Blending Problem

Importing Modules

The gamspy Python package is loaded in order to access GAMSPy syntax.

from gamspy import Container, Set, Parameter, Variable, Equation, Model, Sum, Sense
import numpy as np

Data

m = Container()

# Set
alloy = Set(
    container=m, name="alloy", records=["a", "b", "c", "d", "e", "f", "g", "h", "i"]
)
elem = Set(container=m, name="elem", records=["lead", "zinc", "tin"])

# Data
compdat = Parameter(
    container=m,
    name="compdat",
    domain=[elem, alloy],
    records=np.array(
        [
            [10, 10, 40, 60, 30, 30, 30, 50, 20],
            [10, 30, 50, 30, 30, 40, 20, 40, 30],
            [80, 60, 10, 10, 40, 30, 50, 10, 50],
        ]
    ),
)
price = Parameter(
    container=m,
    name="price",
    domain=alloy,
    records=np.array([4.1, 4.3, 5.8, 6.0, 7.6, 7.5, 7.3, 6.9, 7.3]),
)
rb = Parameter(container=m, name="rb", domain=elem, records=np.array([30, 30, 40]))

# Variable
v = Variable(container=m, name="v", domain=alloy, type="Positive")

Model

pc = Equation(container=m, name="pc", domain=elem)
mb = Equation(container=m, name="mb")

pc[elem] = Sum(alloy, compdat[elem, alloy] * v[alloy]) == rb[elem]
mb[...] = Sum(alloy, v[alloy]) == 1

b1 = Model(
    container=m,
    name="b1",
    equations=[pc],
    problem="LP",
    sense=Sense.MIN,
    objective=Sum(alloy, price[alloy] * v[alloy]),
)

b2 = Model(
    container=m,
    name="b2",
    equations=[pc, mb],
    problem="LP",
    sense=Sense.MIN,
    objective=Sum(alloy, price[alloy] * v[alloy]),
)

Solve

report = Parameter(container=m, name="report", domain=[alloy, "*"])

b1.solve()
report[alloy, "blend-1"] = v.l[alloy]

b2.solve()
report[alloy, "blend-2"] = v.l[alloy]

Reporting

report.pivot()

	blend-1	blend-2
b	0.6	0.6
d	0.4	0.4