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Blend: A model for mineral blending
Type: Blending
Rating: 1 (simple)
Description: Several ores are blended to a final product that must have a certain quality ('grade'). We wish to determine the quantity of every ore to be used in the blend with the objective to maximize the total profit (calculated as sales revenues - raw material cost).
File(s): blend.py, blend2.py
Data file(s): blend_data.py

blend.py
# Example for the use of the Python language (Blending problem).
#
# Reading data from file.
#
# (C) 2018-2025 Fair Isaac Corporation

import xpress as xp
from Data.blend_data import COST, AVAIL, GRADE

p = xp.problem()

ROres = range(2)
REV = 125                     # Unit revenue of product.
MINGRADE = 4                  # Min permitted grade of product.
MAXGRADE = 5                  # Max permitted grade of product.

x = [p.addVariable(ub=AVAIL[o]) for o in ROres]

# Objective: maximize total profit.
p.setObjective(xp.Sum((REV - COST[o]) * x[o] for o in ROres),
               sense=xp.maximize)

# Lower and upper bounds on ore quality.
p.addConstraint(xp.Sum((GRADE[o] - MINGRADE) * x[o] for o in ROres) >= 0)
p.addConstraint(xp.Sum((MAXGRADE - GRADE[o]) * x[o] for o in ROres) >= 0)

p.optimize()

# Print out the solution.
print("Solution:\n Objective:", p.attributes.objval)
xsol = p.getSolution(x)
for o in ROres:
    print(" x(", o, "): ", xsol[o])
print("Grade: ", sum(GRADE[o] * xsol[o] for o in ROres)
      / sum(xsol[o] for o in ROres),
      " [min,max]: [", MINGRADE, ",", MAXGRADE, "]")
blend2.py
# Example for the use of the Python language (Blending problem).
#
# Data given in the model.
#
# (C) 2018-2025 Fair Isaac Corporation

import xpress as xp

p = xp.problem()

ROres = range(2)
REV = 125                     # Unit revenue of product.
MINGRADE = 4                  # Min permitted grade of product.
MAXGRADE = 5                  # Max permitted grade of product.

COST = [85.00, 93.00]
AVAIL = [60.00, 45.00]
GRADE = [2.1, 6.3]

x = [p.addVariable(ub=AVAIL[o]) for o in ROres]

# Objective: maximize total profit.
p.setObjective(xp.Sum((REV - COST[o]) * x[o] for o in ROres),
               sense=xp.maximize)

# Lower and upper bounds on ore quality.
p.addConstraint(xp.Sum((GRADE[o] - MINGRADE) * x[o] for o in ROres) >= 0)
p.addConstraint(xp.Sum((MAXGRADE - GRADE[o]) * x[o] for o in ROres) >= 0)

p.optimize()
Parent Topic Modeling examples

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