Variables

The decision is the quantity shipped on each route: one variable indexed over plants and warehouses.

Declaring a variable

A Model contains variables, constraints and the objective. m.var(name, sets) declares a variable indexed over a tuple of sets and returns a handle for use in expressions.

import numpy as np
from nimopt import Model, Set

P = Set("P", np.array(["lisbon", "porto"]))
W = Set("W", np.array(["berlin", "paris", "rome"]))

m = Model("transport")
x = m.var("x", (P, W))

print(x.dims)
print(x.n_columns)

▶ Run this example

Output

('P', 'W')
6

Two plants by three warehouses give six members. x therefore occupies six columns of the coefficient matrix. A column index is computed from the positions of a member in each set, and nothing stores a column per member. A variable over a million members costs the same to declare as one over six.

Bounds and integrality

A variable has a lower bound of 0 and no upper bound unless declared otherwise. lower= and upper= take a number that applies to every column. integer=True restricts the columns to integer values and makes the model a MILP.

import numpy as np
from nimopt import Model, Set

P = Set("P", np.array(["lisbon", "porto"]))
W = Set("W", np.array(["berlin", "paris", "rome"]))

m = Model("transport")
x = m.var("x", (P, W), upper=20.0)
trucks = m.var("trucks", (P,), integer=True)

lower, upper = m.column_bounds()
print(lower)
print(upper)
print(m.integrality())
print(m.n_columns)

▶ Run this example

Output

[0. 0. 0. 0. 0. 0. 0. 0.]
[20. 20. 20. 20. 20. 20. inf inf]
[0 0 0 0 0 0 1 1]
8

A model has one column space shared by all its variables: x occupies columns 0 to 5 and trucks columns 6 and 7. column_bounds() returns the lower and upper bound vectors in column order, and integrality() returns one flag per column.

A parameter in place of a number gives each column its own bound; see Bounds from a parameter.

Next: Expressions.