"""
The Beer Distribution Problem for the PuLP Modeller
Illustrates changing a constraint and solving

Authors: Antony Phillips, Dr Stuart Mitchell  2007
"""

# Import PuLP modeler functions
from pulp import *

# Creates a list of all the supply nodes
Warehouses = ["A", "B"]

# Creates a dictionary for the number of units of supply for each supply node
supply = {"A": 1000,
          "B": 4000}

# Creates a list of all demand nodes
Bars = ["1", "2", "3", "4", "5"]

# Creates a dictionary for the number of units of demand for each demand node
demand = {"1":500,
          "2":900,
          "3":1800,
          "4":200,
          "5":700,}

# Creates a list of costs of each transportation path
costs = [   #Bars
         #1 2 3 4 5
         [2,4,5,2,1],#A   Warehouses
         [3,1,3,2,3] #B
         ]

# The cost data is made into a dictionary
costs = makeDict([Warehouses,Bars],costs,0)

# Creates the 'prob' variable to contain the problem data
prob = LpProblem("Beer Distribution Problem",LpMinimize)

# Creates a list of tuples containing all the possible routes for transport
Routes = [(w,b) for w in Warehouses for b in Bars]

# A dictionary called 'Vars' is created to contain the referenced variables(the routes)
vars = LpVariable.dicts("Route",(Warehouses,Bars),0,None,LpInteger)

# The objective function is added to 'prob' first
prob += lpSum([vars[w][b]*costs[w][b] for (w,b) in Routes]), "Sum_of_Transporting_Costs"

# The supply maximum constraints are added to prob for each supply node (warehouse)
for w in Warehouses:
    prob += lpSum([vars[w][b] for b in Bars])<=supply[w], "Sum_of_Products_out_of_Warehouse_%s"%w

# The demand minimum constraints are added to prob for each demand node (bar)
# These constraints are stored for resolve later
bar_demand_constraint = {}
for b in Bars:
    constraint = lpSum([vars[w][b] for w in Warehouses])>=demand[b]
    prob += constraint, "Sum_of_Products_into_Bar_%s"%b
    bar_demand_constraint[b] = constraint

# The problem data is written to an .lp file
prob.writeLP("BeerDistributionProblem.lp")
for demand in range(500, 601, 10):
    # reoptimise the problem by increasing demand at bar '1'
    # note the constant is stored as the LHS constant not the RHS of the constraint
    bar_demand_constraint['1'].constant = - demand
    #or alternatively,
    #prob.constraints["Sum_of_Products_into_Bar_1"].constant = - demand

    # The problem is solved using PuLP's choice of Solver
    prob.solve()

    # The status of the solution is printed to the screen
    print "Status:", LpStatus[prob.status]

    # Each of the variables is printed with it's resolved optimum value
    for v in prob.variables():
        print v.name, "=", v.varValue

    # The optimised objective function value is printed to the screen
    print "Total Cost of Transportation = ", value(prob.objective)
