transp_nofn.py

##@file transp_nofn.py
# @brief 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 pyscipopt import Model, quicksum

d = {1: 80, 2: 270, 3: 250, 4: 160, 5: 180}  # demand
I = d.keys()

M = {1: 500, 2: 500, 3: 500}  # capacity
J = M.keys()

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))

# Demand constraints
for i in I:
    model.addCons(sum(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.addCons(sum(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), "minimize")

model.optimize()

print("Optimal value:", model.getObjVal())

EPS = 1.e-6

for (i, j) in x:
    if model.getVal(x[i, j]) > EPS:
        print("sending quantity %10s from factory %3s to customer %3s" % (model.getVal(x[i, j]), j, i))