chemical_balance_lp.py

#!/usr/bin/env python3
# Copyright 2010-2024 Google LLC
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""We are trying to group items in equal sized groups.
Each item has a color and a value. We want the sum of values of each group to
be as close to the average as possible.
Furthermore, if one color is an a group, at least k items with this color must
be in that group."""

from ortools.linear_solver import pywraplp

# Data

max_quantities = [
    ["N_Total", 1944],
    ["P2O5", 1166.4],
    ["K2O", 1822.5],
    ["CaO", 1458],
    ["MgO", 486],
    ["Fe", 9.7],
    ["B", 2.4],
]

chemical_set = [
    ["A", 0, 0, 510, 540, 0, 0, 0],
    ["B", 110, 0, 0, 0, 160, 0, 0],
    ["C", 61, 149, 384, 0, 30, 1, 0.2],
    ["D", 148, 70, 245, 0, 15, 1, 0.2],
    ["E", 160, 158, 161, 0, 10, 1, 0.2],
]

NUM_PRODUCTS = len(max_quantities)
ALL_PRODUCTS = range(NUM_PRODUCTS)

NUM_SETS = len(chemical_set)
ALL_SETS = range(NUM_SETS)

# Model

max_set = [
    min(max_quantities[q][1] / chemical_set[s][q + 1] for q in ALL_PRODUCTS
        if chemical_set[s][q + 1] != 0.0) for s in ALL_SETS
]

solver = pywraplp.Solver("chemical_set_lp",
                         pywraplp.Solver.GLOP_LINEAR_PROGRAMMING)

set_vars = [solver.NumVar(0, max_set[s], f"set_{s}") for s in ALL_SETS]

epsilon = solver.NumVar(0, 1000, "epsilon")

for p in ALL_PRODUCTS:
    solver.Add(
        sum(chemical_set[s][p + 1] * set_vars[s]
            for s in ALL_SETS) <= max_quantities[p][1])
    solver.Add(
        sum(chemical_set[s][p + 1] * set_vars[s]
            for s in ALL_SETS) >= max_quantities[p][1] - epsilon)

solver.Minimize(epsilon)

print(f"Number of variables = {solver.NumVariables()}")
print(f"Number of constraints = {solver.NumConstraints()}")

result_status = solver.Solve()

# The problem has an optimal solution.
assert result_status == pywraplp.Solver.OPTIMAL

assert solver.VerifySolution(1e-7, True)

print(f"Problem solved in {solver.wall_time()} milliseconds")

# The objective value of the solution.
print(f"Optimal objective value = {solver.Objective().Value()}")

for s in ALL_SETS:
    print(f"  {chemical_set[s][0]} = {set_vars[s].solution_value()}", end=" ")
    print()
for p in ALL_PRODUCTS:
    name = max_quantities[p][0]
    max_quantity = max_quantities[p][1]
    quantity = sum(set_vars[s].solution_value() * chemical_set[s][p + 1]
                   for s in ALL_SETS)
    print(f"{name}: {quantity} out of {max_quantity}")