lo_wines.py

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"""
It solves the same instance as lo_wines_simple.py:
 
maximize  15x + 18y + 30z
subject to 2x +   y +   z <= 60
           x  +  2y +   z <= 60
                        z <= 30
           x,y,z >= 0
Variables correspond to the production of three types of wine blends,
made from pure-grape wines.
Constraints correspond to the inventory of pure-grape wines.
 
Copyright (c) by Joao Pedro PEDROSO and Mikio KUBO, 2012
"""
from pyscipopt import Model, quicksum, SCIP_PARAMSETTING
 
# Initialize model
model = Model("Wine blending")
model.setPresolve(SCIP_PARAMSETTING.OFF)
 
Inventory = {"Alfrocheiro": 60, "Baga": 60, "Castelao": 30}
Grapes = Inventory.keys()
 
Profit = {"Dry": 15, "Medium": 18, "Sweet": 30}
Blends = Profit.keys()
 
Use = {
    ("Alfrocheiro", "Dry"): 2,
    ("Alfrocheiro", "Medium"): 1,
    ("Alfrocheiro", "Sweet"): 1,
    ("Baga", "Dry"): 1,
    ("Baga", "Medium"): 2,
    ("Baga", "Sweet"): 1,
    ("Castelao", "Dry"): 0,
    ("Castelao", "Medium"): 0,
    ("Castelao", "Sweet"): 1
}
 
# Create variables
x = {}
for j in Blends:
    x[j] = model.addVar(vtype="C", name="x(%s)" % j)
 
# Create constraints
c = {}
for i in Grapes:
    c[i] = model.addCons(quicksum(Use[i, j] * x[j] for j in Blends) <= Inventory[i], name="Use(%s)" % i)
 
# Objective
model.setObjective(quicksum(Profit[j] * x[j] for j in Blends), "maximize")
 
model.optimize()
 
if model.getStatus() == "optimal":
    print("Optimal value:", model.getObjVal())
 
    for j in x:
        print(x[j].name, "=", model.getVal(x[j]), " (red. cost: ", model.getVarRedcost(x[j]), ")")
    for i in c:
        try:
            dual = model.getDualsolLinear(c[i])
        except:
            dual = None
        print("dual of", c[i].name, ":", dual)
else:
    print("Problem could not be solved to optimality")