

model = Model("transportation")

# Create variables
x = {}
for i in I:
    for j in J:
        x[i,j] = model.addVar(vtype="C", name="x(%s,%s)" % (i,j))
model.update()

# Demand constraints
for i in I:
    model.addConstr(quicksum(x[i,j] for j in J if (i,j) in x) == d[i], name="Demand(%s)" % i)

# Capacity constraints
for j in J:
    model.addConstr(quicksum(x[i,j] for i in I if (i,j) in x) <= M[j], name="Capacity(%s)" % j)

# Objective
model.setObjective(quicksum(c[i,j]*x[i,j]  for (i,j) in x), GRB.MINIMIZE)

model.optimize()
print "Optimal value:", model.ObjVal

EPS = 1.e-6
for (i,j) in x:
    if x[i,j].X > EPS:
        print "sending quantity %10s from factory %3s to customer %3s" % (x[i,j].X,j,i)