"""
transp.py: a model for the multi-commodity transportation problem

Model for solving the multi-commodity transportation problem:
minimize the total transportation cost for satisfying demand at
customers, from capacitated facilities.
            
Copyright (c) by Joao Pedro PEDROSO and Mikio KUBO, 2012
"""

from gurobipy import *

def mctransp(I,J,K,c,d,M):
    """mctransp -- model for solving the Multi-commodity Transportation Problem
    Parameters:
        - I: set of customers
        - J: set of facilities
        - K: set of commodities
        - c[i,j,k]: unit transportation cost on arc (i,j) for commodity k
        - d[i][k]: demand for commodity k at node i
        - M[j]: capacity
    Returns a model, ready to be solved.
    """
    
    model = Model("multi-commodity transportation")

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

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

    # Capacity constraints
    for j in J:
        model.addConstr(quicksum(x[i,j,k] for (i,j2,k) in x if j2 == j) <= M[j], "Capacity(%s)" % j)

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

    model.update()
    model.__data = x
    return model


def make_inst1():
    d = {(1,1):80,   (1,2):85,   (1,3):300,  (1,4):6, # {(customer,commodity):demand}}
         (2,1):270,  (2,2):160,  (2,3):400,  (2,4):7,
         (3,1):250,  (3,2):130,  (3,3):350,  (3,4):4,
         (4,1):160,  (4,2):60,   (4,3):200,  (4,4):3,
         (5,1):180,  (5,2):40,   (5,3):150,  (5,4):5
         }
    I = set([i for (i,k) in d])
    K = set([k for (i,k) in d])
    J,M = multidict({1:3000, 2:3000, 3:3000})  # capacity

    produce = {1:[2,4], 2:[1,2,3], 3:[2,3,4]}  # products that can be produced in each facility
    weight = {1:5, 2:2, 3:3, 4:4}              # {commodity: weight}
    cost = {(1,1):4,  (1,2):6, (1,3):9,        # {(customer,factory): 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
            }
    c = {}
    for i in I:
        for j in J:
            for k in produce[j]:
                c[i,j,k] = cost[i,j] * weight[k]

    return I,J,K,c,d,M

def make_inst2():
    d = {(1,1):45,                             # {(customer,commodity):demand}}
         (2,1):20,
         (3,1):30,
         (4,1):30,
         }
    I = set([i for (i,k) in d])
    K = set([k for (i,k) in d])
    J,M = multidict({1:35, 2:50, 3:40})       # {factory: capacity}}
    produce = {1:[1], 2:[1], 3:[1]}           # products that can be produced in each facility
    weight = {1:1}                            # {commodity: weight}
    cost = {(1,1):8,    (1,2):9,    (1,3):14, # {(customer,factory): cost}
            (2,1):6,    (2,2):12,   (2,3):9 ,
            (3,1):10,   (3,2):13,   (3,3):16,
            (4,1):9,    (4,2):7,    (4,3):5 ,
            }
    c = {}
    for i in I:
        for j in J:
            for k in produce[j]:
                c[i,j,k] = cost[i,j] * weight[k]

    return I,J,K,c,d,M


def make_inst3():
    d = {(1,1):40,   (1,2):30,   (1,3):10,  # {(customer,commodity):demand}}
         (2,1):70,   (2,2):100,  (2,3):100,
         (3,1):0,    (3,2):0,    (3,3):250,
         (4,1):60,   (4,2):100,  (4,3):0,
         (5,1):180,  (5,2):0,    (5,3):0
         }
    I = set([i for (i,k) in d])
    K = set([k for (i,k) in d])
    J,M = multidict({1:500, 2:500, 3:500})  # capacity

    produce = {1:[2,4], 2:[1,2,3], 3:[2,3,4]}  # products that can be produced in each facility
    weight = {1:5, 2:2, 3:3, 4:4}              # {commodity: weight}
    cost = {(1,1):4,  (1,2):6, (1,3):9,        # {(customer,factory): 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
            }
    c = {}
    for i in I:
        for j in J:
            for k in produce[j]:
                c[i,j,k] = cost[i,j] * weight[k]

    return I,J,K,c,d,M



if __name__ == "__main__":
    I,J,K,c,d,M = make_inst3();
    model = mctransp(I,J,K,c,d,M)
    model.write("transp.lp")
    model.optimize()
    print "Optimal value:",model.ObjVal

    EPS = 1.e-6
    x = model.__data
    for (i,j,k) in x:
        if x[i,j,k].X > EPS:
            print "sending %10s units of %3s from plant %3s to customer %3s" % (x[i,j,k].X,k,j,i)