ILP

linear_program.py

#!/usr/bin/python

"""linear_program.py: Solves an simple integer linear program.

   Maximize
     f(x) = 6x₁ + 4x₂

  with
    x₁, x₂ ∈ ℕ

   Constraints
     x₁ + 2x₂ <= 8
     3x₁ + x₂ <= 9

"""

__author__ = "Benno Bielmeier"
__copyright__ = "Copyright 2020, Planet Earth"
__license__ = "Unlicense"
__version__ = "1.0"

from ortools.linear_solver import pywraplp

solver = pywraplp.Solver(
    "simple integer linear program", pywraplp.Solver.GLOP_LINEAR_PROGRAMMING
)

# variables
x1 = solver.NumVar(0, solver.infinity(), "x1")
x2 = solver.NumVar(0, solver.infinity(), "x2")

# constraints
ct1 = solver.Constraint(-solver.infinity(), 8, "constraint 1")
ct1.SetCoefficient(x1, 1)
ct1.SetCoefficient(x2, 2)

ct2 = solver.Constraint(-solver.infinity(), 9, "constraint 2")
ct2.SetCoefficient(x1, 3)
ct2.SetCoefficient(x2, 1)

# objective function
objective = solver.Objective()
objective.SetCoefficient(x1, 6)
objective.SetCoefficient(x2, 4)
objective.SetMaximization()

solver.Solve()

# print solution
print("max value = ", objective.Value())
print("x1 = ", x1.solution_value())
print("x2 = ", x2.solution_value())