"""
The Beer Distribution Problem for the PuLP Modeller

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

# Import PuLP modeler functions
import pulp

# 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 = pulp.makeDict([warehouses, bars], costs, 0)

# Creates the 'prob' variable to contain the problem data
prob = pulp.LpProblem("Beer Distribution Problem", pulp.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 x is created to contain quantity shipped on the routes
x = pulp.LpVariable.dicts("route", (warehouses, bars), lowBound=0, cat=pulp.LpInteger)

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

# Supply maximum constraints are added to prob for each supply node (warehouse)
for w in warehouses:
    prob += (
        sum([x[w][b] for b in bars]) <= supply[w],
        "Sum_of_Products_out_of_Warehouse_%s" % w,
    )

# Demand minimum constraints are added to prob for each demand node (bar)
for b in bars:
    prob += (
        sum([x[w][b] for w in warehouses]) >= demand[b],
        "Sum_of_Products_into_Bar%s" % b,
    )

# The problem data is written to an .lp file
prob.writeLP("BeerDistributionProblem.lp")

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

# The status of the solution is printed to the screen
print("Status:", pulp.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 = ", prob.objective.value())