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StiglerMIP.java
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StiglerMIP.java
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/*
* Copyright 2017 Darian Sastre darian.sastre@minimaxlabs.com
* 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.
*
* ************************************************************************
*
* This model was created by Hakan Kjellerstrand (hakank@gmail.com)
*
* Java version by Darian Sastre (darian.sastre@minimaxlabs.com)
*/
package com.google.ortools.contrib;
import com.google.ortools.Loader;
import com.google.ortools.linearsolver.MPConstraint;
import com.google.ortools.linearsolver.MPObjective;
import com.google.ortools.linearsolver.MPSolver;
import com.google.ortools.linearsolver.MPVariable;
import java.math.RoundingMode;
import java.text.DecimalFormat;
public class StiglerMIP {
private static void solve(String solverType) {
System.out.println("---- StiglerMIP with " + solverType);
MPSolver solver = MPSolver.createSolver(solverType);
if (solver == null)
return;
double infinity = MPSolver.infinity();
/** invariants */
double days = 365.25;
int nutrientsCount = 9;
int commoditiesCount = 77;
String[] nutrients = {
"calories", // Calories, unit = 1000
"protein", // Protein, unit = grams
"calcium", // Calcium, unit = grams
"iron", // Iron, unit = milligrams
"vitaminA", // Vitamin A, unit = 1000 International Units
"thiamine", // Thiamine, Vit. B1, unit = milligrams
"riboflavin", // Riboflavin, Vit. B2, unit = milligrams
"niacin", // Niacin (Nicotinic Acid), unit = milligrams
"ascorbicAcid" // Ascorbic Acid, Vit. C, unit = milligrams
};
String[] commodities = {"Wheat Flour (Enriched), 10 lb.", "Macaroni, 1 lb.",
"Wheat Cereal (Enriched), 28 oz.", "Corn Flakes, 8 oz.", "Corn Meal, 1 lb.",
"Hominy Grits, 24 oz.", "Rice, 1 lb.", "Rolled Oats, 1 lb.",
"White Bread (Enriched), 1 lb.", "Whole Wheat Bread, 1 lb.", "Rye Bread, 1 lb.",
"Pound Cake, 1 lb.", "Soda Crackers, 1 lb.", "Milk, 1 qt.",
"Evaporated Milk (can), 14.5 oz.", "Butter, 1 lb.", "Oleomargarine, 1 lb.", "Eggs, 1 doz.",
"Cheese (Cheddar), 1 lb.", "Cream, 1/2 pt.", "Peanut Butter, 1 lb.", "Mayonnaise, 1/2 pt.",
"Crisco, 1 lb.", "Lard, 1 lb.", "Sirloin Steak, 1 lb.", "Round Steak, 1 lb.",
"Rib Roast, 1 lb.", "Chuck Roast, 1 lb.", "Plate, 1 lb.", "Liver (Beef), 1 lb.",
"Leg of Lamb, 1 lb.", "Lamb Chops (Rib), 1 lb.", "Pork Chops, 1 lb.",
"Pork Loin Roast, 1 lb.", "Bacon, 1 lb.", "Ham - smoked, 1 lb.", "Salt Pork, 1 lb.",
"Roasting Chicken, 1 lb.", "Veal Cutlets, 1 lb.", "Salmon, Pink (can), 16 oz.",
"Apples, 1 lb.", "Bananas, 1 lb.", "Lemons, 1 doz.", "Oranges, 1 doz.",
"Green Beans, 1 lb.", "Cabbage, 1 lb.", "Carrots, 1 bunch", "Celery, 1 stalk",
"Lettuce, 1 head", "Onions, 1 lb.", "Potatoes, 15 lb.", "Spinach, 1 lb.",
"Sweet Potatoes, 1 lb.", "Peaches (can), No. 2 1/2", "Pears (can), No. 2 1/2,",
"Pineapple (can), No. 2 1/2", "Asparagus (can), No. 2", "Grean Beans (can), No. 2",
"Pork and Beans (can), 16 oz.", "Corn (can), No. 2", "Peas (can), No. 2",
"Tomatoes (can), No. 2", "Tomato Soup (can), 10 1/2 oz.", "Peaches, Dried, 1 lb.",
"Prunes, Dried, 1 lb.", "Raisins, Dried, 15 oz.", "Peas, Dried, 1 lb.",
"Lima Beans, Dried, 1 lb.", "Navy Beans, Dried, 1 lb.", "Coffee, 1 lb.", "Tea, 1/4 lb.",
"Cocoa, 8 oz.", "Chocolate, 8 oz.", "Sugar, 10 lb.", "Corn Sirup, 24 oz.",
"Molasses, 18 oz.", "Strawberry Preserve, 1 lb."};
// price and weight per unit correspond to the two first columns
double[][] data = {{36.0, 12600.0, 44.7, 1411.0, 2.0, 365.0, 0.0, 55.4, 33.3, 441.0, 0.0},
{14.1, 3217.0, 11.6, 418.0, 0.7, 54.0, 0.0, 3.2, 1.9, 68.0, 0.0},
{24.2, 3280.0, 11.8, 377.0, 14.4, 175.0, 0.0, 14.4, 8.8, 114.0, 0.0},
{7.1, 3194.0, 11.4, 252.0, 0.1, 56.0, 0.0, 13.5, 2.3, 68.0, 0.0},
{4.6, 9861.0, 36.0, 897.0, 1.7, 99.0, 30.9, 17.4, 7.9, 106.0, 0.0},
{8.5, 8005.0, 28.6, 680.0, 0.8, 80.0, 0.0, 10.6, 1.6, 110.0, 0.0},
{7.5, 6048.0, 21.2, 460.0, 0.6, 41.0, 0.0, 2.0, 4.8, 60.0, 0.0},
{7.1, 6389.0, 25.3, 907.0, 5.1, 341.0, 0.0, 37.1, 8.9, 64.0, 0.0},
{7.9, 5742.0, 15.6, 488.0, 2.5, 115.0, 0.0, 13.8, 8.5, 126.0, 0.0},
{9.1, 4985.0, 12.2, 484.0, 2.7, 125.0, 0.0, 13.9, 6.4, 160.0, 0.0},
{9.2, 4930.0, 12.4, 439.0, 1.1, 82.0, 0.0, 9.9, 3.0, 66.0, 0.0},
{24.8, 1829.0, 8.0, 130.0, 0.4, 31.0, 18.9, 2.8, 3.0, 17.0, 0.0},
{15.1, 3004.0, 12.5, 288.0, 0.5, 50.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{11.0, 8867.0, 6.1, 310.0, 10.5, 18.0, 16.8, 4.0, 16.0, 7.0, 177.0},
{6.7, 6035.0, 8.4, 422.0, 15.1, 9.0, 26.0, 3.0, 23.5, 11.0, 60.0},
{20.8, 1473.0, 10.8, 9.0, 0.2, 3.0, 44.2, 0.0, 0.2, 2.0, 0.0},
{16.1, 2817.0, 20.6, 17.0, 0.6, 6.0, 55.8, 0.2, 0.0, 0.0, 0.0},
{32.6, 1857.0, 2.9, 238.0, 1.0, 52.0, 18.6, 2.8, 6.5, 1.0, 0.0},
{24.2, 1874.0, 7.4, 448.0, 16.4, 19.0, 28.1, 0.8, 10.3, 4.0, 0.0},
{14.1, 1689.0, 3.5, 49.0, 1.7, 3.0, 16.9, 0.6, 2.5, 0.0, 17.0},
{17.9, 2534.0, 15.7, 661.0, 1.0, 48.0, 0.0, 9.6, 8.1, 471.0, 0.0},
{16.7, 1198.0, 8.6, 18.0, 0.2, 8.0, 2.7, 0.4, 0.5, 0.0, 0.0},
{20.3, 2234.0, 20.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{9.8, 4628.0, 41.7, 0.0, 0.0, 0.0, 0.2, 0.0, 0.5, 5.0, 0.0},
{39.6, 1145.0, 2.9, 166.0, 0.1, 34.0, 0.2, 2.1, 2.9, 69.0, 0.0},
{36.4, 1246.0, 2.2, 214.0, 0.1, 32.0, 0.4, 2.5, 2.4, 87.0, 0.0},
{29.2, 1553.0, 3.4, 213.0, 0.1, 33.0, 0.0, 0.0, 2.0, 0.0, 0.0},
{22.6, 2007.0, 3.6, 309.0, 0.2, 46.0, 0.4, 1.0, 4.0, 120.0, 0.0},
{14.6, 3107.0, 8.5, 404.0, 0.2, 62.0, 0.0, 0.9, 0.0, 0.0, 0.0},
{26.8, 1692.0, 2.2, 333.0, 0.2, 139.0, 169.2, 6.4, 50.8, 316.0, 525.0},
{27.6, 1643.0, 3.1, 245.0, 0.1, 20.0, 0.0, 2.8, 3.0, 86.0, 0.0},
{36.6, 1239.0, 3.3, 140.0, 0.1, 15.0, 0.0, 1.7, 2.7, 54.0, 0.0},
{30.7, 1477.0, 3.5, 196.0, 0.2, 80.0, 0.0, 17.4, 2.7, 60.0, 0.0},
{24.2, 1874.0, 4.4, 249.0, 0.3, 37.0, 0.0, 18.2, 3.6, 79.0, 0.0},
{25.6, 1772.0, 10.4, 152.0, 0.2, 23.0, 0.0, 1.8, 1.8, 71.0, 0.0},
{27.4, 1655.0, 6.7, 212.0, 0.2, 31.0, 0.0, 9.9, 3.3, 50.0, 0.0},
{16.0, 2835.0, 18.8, 164.0, 0.1, 26.0, 0.0, 1.4, 1.8, 0.0, 0.0},
{30.3, 1497.0, 1.8, 184.0, 0.1, 30.0, 0.1, 0.9, 1.8, 68.0, 46.0},
{42.3, 1072.0, 1.7, 156.0, 0.1, 24.0, 0.0, 1.4, 2.4, 57.0, 0.0},
{13.0, 3489.0, 5.8, 705.0, 6.8, 45.0, 3.5, 1.0, 4.9, 209.0, 0.0},
{4.4, 9072.0, 5.8, 27.0, 0.5, 36.0, 7.3, 3.6, 2.7, 5.0, 544.0},
{6.1, 4982.0, 4.9, 60.0, 0.4, 30.0, 17.4, 2.5, 3.5, 28.0, 498.0},
{26.0, 2380.0, 1.0, 21.0, 0.5, 14.0, 0.0, 0.5, 0.0, 4.0, 952.0},
{30.9, 4439.0, 2.2, 40.0, 1.1, 18.0, 11.1, 3.6, 1.3, 10.0, 1993.0},
{7.1, 5750.0, 2.4, 138.0, 3.7, 80.0, 69.0, 4.3, 5.8, 37.0, 862.0},
{3.7, 8949.0, 2.6, 125.0, 4.0, 36.0, 7.2, 9.0, 4.5, 26.0, 5369.0},
{4.7, 6080.0, 2.7, 73.0, 2.8, 43.0, 188.5, 6.1, 4.3, 89.0, 608.0},
{7.3, 3915.0, 0.9, 51.0, 3.0, 23.0, 0.9, 1.4, 1.4, 9.0, 313.0},
{8.2, 2247.0, 0.4, 27.0, 1.1, 22.0, 112.4, 1.8, 3.4, 11.0, 449.0},
{3.6, 11844.0, 5.8, 166.0, 3.8, 59.0, 16.6, 4.7, 5.9, 21.0, 1184.0},
{34.0, 16810.0, 14.3, 336.0, 1.8, 118.0, 6.7, 29.4, 7.1, 198.0, 2522.0},
{8.1, 4592.0, 1.1, 106.0, 0.0, 138.0, 918.4, 5.7, 13.8, 33.0, 2755.0},
{5.1, 7649.0, 9.6, 138.0, 2.7, 54.0, 290.7, 8.4, 5.4, 83.0, 1912.0},
{16.8, 4894.0, 3.7, 20.0, 0.4, 10.0, 21.5, 0.5, 1.0, 31.0, 196.0},
{20.4, 4030.0, 3.0, 8.0, 0.3, 8.0, 0.8, 0.8, 0.8, 5.0, 81.0},
{21.3, 3993.0, 2.4, 16.0, 0.4, 8.0, 2.0, 2.8, 0.8, 7.0, 399.0},
{27.7, 1945.0, 0.4, 33.0, 0.3, 12.0, 16.3, 1.4, 2.1, 17.0, 272.0},
{10.0, 5386.0, 1.0, 54.0, 2.0, 65.0, 53.9, 1.6, 4.3, 32.0, 431.0},
{7.1, 6389.0, 7.5, 364.0, 4.0, 134.0, 3.5, 8.3, 7.7, 56.0, 0.0},
{10.4, 5452.0, 5.2, 136.0, 0.2, 16.0, 12.0, 1.6, 2.7, 42.0, 218.0},
{13.8, 4109.0, 2.3, 136.0, 0.6, 45.0, 34.9, 4.9, 2.5, 37.0, 370.0},
{8.6, 6263.0, 1.3, 63.0, 0.7, 38.0, 53.2, 3.4, 2.5, 36.0, 1253.0},
{7.6, 3917.0, 1.6, 71.0, 0.6, 43.0, 57.9, 3.5, 2.4, 67.0, 862.0},
{15.7, 2889.0, 8.5, 87.0, 1.7, 173.0, 86.8, 1.2, 4.3, 55.0, 57.0},
{9.0, 4284.0, 12.8, 99.0, 2.5, 154.0, 85.7, 3.9, 4.3, 65.0, 257.0},
{9.4, 4524.0, 13.5, 104.0, 2.5, 136.0, 4.5, 6.3, 1.4, 24.0, 136.0},
{7.9, 5742.0, 20.0, 1367.0, 4.2, 345.0, 2.9, 28.7, 18.4, 162.0, 0.0},
{8.9, 5097.0, 17.4, 1055.0, 3.7, 459.0, 5.1, 26.9, 38.2, 93.0, 0.0},
{5.9, 7688.0, 26.9, 1691.0, 11.4, 792.0, 0.0, 38.4, 24.6, 217.0, 0.0},
{22.4, 2025.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 5.1, 50.0, 0.0},
{17.4, 652.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 2.3, 42.0, 0.0},
{8.6, 2637.0, 8.7, 237.0, 3.0, 72.0, 0.0, 2.0, 11.9, 40.0, 0.0},
{16.2, 1400.0, 8.0, 77.0, 1.3, 39.0, 0.0, 0.9, 3.4, 14.0, 0.0},
{51.7, 8773.0, 34.9, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{13.7, 4996.0, 14.7, 0.0, 0.5, 74.0, 0.0, 0.0, 0.0, 5.0, 0.0},
{13.6, 3752.0, 9.0, 0.0, 10.3, 244.0, 0.0, 1.9, 7.5, 146.0, 0.0},
{20.5, 2213.0, 6.4, 11.0, 0.4, 7.0, 0.2, 0.2, 0.4, 3.0, 0.0}};
// recommended daily nutritional allowance
double[] allowance = {3.0, 70.0, 0.8, 12.0, 5.0, 1.8, 2.7, 18.0, 75.0};
/** variables */
MPVariable[] x = solver.makeNumVarArray(commoditiesCount, 0, 1000);
MPVariable[] xCost = solver.makeNumVarArray(commoditiesCount, 0, 1000);
MPVariable[] quant = solver.makeNumVarArray(commoditiesCount, 0, 1000);
MPVariable totalCost = solver.makeNumVar(0, 1000, "total_cost");
/** constraints & objective */
MPObjective obj = solver.objective();
MPConstraint[] costConstraint = new MPConstraint[2 * commoditiesCount];
MPConstraint[] quantConstraint = new MPConstraint[2 * commoditiesCount];
MPConstraint totalCostConstraint = solver.makeConstraint(0, 0);
for (int i = 0; i < commoditiesCount; i++) {
totalCostConstraint.setCoefficient(x[i], days);
costConstraint[i] = solver.makeConstraint(0, 0);
costConstraint[i].setCoefficient(x[i], days);
costConstraint[i].setCoefficient(xCost[i], -1);
quantConstraint[i] = solver.makeConstraint(0, 0);
quantConstraint[i].setCoefficient(x[i], days * 100 / data[i][0]);
quantConstraint[i].setCoefficient(quant[i], -1);
obj.setCoefficient(x[i], 1);
}
totalCostConstraint.setCoefficient(totalCost, -1);
MPConstraint[] nutrientConstraint = new MPConstraint[nutrientsCount];
for (int i = 0; i < nutrientsCount; i++) {
nutrientConstraint[i] = solver.makeConstraint(allowance[i], infinity);
for (int j = 0; j < commoditiesCount; j++) {
nutrientConstraint[i].setCoefficient(x[j], data[j][i + 2]);
}
}
final MPSolver.ResultStatus resultStatus = solver.solve();
/** printing */
if (resultStatus != MPSolver.ResultStatus.OPTIMAL) {
System.err.println("The problem does not have an optimal solution!");
}
DecimalFormat df = new DecimalFormat("#.##");
df.setRoundingMode(RoundingMode.CEILING);
System.out.println("Min cost: " + df.format(obj.value()));
System.out.println("Total cost: " + df.format(totalCost.solutionValue()));
for (int i = 0; i < commoditiesCount; i++) {
if (x[i].solutionValue() > 0) {
System.out.println(commodities[i] + ": " + df.format(xCost[i].solutionValue()) + " "
+ df.format(quant[i].solutionValue()));
}
}
}
public static void main(String[] args) {
Loader.loadNativeLibraries();
solve("SCIP");
solve("CBC");
solve("GLPK");
}
}