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"""
The Computer Plant Problem for the PuLP Modeller
Authors: Antony Phillips, Dr Stuart Mitchell 2007
"""
# Import PuLP modeler functions
from pulp import *
# Creates a list of all the supply nodes
Plants = ["San Francisco", "Los Angeles", "Phoenix", "Denver"]
# Creates a dictionary of lists for the number of units of supply at
# each plant and the fixed cost of running each plant
supplyData = { # Plant Supply Fixed Cost
"San Francisco": [1700, 70000],
"Los Angeles": [2000, 70000],
"Phoenix": [1700, 65000],
"Denver": [2000, 70000],
}
# Creates a list of all demand nodes
Stores = ["San Diego", "Barstow", "Tucson", "Dallas"]
# Creates a dictionary for the number of units of demand at each store
demand = { # Store Demand
"San Diego": 1700,
"Barstow": 1000,
"Tucson": 1500,
"Dallas": 1200,
}
# Creates a list of costs for each transportation path
costs = [ # Stores
# SD BA TU DA
[5, 3, 2, 6], # SF
[4, 7, 8, 10], # LA Plants
[6, 5, 3, 8], # PH
[9, 8, 6, 5], # DE
]
# Creates a list of tuples containing all the possible routes for transport
Routes = [(p, s) for p in Plants for s in Stores]
# Splits the dictionaries to be more understandable
(supply, fixedCost) = splitDict(supplyData)
# The cost data is made into a dictionary
costs = makeDict([Plants, Stores], costs, 0)
# Creates the problem variables of the Flow on the Arcs
flow = LpVariable.dicts("Route", (Plants, Stores), 0, None, LpInteger)
# Creates the master problem variables of whether to build the Plants or not
build = LpVariable.dicts("BuildaPlant", Plants, 0, 1, LpInteger)
# Creates the 'prob' variable to contain the problem data
prob = LpProblem("Computer Plant Problem", LpMinimize)
# The objective function is added to prob - The sum of the transportation costs and the building fixed costs
prob += (
lpSum([flow[p][s] * costs[p][s] for (p, s) in Routes])
+ lpSum([fixedCost[p] * build[p] for p in Plants]),
"Total Costs",
)
# The Supply maximum constraints are added for each supply node (plant)
for p in Plants:
prob += (
lpSum([flow[p][s] for s in Stores]) <= supply[p] * build[p],
"Sum of Products out of Plant %s" % p,
)
# The Demand minimum constraints are added for each demand node (store)
for s in Stores:
prob += (
lpSum([flow[p][s] for p in Plants]) >= demand[s],
"Sum of Products into Stores %s" % s,
)
# The problem data is written to an .lp file
prob.writeLP("ComputerPlantProblem.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:", 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 Costs = ", value(prob.objective))
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