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stigler_diet.py
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#!/usr/bin/env python
# This Python file uses the following encoding: utf-8
# Copyright 2018 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.
"""Stigler diet example"""
from ortools.linear_solver import pywraplp
def main():
"""Entry point of the program"""
# Nutrient minimums.
nutrients = [['Calories (kcal)', 3], ['Protein (g)', 70], [
'Calcium (g)', 0.8
], ['Iron (mg)', 12], ['Vitamin A (KIU)', 5], ['Vitamin B1 (mg)', 1.8],
['Vitamin B2 (mg)', 2.7], ['Niacin (mg)',
18], ['Vitamin C (mg)', 75]]
# Commodity, Unit, 1939 price (cents), Calories (kcal), Protein (g), Calcium (g), Iron (mg),
# Vitamin A (KIU), Vitamin B1 (mg), Vitamin B2 (mg), Niacin (mg), Vitamin C (mg)
data = [[
'Wheat Flour (Enriched)', '10 lb.', 36, 44.7, 1411, 2, 365, 0, 55.4,
33.3, 441, 0
], ['Macaroni', '1 lb.', 14.1, 11.6, 418, 0.7, 54, 0, 3.2, 1.9, 68, 0], [
'Wheat Cereal (Enriched)', '28 oz.', 24.2, 11.8, 377, 14.4, 175, 0,
14.4, 8.8, 114, 0
], ['Corn Flakes', '8 oz.', 7.1, 11.4, 252, 0.1, 56, 0, 13.5, 2.3, 68, 0], [
'Corn Meal', '1 lb.', 4.6, 36.0, 897, 1.7, 99, 30.9, 17.4, 7.9, 106, 0
], [
'Hominy Grits', '24 oz.', 8.5, 28.6, 680, 0.8, 80, 0, 10.6, 1.6, 110, 0
], ['Rice', '1 lb.', 7.5, 21.2, 460, 0.6, 41, 0, 2, 4.8, 60, 0], [
'Rolled Oats', '1 lb.', 7.1, 25.3, 907, 5.1, 341, 0, 37.1, 8.9, 64, 0
], [
'White Bread (Enriched)', '1 lb.', 7.9, 15.0, 488, 2.5, 115, 0, 13.8,
8.5, 126, 0
], [
'Whole Wheat Bread', '1 lb.', 9.1, 12.2, 484, 2.7, 125, 0, 13.9, 6.4,
160, 0
], ['Rye Bread', '1 lb.', 9.1, 12.4, 439, 1.1, 82, 0, 9.9, 3, 66, 0], [
'Pound Cake', '1 lb.', 24.8, 8.0, 130, 0.4, 31, 18.9, 2.8, 3, 17, 0
], ['Soda Crackers', '1 lb.', 15.1, 12.5, 288, 0.5, 50, 0, 0, 0, 0, 0], [
'Milk', '1 qt.', 11, 6.1, 310, 10.5, 18, 16.8, 4, 16, 7, 177
], [
'Evaporated Milk (can)', '14.5 oz.', 6.7, 8.4, 422, 15.1, 9, 26, 3,
23.5, 11, 60
], ['Butter', '1 lb.', 30.8, 10.8, 9, 0.2, 3, 44.2, 0, 0.2, 2, 0], [
'Oleomargarine', '1 lb.', 16.1, 20.6, 17, 0.6, 6, 55.8, 0.2, 0, 0, 0
], ['Eggs', '1 doz.', 32.6, 2.9, 238, 1.0, 52, 18.6, 2.8, 6.5, 1, 0], [
'Cheese (Cheddar)', '1 lb.', 24.2, 7.4, 448, 16.4, 19, 28.1, 0.8, 10.3,
4, 0
], ['Cream', '1/2 pt.', 14.1, 3.5, 49, 1.7, 3, 16.9, 0.6, 2.5, 0, 17], [
'Peanut Butter', '1 lb.', 17.9, 15.7, 661, 1.0, 48, 0, 9.6, 8.1, 471, 0
], ['Mayonnaise', '1/2 pt.', 16.7, 8.6, 18, 0.2, 8, 2.7, 0.4, 0.5, 0, 0], [
'Crisco', '1 lb.', 20.3, 20.1, 0, 0, 0, 0, 0, 0, 0, 0
], ['Lard', '1 lb.', 9.8, 41.7, 0, 0, 0, 0.2, 0, 0.5, 5, 0], [
'Sirloin Steak', '1 lb.', 39.6, 2.9, 166, 0.1, 34, 0.2, 2.1, 2.9, 69, 0
], ['Round Steak', '1 lb.', 36.4, 2.2, 214, 0.1, 32, 0.4, 2.5, 2.4, 87, 0
], ['Rib Roast', '1 lb.', 29.2, 3.4, 213, 0.1, 33, 0, 0, 2, 0, 0], [
'Chuck Roast', '1 lb.', 22.6, 3.6, 309, 0.2, 46, 0.4, 1, 4, 120, 0
], ['Plate', '1 lb.', 14.6, 8.5, 404, 0.2, 62, 0, 0.9, 0, 0, 0], [
'Liver (Beef)', '1 lb.', 26.8, 2.2, 333, 0.2, 139, 169.2, 6.4, 50.8,
316, 525
], [
'Leg of Lamb', '1 lb.', 27.6, 3.1, 245, 0.1, 20, 0, 2.8, 3.9, 86, 0
], [
'Lamb Chops (Rib)',
'1 lb.', 36.6, 3.3, 140, 0.1, 15, 0, 1.7, 2.7, 54, 0
], [
'Pork Chops', '1 lb.', 30.7, 3.5, 196, 0.2, 30, 0, 17.4, 2.7, 60, 0
], [
'Pork Loin Roast',
'1 lb.', 24.2, 4.4, 249, 0.3, 37, 0, 18.2, 3.6, 79, 0
], ['Bacon', '1 lb.', 25.6, 10.4, 152, 0.2, 23, 0, 1.8, 1.8, 71, 0], [
'Ham, smoked', '1 lb.', 27.4, 6.7, 212, 0.2, 31, 0, 9.9, 3.3, 50, 0
], ['Salt Pork', '1 lb.', 16, 18.8, 164, 0.1, 26, 0, 1.4, 1.8, 0, 0], [
'Roasting Chicken', '1 lb.', 30.3, 1.8, 184, 0.1, 30, 0.1, 0.9, 1.8,
68, 46
], [
'Veal Cutlets', '1 lb.', 42.3, 1.7, 156, 0.1, 24, 0, 1.4, 2.4, 57, 0
], [
'Salmon, Pink (can)', '16 oz.', 13, 5.8, 705, 6.8, 45, 3.5,
1, 4.9, 209, 0
], ['Apples', '1 lb.', 4.4, 5.8, 27, 0.5, 36, 7.3, 3.6, 2.7, 5, 544], [
'Bananas', '1 lb.', 6.1, 4.9, 60, 0.4, 30, 17.4, 2.5, 3.5, 28, 498
], ['Lemons', '1 doz.', 26, 1.0, 21, 0.5, 14, 0, 0.5, 0, 4, 952], [
'Oranges', '1 doz.', 30.9, 2.2, 40, 1.1, 18, 11.1, 3.6, 1.3, 10, 1998
], [
'Green Beans', '1 lb.', 7.1, 2.4, 138, 3.7, 80, 69, 4.3, 5.8, 37, 862
], ['Cabbage', '1 lb.', 3.7, 2.6, 125, 4.0, 36, 7.2, 9, 4.5, 26, 5369], [
'Carrots', '1 bunch', 4.7, 2.7, 73, 2.8, 43, 188.5, 6.1, 4.3, 89, 608
], ['Celery', '1 stalk', 7.3, 0.9, 51, 3.0, 23, 0.9, 1.4, 1.4, 9, 313], [
'Lettuce', '1 head', 8.2, 0.4, 27, 1.1, 22, 112.4, 1.8, 3.4, 11, 449
], ['Onions', '1 lb.', 3.6, 5.8, 166, 3.8, 59, 16.6, 4.7, 5.9, 21,
1184], [
'Potatoes', '15 lb.', 34, 14.3, 336, 1.8, 118, 6.7, 29.4, 7.1,
198, 2522
], [
'Spinach', '1 lb.', 8.1, 1.1, 106, 0, 138, 918.4, 5.7, 13.8, 33,
2755
], [
'Sweet Potatoes', '1 lb.', 5.1, 9.6, 138, 2.7, 54, 290.7, 8.4,
5.4, 83, 1912
], [
'Peaches (can)', 'No. 2 1/2', 16.8, 3.7, 20, 0.4, 10, 21.5, 0.5,
1, 31, 196
], [
'Pears (can)', 'No. 2 1/2', 20.4, 3.0, 8, 0.3, 8, 0.8, 0.8, 0.8,
5, 81
], [
'Pineapple (can)', 'No. 2 1/2', 21.3, 2.4, 16, 0.4, 8, 2, 2.8,
0.8, 7, 399
], [
'Asparagus (can)', 'No. 2', 27.7, 0.4, 33, 0.3, 12, 16.3, 1.4,
2.1, 17, 272
], [
'Green Beans (can)', 'No. 2', 10, 1.0, 54, 2, 65, 53.9, 1.6, 4.3,
32, 431
], [
'Pork and Beans (can)', '16 oz.', 7.1, 7.5, 364, 4, 134, 3.5,
8.3, 7.7, 56, 0
], [
'Corn (can)', 'No. 2', 10.4, 5.2, 136, 0.2, 16, 12, 1.6, 2.7, 42,
218
], [
'Peas (can)', 'No. 2', 13.8, 2.3, 136, 0.6, 45, 34.9, 4.9, 2.5,
37, 370
], [
'Tomatoes (can)', 'No. 2', 8.6, 1.3, 63, 0.7, 38, 53.2, 3.4, 2.5,
36, 1253
], [
'Tomato Soup (can)', '10 1/2 oz.', 7.6, 1.6, 71, 0.6, 43, 57.9,
3.5, 2.4, 67, 862
], [
'Peaches, Dried', '1 lb.', 15.7, 8.5, 87, 1.7, 173, 86.8, 1.2,
4.3, 55, 57
], [
'Prunes, Dried', '1 lb.', 9, 12.8, 99, 2.5, 154, 85.7, 3.9, 4.3,
65, 257
], [
'Raisins, Dried', '15 oz.', 9.4, 13.5, 104, 2.5, 136, 4.5, 6.3,
1.4, 24, 136
], [
'Peas, Dried', '1 lb.', 7.9, 20.0, 1367, 4.2, 345, 2.9, 28.7,
18.4, 162, 0
], [
'Lima Beans, Dried', '1 lb.', 8.9, 17.4, 1055, 3.7, 459, 5.1,
26.9, 38.2, 93, 0
], [
'Navy Beans, Dried', '1 lb.', 5.9, 26.9, 1691, 11.4, 792, 0,
38.4, 24.6, 217, 0
], ['Coffee', '1 lb.', 22.4, 0, 0, 0, 0, 0, 4, 5.1, 50,
0], ['Tea', '1/4 lb.', 17.4, 0, 0, 0, 0, 0, 0, 2.3, 42, 0],
['Cocoa', '8 oz.', 8.6, 8.7, 237, 3, 72, 0, 2, 11.9, 40, 0], [
'Chocolate', '8 oz.', 16.2, 8.0, 77, 1.3, 39, 0, 0.9, 3.4, 14, 0
], ['Sugar', '10 lb.', 51.7, 34.9, 0, 0, 0, 0, 0, 0, 0, 0],
['Corn Syrup', '24 oz.', 13.7, 14.7, 0, 0.5, 74, 0, 0, 0, 5, 0], [
'Molasses', '18 oz.', 13.6, 9.0, 0, 10.3, 244, 0, 1.9, 7.5, 146,
0
], [
'Strawberry Preserves', '1 lb.', 20.5, 6.4, 11, 0.4, 7, 0.2,
0.2, 0.4, 3, 0
]]
# Instantiate a Glop solver, naming it LinearExample.
solver = pywraplp.Solver('StiglerDietExample',
pywraplp.Solver.GLOP_LINEAR_PROGRAMMING)
# Declare an array to hold our variables.
foods = [solver.NumVar(0.0, solver.infinity(), item[0]) for item in data]
# Objective function: Minimize the sum of (price-normalized) foods.
objective = solver.Objective()
for food in foods:
objective.SetCoefficient(food, 1)
objective.SetMinimization()
# Create the constraints, one per nutrient.
constraints = []
for i, nutrient in enumerate(nutrients):
constraints.append(solver.Constraint(nutrient[1], solver.infinity()))
for j, item in enumerate(data):
constraints[i].SetCoefficient(foods[j], item[i + 3])
print('Number of variables =', solver.NumVariables())
print('Number of constraints =', solver.NumConstraints())
# Solve the system.
status = solver.Solve()
# Check that the problem has an optimal solution.
if status != pywraplp.Solver.OPTIMAL:
print("The problem does not have an optimal solution!")
exit(1)
nutrients_result = [0] * len(nutrients)
print('')
print('Annual Foods:')
for i, food in enumerate(foods):
if food.solution_value() > 0.0:
print('{}: ${}'.format(data[i][0], 365. * food.solution_value()))
for j, nutrient in enumerate(nutrients):
nutrients_result[j] += data[i][j + 3] * food.solution_value()
print('')
print('Optimal annual price: ${:.4f}'.format(365. * objective.Value()))
print('')
print('Nutrients per day:')
for i, nutrient in enumerate(nutrients):
print('{}: {:.2f} (min {})'.format(nutrient[0], nutrients_result[i],
nutrient[1]))
print('')
print('Advanced usage:')
print('Problem solved in ', solver.wall_time(), ' milliseconds')
print('Problem solved in ', solver.iterations(), ' iterations')
if __name__ == '__main__':
main()