このセクションでは、経済学の受賞者であるジョージ スティグラーにちなんで名付けられた「スティグラー ダイエット」という古典的な問題の解決方法を説明します。彼は、一連の食品で基本的な栄養ニーズを満たす方法を低費用で計算しました。彼はこれを数学的な演習として提案し、摂取を推奨するものではありませんでしたが、近年、最適な栄養量を計算するという考えが流行しているのです。
スティグラーの食生活では、次の最低限を満たすことを義務付けていました。
栄養素一覧
| 栄養素 | 1 日の推奨摂取量 |
|---|---|
| カロリー | 3,000 カロリー |
| タンパク質 | 70 g |
| カルシウム | 0.8 g |
| 鉄 | 12 ミリグラム |
| ビタミン A | 5,000 IU |
| チアミン（ビタミン B1） | 1.8 ミリグラム |
| リボフラビン（ビタミン B2） | 2.7 ミリグラム |
| ナイアシン | 18 ミリグラム |
| アスコルビン酸（ビタミン C） | 75 ミリグラム |
スティグラーが評価した一連の食品は、1944 年時点を反映したものです。以下の栄養データは単位単位ではなく 1 ドルあたりの量であるため、各食品に費やす金額を特定することが目的です。
商品リスト
| コモディティ | 単位 | 1939 年の価格（セント） | カロリー（kcal） | タンパク質 (g) | カルシウム (g) | 鉄（mg） | ビタミン A（KIU） | チアミン（mg） | リボフラビン（mg） | ナイアシン（mg） | アスコルビン酸（mg） |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 小麦粉（濃縮） | 4.5 kg | 36 | 4,470 万台 | 1411 | 2 | 365 | 0 | 55.4 | 33.3 | 441 | 0 |
| マスタード | 4.5 kg | 14.1 | 11.6 | 418 | 0.7 | 54 | 0 | 3.2 | 1.9 | 68 | 0 |
| 小麦用シリアル（濃縮） | 28 オンス | 24.2 | 11.8 | 377 | 14.4 | 175 | 0 | 14.4 | 8.8 | 114 | 0 |
| コーンフレーク | 8 オンス | 7.1 | 11.4 | 252 | 0.1 | 56 | 0 | 13.5 | 2.3 | 68 | 0 |
| コーンミール | 4.5 kg | 4.6 | 36.0 | 897 | 1.7 | 99 | 30.9 | 17.4 | 7.9 | 106 | 0 |
| オニキス | 24 オンス | 8.5 | 28.6 | 680 | 0.8 | 80 | 0 | 10.6 | 1.6 | 110 | 0 |
| 米 | 4.5 kg | 7.5 | 21.2 | 460 | 0.6 | 41 | 0 | 2 | 4.8 | 60 | 0 |
| ロールドオーツ | 4.5 kg | 7.1 | 25.3 | 907 | 5.1 | 341 | 0 | 37.1 | 8.9 | 64 | 0 |
| 白パン（濃縮） | 4.5 kg | 7.9 | 15.0 | 488 | 2.5 | 115 | 0 | 13.8 | 8.5 | 126 | 0 |
| 全粒小麦パン | 4.5 kg | 9.1 | 12.2 | 484 | 2.7 | 125 | 0 | 13.9 | 6.4 | 160 | 0 |
| ライパン | 4.5 kg | 9.1 | 12.4 | 439 | 1.1 | 82 | 0 | 9.9 | 3 | 66 | 0 |
| パウンドケーキ | 4.5 kg | 24.8 | 8.0 | 130 | 0.4 | 31 | 1,890 万台 | 2.8 | 3 | 17 | 0 |
| ソーダクラッカー | 4.5 kg | 15.1 | 12.5 | 288 | 0.5 | 50 | 0 | 0 | 0 | 0 | 0 |
| 牛乳 | 1 四半期 | 11 | 6.1 | 310 | 10.5 | 18 | 16.8 | 4 | 16 | 7 | 177 |
| エバポレート ミルク（缶） | 14.5 オンス。 | 6.7 | 8.4 | 422 | 15.1 | 9 | 26 | 3 | 23.5 | 11 | 60 |
| バター | 4.5 kg | 30.8 | 10.8 | 9 | 0.2 | 3 | 44.2 | 0 | 0.2 | 2 | 0 |
| オレオマーガリン | 4.5 kg | 16.1 | 20.6 | 17 | 0.6 | 6 | 55.8 | 0.2 | 0 | 0 | 0 |
| 卵 | 1 晩。 | 32.6 | 2.9 | 238 | 1.0 | 52 | 18.6 | 2.8 | 6.5 | 1 | 0 |
| チーズ（チェダー） | 4.5 kg | 24.2 | 7.4 | 448 | 16.4 | 19 | 28.1 | 0.8 | 10.3 | 4 | 0 |
| クリーム | 1/2 ポイント | 14.1 | 3.5 | 49 | 1.7 | 3 | 1,690 万台 | 0.6 | 2.5 | 0 | 17 |
| ピーナッツバター | 4.5 kg | 1,790 万台 | 15.7 | 661 | 1.0 | 48 | 0 | 9.6 | 8.1 | 471 | 0 |
| マヨネーズ | 1/2 ポイント | 16.7 | 8.6 | 18 | 0.2 | 8 | 2.7 | 0.4 | 0.5 | 0 | 0 |
| クリスコ | 4.5 kg | 20.3 | 20.1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ラード | 豚脂 | 4.5 kg | 9.8 | 41.7 | 0 | 0 | 0 | 0.2 | 0 | 0.5 | 5 | 0 |
| サーロインステーキ | 4.5 kg | 39.6 | 2.9 | 166 | 0.1 | 34 | 0.2 | 2.1 | 2.9 | 69 | 0 |
| ラウンドステーキ | 4.5 kg | 36.4 | 2.2 | 214 | 0.1 | 32 | 0.4 | 2.5 | 2.4 | 87 | 0 |
| リブロースト | 4.5 kg | 29.2 | 3.4 | 213 | 0.1 | 33 | 0 | 0 | 2 | 0 | 0 |
| チャック・ロースト | 4.5 kg | 22.6 | 3.6 | 309 | 0.2 | 46 | 0.4 | 1 | 4 | 120 | 0 |
| プレート | 4.5 kg | 14.6 | 8.5 | 404 | 0.2 | 62 | 0 | 0.9 | 0 | 0 | 0 |
| レバー（牛肉） | 4.5 kg | 26.8 | 2.2 | 333 | 0.2 | 139 | 169.2 | 6.4 | 50.8 | 316 | 525 |
| ラム肉 | 4.5 kg | 27.6 | 3.1 | 245 | 0.1 | 20 | 0 | 2.8 | 3.9 | 86 | 0 |
| ラムチョップ（リブ） | 4.5 kg | 3,660 万台 | 3.3 | 140 | 0.1 | 15 | 0 | 1.7 | 2.7 | 54 | 0 |
| ポークチョップ | 4.5 kg | 3,070 万台 | 3.5 | 196 | 0.2 | 30 | 0 | 17.4 | 2.7 | 60 | 0 |
| ポークローインロースト | 4.5 kg | 24.2 | 4.4 | 249 | 0.3 | 37 | 0 | 18.2 | 3.6 | 79 | 0 |
| ベーコン | 4.5 kg | 25.6 | 10.4 | 152 | 0.2 | 23 | 0 | 1.8 | 1.8 | 71 | 0 |
| ハム、喫煙 | 4.5 kg | 27.4 | 6.7 | 212 | 0.2 | 31 | 0 | 9.9 | 3.3 | 50 | 0 |
| ソルトポーク | 4.5 kg | 16 | 18.8 | 164 | 0.1 | 26 | 0 | 1.4 | 1.8 | 0 | 0 |
| ローストチキン | 4.5 kg | 30.3 | 1.8 | 184 | 0.1 | 30 | 0.1 | 0.9 | 1.8 | 68 | 46 |
| 子牛カツ | 4.5 kg | 42.3 | 1.7 | 156 | 0.1 | 24 | 0 | 1.4 | 2.4 | 57 | 0 |
| サーモン、ピンク（缶） | 16 オンス | 13 | 5.8 | 705 | 6.8 | 45 | 3.5 | 1 | 4.9 | 209 | 0 |
| 同一条件で | 4.5 kg | 4.4 | 5.8 | 27 | 0.5 | 36 | 7.3 | 3.6 | 2.7 | 5 | 544 |
| バナナ | 4.5 kg | 6.1 | 4.9 | 60 | 0.4 | 30 | 17.4 | 2.5 | 3.5 | 28 | 498 |
| レモン | 1 晩。 | 26 | 1.0 | 21 | 0.5 | 14 | 0 | 0.5 | 0 | 4 | 952 |
| オレンジ | 1 晩。 | 30.9 | 2.2 | 40 | 1.1 | 18 | 11.1 | 3.6 | 1.3 | 10 | 1998 |
| サヤインゲン | 4.5 kg | 7.1 | 2.4 | 138 | 3.7 | 80 | 69 | 4.3 | 5.8 | 37 | 862 |
| キャベツ | 4.5 kg | 3.7 | 2.6 | 125 | 4.0 | 36 | 7.2 | 9 | 4.5 | 26 | 5369 |
| ニンジン | 1 房 | 4.7 | 2.7 | 73 | 2.8 | 43 | 188.5 | 6.1 | 4.3 | 89 | 608 |
| セロリ | 1 本 | 7.3 | 0.9 | 51 | 3.0 | 23 | 0.9 | 1.4 | 1.4 | 9 | 313 |
| CANNOT TRANSLATE | 1 個のヘッド | 8.2 | 0.4 | 27 | 1.1 | 22 | 112.4 | 1.8 | 3.4 | 11 | 449 |
| タマネギ | 4.5 kg | 3.6 | 5.8 | 166 | 3.8 | 59 | 16.6 | 4.7 | 5.9 | 21 | 1184 |
| ジャガイモ | 4.5 kg | 34 | 14.3 | 336 | 1.8 | 118 | 6.7 | 29.4 | 7.1 | 198 | 2522 |
| ほうれん草 | 4.5 kg | 8.1 | 1.1 | 106 | 0 | 138 | 9,184 万台 | 5.7 | 13.8 | 33 | 2755 |
| サツマイモ | 4.5 kg | 5.1 | 9.6 | 138 | 2.7 | 54 | 290.7 | 8.4 | 5.4 | 83 | 1912 |
| ピーチ（缶） | No. 2 1/2 | 16.8 | 3.7 | 20 | 0.4 | 10 | 21.5 | 0.5 | 1 | 31 | 196 |
| 洋ナシ（缶） | No. 2 1/2 | 20.4 | 3.0 | 8 | 0.3 | 8 | 0.8 | 0.8 | 0.8 | 5 | 81 |
| パイナップル（缶） | No. 2 1/2 | 21.3 | 2.4 | 16 | 0.4 | 8 | 2 | 2.8 | 0.8 | 7 | 399 |
| アスパラガス（缶） | 2 | 2,770 万台 | 0.4 | 33 | 0.3 | 12 | 16.3 | 1.4 | 2.1 | 17 | 272 |
| サヤインゲン（缶） | 2 | 10 | 1.0 | 54 | 2 | 65 | 53.9 | 1.6 | 4.3 | 32 | 431 |
| ポーク・ビーンズ（缶） | 16 オンス | 7.1 | 7.5 | 364 | 4 | 134 | 3.5 | 8.3 | 7.7 | 56 | 0 |
| トウモロコシ（缶） | 2 | 10.4 | 5.2 | 136 | 0.2 | 16 | 12 | 1.6 | 2.7 | 42 | 218 |
| エンドウ豆（缶） | 2 | 13.8 | 2.3 | 136 | 0.6 | 45 | 34.9 | 4.9 | 2.5 | 37 | 370 |
| トマト（缶） | 2 | 8.6 | 1.3 | 63 | 0.7 | 38 | 53.2 | 3.4 | 2.5 | 36 | 1253 |
| トマトスープ（缶） | 10 1/2 オンス。 | 7.6 | 1.6 | 71 | 0.6 | 43 | 57.9 | 3.5 | 2.4 | 67 | 862 |
| ピーチ、乾燥 | 4.5 kg | 15.7 | 8.5 | 87 | 1.7 | 173 | 86.8 | 1.2 | 4.3 | 55 | 57 |
| プルーン、乾燥 | 4.5 kg | 9 | 12.8 | 99 | 2.5 | 154 | 85.7 | 3.9 | 4.3 | 65 | 257 |
| レーズン、乾燥 | 15 オンス | 9.4 | 13.5 | 104 | 2.5 | 136 | 4.5 | 6.3 | 1.4 | 24 | 136 |
| エンドウ豆、乾燥 | 4.5 kg | 7.9 | 20.0 | 1,367 | 4.2 | 345 | 2.9 | 28.7 | 18.4 | 162 | 0 |
| リマビーンズ、ドライ | 4.5 kg | 8.9 | 17.4 | 1,055 | 3.7 | 459 | 5.1 | 26.9 | 38.2 | 93 | 0 |
| ネイビービーンズ、ドライフラワー | 4.5 kg | 5.9 | 26.9 | 1691 | 11.4 | 792 | 0 | 38.4 | 2,460 万台 | 217 | 0 |
| コーヒー | 4.5 kg | 22.4 | 0 | 0 | 0 | 0 | 0 | 4 | 5.1 | 50 | 0 |
| 茶 | 1/4 lb. | 17.4 | 0 | 0 | 0 | 0 | 0 | 0 | 2.3 | 42 | 0 |
| ココア | 8 オンス | 8.6 | 8.7 | 237 | 3 | 72 | 0 | 2 | 11.9 | 40 | 0 |
| チョコレート | 8 オンス | 16.2 | 8.0 | 77 | 1.3 | 39 | 0 | 0.9 | 3.4 | 14 | 0 |
| 糖類 | 4.5 kg | 5,170 万台 | 34.9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| コーンシロップ | 24 オンス | 13.7 | 14.7 | 0 | 0.5 | 74 | 0 | 0 | 0 | 5 | 0 |
| 糖質 | 18 オンス | 13.6 | 9.0 | 0 | 10.3 | 244 | 0 | 1.9 | 7.5 | 146 | 0 |
| ストロベリー プリザーブ | 4.5 kg | 20.5 | 6.4 | 11 | 0.4 | 7 | 0.2 | 0.2 | 0.4 | 3 | 0 |
栄養素はすべて価格によって正規化されているため、目標は単に食品の合計を最小限に抑えることにあります。
1944 年、スティグラーは悲しみを込めて、可能な限り最適な答えを導き出しました。
...線形条件に従う線形関数の最小値を見つける直接的な方法はないように思われます。
彼は 1939 ドルで年額 39.93 ドルのダイエットを見つけました。1947 年、ジャック ラダーマンがシンプレックス法（当時は最近の発明）で最適な解を導き出しました。机上計算機を使って 9 人の事務員が答えにたどり着くまでに 120 人日かかりました。
線形解法を使った解
以下のセクションでは、スティグラーの食生活の問題を解決するプログラムを紹介します。
線形ソルバーのラッパーをインポートする
以下に示すように、[GLOP](/optimization/mip/glop0 線形ソルバー) のインターフェースである OR-Tools の線形ソルバーラッパーをインポートします。
Python
from ortools.linear_solver import pywraplp
C++
#include <array> #include <memory> #include <string> #include <utility> // std::pair #include <vector> #include "absl/flags/flag.h" #include "absl/log/flags.h" #include "ortools/base/init_google.h" #include "ortools/base/logging.h" #include "ortools/linear_solver/linear_solver.h"
Java
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.util.ArrayList; import java.util.List;
C#
using System; using System.Collections.Generic; using Google.OrTools.LinearSolver;
問題に関するデータ
次のコードは、任意のソリューションで、最小栄養素要件用の配列 nutrients と、栄養データ テーブル用の配列 data を作成します。
Python
# 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 = [
# fmt: off
['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],
# fmt: on
]
C++
// Nutrient minimums.
const std::vector<std::pair<std::string, double>> nutrients = {
{"Calories (kcal)", 3.0}, {"Protein (g)", 70.0},
{"Calcium (g)", 0.8}, {"Iron (mg)", 12.0},
{"Vitamin A (kIU)", 5.0}, {"Vitamin B1 (mg)", 1.8},
{"Vitamin B2 (mg)", 2.7}, {"Niacin (mg)", 18.0},
{"Vitamin C (mg)", 75.0}};
struct Commodity {
std::string name; //!< Commodity name
std::string unit; //!< Unit
double price; //!< 1939 price per unit (cents)
//! Calories (kcal),
//! Protein (g),
//! Calcium (g),
//! Iron (mg),
//! Vitamin A (kIU),
//! Vitamin B1 (mg),
//! Vitamin B2 (mg),
//! Niacin (mg),
//! Vitamin C (mg)
std::array<double, 9> nutrients;
};
std::vector<Commodity> 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}}};
Java
// Nutrient minimums.
List<Object[]> nutrients = new ArrayList<>();
nutrients.add(new Object[] {"Calories (kcal)", 3.0});
nutrients.add(new Object[] {"Protein (g)", 70.0});
nutrients.add(new Object[] {"Calcium (g)", 0.8});
nutrients.add(new Object[] {"Iron (mg)", 12.0});
nutrients.add(new Object[] {"Vitamin A (kIU)", 5.0});
nutrients.add(new Object[] {"Vitamin B1 (mg)", 1.8});
nutrients.add(new Object[] {"Vitamin B2 (mg)", 2.7});
nutrients.add(new Object[] {"Niacin (mg)", 18.0});
nutrients.add(new Object[] {"Vitamin C (mg)", 75.0});
List<Object[]> data = new ArrayList<>();
data.add(new Object[] {"Wheat Flour (Enriched)", "10 lb.", 36,
new double[] {44.7, 1411, 2, 365, 0, 55.4, 33.3, 441, 0}});
data.add(new Object[] {
"Macaroni", "1 lb.", 14.1, new double[] {11.6, 418, 0.7, 54, 0, 3.2, 1.9, 68, 0}});
data.add(new Object[] {"Wheat Cereal (Enriched)", "28 oz.", 24.2,
new double[] {11.8, 377, 14.4, 175, 0, 14.4, 8.8, 114, 0}});
data.add(new Object[] {
"Corn Flakes", "8 oz.", 7.1, new double[] {11.4, 252, 0.1, 56, 0, 13.5, 2.3, 68, 0}});
data.add(new Object[] {
"Corn Meal", "1 lb.", 4.6, new double[] {36.0, 897, 1.7, 99, 30.9, 17.4, 7.9, 106, 0}});
data.add(new Object[] {
"Hominy Grits", "24 oz.", 8.5, new double[] {28.6, 680, 0.8, 80, 0, 10.6, 1.6, 110, 0}});
data.add(
new Object[] {"Rice", "1 lb.", 7.5, new double[] {21.2, 460, 0.6, 41, 0, 2, 4.8, 60, 0}});
data.add(new Object[] {
"Rolled Oats", "1 lb.", 7.1, new double[] {25.3, 907, 5.1, 341, 0, 37.1, 8.9, 64, 0}});
data.add(new Object[] {"White Bread (Enriched)", "1 lb.", 7.9,
new double[] {15.0, 488, 2.5, 115, 0, 13.8, 8.5, 126, 0}});
data.add(new Object[] {"Whole Wheat Bread", "1 lb.", 9.1,
new double[] {12.2, 484, 2.7, 125, 0, 13.9, 6.4, 160, 0}});
data.add(new Object[] {
"Rye Bread", "1 lb.", 9.1, new double[] {12.4, 439, 1.1, 82, 0, 9.9, 3, 66, 0}});
data.add(new Object[] {
"Pound Cake", "1 lb.", 24.8, new double[] {8.0, 130, 0.4, 31, 18.9, 2.8, 3, 17, 0}});
data.add(new Object[] {
"Soda Crackers", "1 lb.", 15.1, new double[] {12.5, 288, 0.5, 50, 0, 0, 0, 0, 0}});
data.add(
new Object[] {"Milk", "1 qt.", 11, new double[] {6.1, 310, 10.5, 18, 16.8, 4, 16, 7, 177}});
data.add(new Object[] {"Evaporated Milk (can)", "14.5 oz.", 6.7,
new double[] {8.4, 422, 15.1, 9, 26, 3, 23.5, 11, 60}});
data.add(
new Object[] {"Butter", "1 lb.", 30.8, new double[] {10.8, 9, 0.2, 3, 44.2, 0, 0.2, 2, 0}});
data.add(new Object[] {
"Oleomargarine", "1 lb.", 16.1, new double[] {20.6, 17, 0.6, 6, 55.8, 0.2, 0, 0, 0}});
data.add(new Object[] {
"Eggs", "1 doz.", 32.6, new double[] {2.9, 238, 1.0, 52, 18.6, 2.8, 6.5, 1, 0}});
data.add(new Object[] {"Cheese (Cheddar)", "1 lb.", 24.2,
new double[] {7.4, 448, 16.4, 19, 28.1, 0.8, 10.3, 4, 0}});
data.add(new Object[] {
"Cream", "1/2 pt.", 14.1, new double[] {3.5, 49, 1.7, 3, 16.9, 0.6, 2.5, 0, 17}});
data.add(new Object[] {
"Peanut Butter", "1 lb.", 17.9, new double[] {15.7, 661, 1.0, 48, 0, 9.6, 8.1, 471, 0}});
data.add(new Object[] {
"Mayonnaise", "1/2 pt.", 16.7, new double[] {8.6, 18, 0.2, 8, 2.7, 0.4, 0.5, 0, 0}});
data.add(new Object[] {"Crisco", "1 lb.", 20.3, new double[] {20.1, 0, 0, 0, 0, 0, 0, 0, 0}});
data.add(new Object[] {"Lard", "1 lb.", 9.8, new double[] {41.7, 0, 0, 0, 0.2, 0, 0.5, 5, 0}});
data.add(new Object[] {
"Sirloin Steak", "1 lb.", 39.6, new double[] {2.9, 166, 0.1, 34, 0.2, 2.1, 2.9, 69, 0}});
data.add(new Object[] {
"Round Steak", "1 lb.", 36.4, new double[] {2.2, 214, 0.1, 32, 0.4, 2.5, 2.4, 87, 0}});
data.add(
new Object[] {"Rib Roast", "1 lb.", 29.2, new double[] {3.4, 213, 0.1, 33, 0, 0, 2, 0, 0}});
data.add(new Object[] {
"Chuck Roast", "1 lb.", 22.6, new double[] {3.6, 309, 0.2, 46, 0.4, 1, 4, 120, 0}});
data.add(
new Object[] {"Plate", "1 lb.", 14.6, new double[] {8.5, 404, 0.2, 62, 0, 0.9, 0, 0, 0}});
data.add(new Object[] {"Liver (Beef)", "1 lb.", 26.8,
new double[] {2.2, 333, 0.2, 139, 169.2, 6.4, 50.8, 316, 525}});
data.add(new Object[] {
"Leg of Lamb", "1 lb.", 27.6, new double[] {3.1, 245, 0.1, 20, 0, 2.8, 3.9, 86, 0}});
data.add(new Object[] {
"Lamb Chops (Rib)", "1 lb.", 36.6, new double[] {3.3, 140, 0.1, 15, 0, 1.7, 2.7, 54, 0}});
data.add(new Object[] {
"Pork Chops", "1 lb.", 30.7, new double[] {3.5, 196, 0.2, 30, 0, 17.4, 2.7, 60, 0}});
data.add(new Object[] {
"Pork Loin Roast", "1 lb.", 24.2, new double[] {4.4, 249, 0.3, 37, 0, 18.2, 3.6, 79, 0}});
data.add(new Object[] {
"Bacon", "1 lb.", 25.6, new double[] {10.4, 152, 0.2, 23, 0, 1.8, 1.8, 71, 0}});
data.add(new Object[] {
"Ham, smoked", "1 lb.", 27.4, new double[] {6.7, 212, 0.2, 31, 0, 9.9, 3.3, 50, 0}});
data.add(new Object[] {
"Salt Pork", "1 lb.", 16, new double[] {18.8, 164, 0.1, 26, 0, 1.4, 1.8, 0, 0}});
data.add(new Object[] {"Roasting Chicken", "1 lb.", 30.3,
new double[] {1.8, 184, 0.1, 30, 0.1, 0.9, 1.8, 68, 46}});
data.add(new Object[] {
"Veal Cutlets", "1 lb.", 42.3, new double[] {1.7, 156, 0.1, 24, 0, 1.4, 2.4, 57, 0}});
data.add(new Object[] {
"Salmon, Pink (can)", "16 oz.", 13, new double[] {5.8, 705, 6.8, 45, 3.5, 1, 4.9, 209, 0}});
data.add(new Object[] {
"Apples", "1 lb.", 4.4, new double[] {5.8, 27, 0.5, 36, 7.3, 3.6, 2.7, 5, 544}});
data.add(new Object[] {
"Bananas", "1 lb.", 6.1, new double[] {4.9, 60, 0.4, 30, 17.4, 2.5, 3.5, 28, 498}});
data.add(
new Object[] {"Lemons", "1 doz.", 26, new double[] {1.0, 21, 0.5, 14, 0, 0.5, 0, 4, 952}});
data.add(new Object[] {
"Oranges", "1 doz.", 30.9, new double[] {2.2, 40, 1.1, 18, 11.1, 3.6, 1.3, 10, 1998}});
data.add(new Object[] {
"Green Beans", "1 lb.", 7.1, new double[] {2.4, 138, 3.7, 80, 69, 4.3, 5.8, 37, 862}});
data.add(new Object[] {
"Cabbage", "1 lb.", 3.7, new double[] {2.6, 125, 4.0, 36, 7.2, 9, 4.5, 26, 5369}});
data.add(new Object[] {
"Carrots", "1 bunch", 4.7, new double[] {2.7, 73, 2.8, 43, 188.5, 6.1, 4.3, 89, 608}});
data.add(new Object[] {
"Celery", "1 stalk", 7.3, new double[] {0.9, 51, 3.0, 23, 0.9, 1.4, 1.4, 9, 313}});
data.add(new Object[] {
"Lettuce", "1 head", 8.2, new double[] {0.4, 27, 1.1, 22, 112.4, 1.8, 3.4, 11, 449}});
data.add(new Object[] {
"Onions", "1 lb.", 3.6, new double[] {5.8, 166, 3.8, 59, 16.6, 4.7, 5.9, 21, 1184}});
data.add(new Object[] {
"Potatoes", "15 lb.", 34, new double[] {14.3, 336, 1.8, 118, 6.7, 29.4, 7.1, 198, 2522}});
data.add(new Object[] {
"Spinach", "1 lb.", 8.1, new double[] {1.1, 106, 0, 138, 918.4, 5.7, 13.8, 33, 2755}});
data.add(new Object[] {"Sweet Potatoes", "1 lb.", 5.1,
new double[] {9.6, 138, 2.7, 54, 290.7, 8.4, 5.4, 83, 1912}});
data.add(new Object[] {"Peaches (can)", "No. 2 1/2", 16.8,
new double[] {3.7, 20, 0.4, 10, 21.5, 0.5, 1, 31, 196}});
data.add(new Object[] {
"Pears (can)", "No. 2 1/2", 20.4, new double[] {3.0, 8, 0.3, 8, 0.8, 0.8, 0.8, 5, 81}});
data.add(new Object[] {
"Pineapple (can)", "No. 2 1/2", 21.3, new double[] {2.4, 16, 0.4, 8, 2, 2.8, 0.8, 7, 399}});
data.add(new Object[] {"Asparagus (can)", "No. 2", 27.7,
new double[] {0.4, 33, 0.3, 12, 16.3, 1.4, 2.1, 17, 272}});
data.add(new Object[] {
"Green Beans (can)", "No. 2", 10, new double[] {1.0, 54, 2, 65, 53.9, 1.6, 4.3, 32, 431}});
data.add(new Object[] {"Pork and Beans (can)", "16 oz.", 7.1,
new double[] {7.5, 364, 4, 134, 3.5, 8.3, 7.7, 56, 0}});
data.add(new Object[] {
"Corn (can)", "No. 2", 10.4, new double[] {5.2, 136, 0.2, 16, 12, 1.6, 2.7, 42, 218}});
data.add(new Object[] {
"Peas (can)", "No. 2", 13.8, new double[] {2.3, 136, 0.6, 45, 34.9, 4.9, 2.5, 37, 370}});
data.add(new Object[] {
"Tomatoes (can)", "No. 2", 8.6, new double[] {1.3, 63, 0.7, 38, 53.2, 3.4, 2.5, 36, 1253}});
data.add(new Object[] {"Tomato Soup (can)", "10 1/2 oz.", 7.6,
new double[] {1.6, 71, 0.6, 43, 57.9, 3.5, 2.4, 67, 862}});
data.add(new Object[] {
"Peaches, Dried", "1 lb.", 15.7, new double[] {8.5, 87, 1.7, 173, 86.8, 1.2, 4.3, 55, 57}});
data.add(new Object[] {
"Prunes, Dried", "1 lb.", 9, new double[] {12.8, 99, 2.5, 154, 85.7, 3.9, 4.3, 65, 257}});
data.add(new Object[] {"Raisins, Dried", "15 oz.", 9.4,
new double[] {13.5, 104, 2.5, 136, 4.5, 6.3, 1.4, 24, 136}});
data.add(new Object[] {
"Peas, Dried", "1 lb.", 7.9, new double[] {20.0, 1367, 4.2, 345, 2.9, 28.7, 18.4, 162, 0}});
data.add(new Object[] {"Lima Beans, Dried", "1 lb.", 8.9,
new double[] {17.4, 1055, 3.7, 459, 5.1, 26.9, 38.2, 93, 0}});
data.add(new Object[] {"Navy Beans, Dried", "1 lb.", 5.9,
new double[] {26.9, 1691, 11.4, 792, 0, 38.4, 24.6, 217, 0}});
data.add(new Object[] {"Coffee", "1 lb.", 22.4, new double[] {0, 0, 0, 0, 0, 4, 5.1, 50, 0}});
data.add(new Object[] {"Tea", "1/4 lb.", 17.4, new double[] {0, 0, 0, 0, 0, 0, 2.3, 42, 0}});
data.add(
new Object[] {"Cocoa", "8 oz.", 8.6, new double[] {8.7, 237, 3, 72, 0, 2, 11.9, 40, 0}});
data.add(new Object[] {
"Chocolate", "8 oz.", 16.2, new double[] {8.0, 77, 1.3, 39, 0, 0.9, 3.4, 14, 0}});
data.add(new Object[] {"Sugar", "10 lb.", 51.7, new double[] {34.9, 0, 0, 0, 0, 0, 0, 0, 0}});
data.add(new Object[] {
"Corn Syrup", "24 oz.", 13.7, new double[] {14.7, 0, 0.5, 74, 0, 0, 0, 5, 0}});
data.add(new Object[] {
"Molasses", "18 oz.", 13.6, new double[] {9.0, 0, 10.3, 244, 0, 1.9, 7.5, 146, 0}});
data.add(new Object[] {"Strawberry Preserves", "1 lb.", 20.5,
new double[] {6.4, 11, 0.4, 7, 0.2, 0.2, 0.4, 3, 0}});
C#
// Nutrient minimums.
(String Name, double Value)[] nutrients =
new[] { ("Calories (kcal)", 3.0), ("Protein (g)", 70.0), ("Calcium (g)", 0.8),
("Iron (mg)", 12.0), ("Vitamin A (kIU)", 5.0), ("Vitamin B1 (mg)", 1.8),
("Vitamin B2 (mg)", 2.7), ("Niacin (mg)", 18.0), ("Vitamin C (mg)", 75.0) };
(String Name, String Unit, double Price, double[] Nutrients)[] data = new[] {
("Wheat Flour (Enriched)", "10 lb.", 36, new double[] { 44.7, 1411, 2, 365, 0, 55.4, 33.3, 441, 0 }),
("Macaroni", "1 lb.", 14.1, new double[] { 11.6, 418, 0.7, 54, 0, 3.2, 1.9, 68, 0 }),
("Wheat Cereal (Enriched)", "28 oz.", 24.2, new double[] { 11.8, 377, 14.4, 175, 0, 14.4, 8.8, 114, 0 }),
("Corn Flakes", "8 oz.", 7.1, new double[] { 11.4, 252, 0.1, 56, 0, 13.5, 2.3, 68, 0 }),
("Corn Meal", "1 lb.", 4.6, new double[] { 36.0, 897, 1.7, 99, 30.9, 17.4, 7.9, 106, 0 }),
("Hominy Grits", "24 oz.", 8.5, new double[] { 28.6, 680, 0.8, 80, 0, 10.6, 1.6, 110, 0 }),
("Rice", "1 lb.", 7.5, new double[] { 21.2, 460, 0.6, 41, 0, 2, 4.8, 60, 0 }),
("Rolled Oats", "1 lb.", 7.1, new double[] { 25.3, 907, 5.1, 341, 0, 37.1, 8.9, 64, 0 }),
("White Bread (Enriched)", "1 lb.", 7.9, new double[] { 15.0, 488, 2.5, 115, 0, 13.8, 8.5, 126, 0 }),
("Whole Wheat Bread", "1 lb.", 9.1, new double[] { 12.2, 484, 2.7, 125, 0, 13.9, 6.4, 160, 0 }),
("Rye Bread", "1 lb.", 9.1, new double[] { 12.4, 439, 1.1, 82, 0, 9.9, 3, 66, 0 }),
("Pound Cake", "1 lb.", 24.8, new double[] { 8.0, 130, 0.4, 31, 18.9, 2.8, 3, 17, 0 }),
("Soda Crackers", "1 lb.", 15.1, new double[] { 12.5, 288, 0.5, 50, 0, 0, 0, 0, 0 }),
("Milk", "1 qt.", 11, new double[] { 6.1, 310, 10.5, 18, 16.8, 4, 16, 7, 177 }),
("Evaporated Milk (can)", "14.5 oz.", 6.7, new double[] { 8.4, 422, 15.1, 9, 26, 3, 23.5, 11, 60 }),
("Butter", "1 lb.", 30.8, new double[] { 10.8, 9, 0.2, 3, 44.2, 0, 0.2, 2, 0 }),
("Oleomargarine", "1 lb.", 16.1, new double[] { 20.6, 17, 0.6, 6, 55.8, 0.2, 0, 0, 0 }),
("Eggs", "1 doz.", 32.6, new double[] { 2.9, 238, 1.0, 52, 18.6, 2.8, 6.5, 1, 0 }),
("Cheese (Cheddar)", "1 lb.", 24.2, new double[] { 7.4, 448, 16.4, 19, 28.1, 0.8, 10.3, 4, 0 }),
("Cream", "1/2 pt.", 14.1, new double[] { 3.5, 49, 1.7, 3, 16.9, 0.6, 2.5, 0, 17 }),
("Peanut Butter", "1 lb.", 17.9, new double[] { 15.7, 661, 1.0, 48, 0, 9.6, 8.1, 471, 0 }),
("Mayonnaise", "1/2 pt.", 16.7, new double[] { 8.6, 18, 0.2, 8, 2.7, 0.4, 0.5, 0, 0 }),
("Crisco", "1 lb.", 20.3, new double[] { 20.1, 0, 0, 0, 0, 0, 0, 0, 0 }),
("Lard", "1 lb.", 9.8, new double[] { 41.7, 0, 0, 0, 0.2, 0, 0.5, 5, 0 }),
("Sirloin Steak", "1 lb.", 39.6, new double[] { 2.9, 166, 0.1, 34, 0.2, 2.1, 2.9, 69, 0 }),
("Round Steak", "1 lb.", 36.4, new double[] { 2.2, 214, 0.1, 32, 0.4, 2.5, 2.4, 87, 0 }),
("Rib Roast", "1 lb.", 29.2, new double[] { 3.4, 213, 0.1, 33, 0, 0, 2, 0, 0 }),
("Chuck Roast", "1 lb.", 22.6, new double[] { 3.6, 309, 0.2, 46, 0.4, 1, 4, 120, 0 }),
("Plate", "1 lb.", 14.6, new double[] { 8.5, 404, 0.2, 62, 0, 0.9, 0, 0, 0 }),
("Liver (Beef)", "1 lb.", 26.8, new double[] { 2.2, 333, 0.2, 139, 169.2, 6.4, 50.8, 316, 525 }),
("Leg of Lamb", "1 lb.", 27.6, new double[] { 3.1, 245, 0.1, 20, 0, 2.8, 3.9, 86, 0 }),
("Lamb Chops (Rib)", "1 lb.", 36.6, new double[] { 3.3, 140, 0.1, 15, 0, 1.7, 2.7, 54, 0 }),
("Pork Chops", "1 lb.", 30.7, new double[] { 3.5, 196, 0.2, 30, 0, 17.4, 2.7, 60, 0 }),
("Pork Loin Roast", "1 lb.", 24.2, new double[] { 4.4, 249, 0.3, 37, 0, 18.2, 3.6, 79, 0 }),
("Bacon", "1 lb.", 25.6, new double[] { 10.4, 152, 0.2, 23, 0, 1.8, 1.8, 71, 0 }),
("Ham, smoked", "1 lb.", 27.4, new double[] { 6.7, 212, 0.2, 31, 0, 9.9, 3.3, 50, 0 }),
("Salt Pork", "1 lb.", 16, new double[] { 18.8, 164, 0.1, 26, 0, 1.4, 1.8, 0, 0 }),
("Roasting Chicken", "1 lb.", 30.3, new double[] { 1.8, 184, 0.1, 30, 0.1, 0.9, 1.8, 68, 46 }),
("Veal Cutlets", "1 lb.", 42.3, new double[] { 1.7, 156, 0.1, 24, 0, 1.4, 2.4, 57, 0 }),
("Salmon, Pink (can)", "16 oz.", 13, new double[] { 5.8, 705, 6.8, 45, 3.5, 1, 4.9, 209, 0 }),
("Apples", "1 lb.", 4.4, new double[] { 5.8, 27, 0.5, 36, 7.3, 3.6, 2.7, 5, 544 }),
("Bananas", "1 lb.", 6.1, new double[] { 4.9, 60, 0.4, 30, 17.4, 2.5, 3.5, 28, 498 }),
("Lemons", "1 doz.", 26, new double[] { 1.0, 21, 0.5, 14, 0, 0.5, 0, 4, 952 }),
("Oranges", "1 doz.", 30.9, new double[] { 2.2, 40, 1.1, 18, 11.1, 3.6, 1.3, 10, 1998 }),
("Green Beans", "1 lb.", 7.1, new double[] { 2.4, 138, 3.7, 80, 69, 4.3, 5.8, 37, 862 }),
("Cabbage", "1 lb.", 3.7, new double[] { 2.6, 125, 4.0, 36, 7.2, 9, 4.5, 26, 5369 }),
("Carrots", "1 bunch", 4.7, new double[] { 2.7, 73, 2.8, 43, 188.5, 6.1, 4.3, 89, 608 }),
("Celery", "1 stalk", 7.3, new double[] { 0.9, 51, 3.0, 23, 0.9, 1.4, 1.4, 9, 313 }),
("Lettuce", "1 head", 8.2, new double[] { 0.4, 27, 1.1, 22, 112.4, 1.8, 3.4, 11, 449 }),
("Onions", "1 lb.", 3.6, new double[] { 5.8, 166, 3.8, 59, 16.6, 4.7, 5.9, 21, 1184 }),
("Potatoes", "15 lb.", 34, new double[] { 14.3, 336, 1.8, 118, 6.7, 29.4, 7.1, 198, 2522 }),
("Spinach", "1 lb.", 8.1, new double[] { 1.1, 106, 0, 138, 918.4, 5.7, 13.8, 33, 2755 }),
("Sweet Potatoes", "1 lb.", 5.1, new double[] { 9.6, 138, 2.7, 54, 290.7, 8.4, 5.4, 83, 1912 }),
("Peaches (can)", "No. 2 1/2", 16.8, new double[] { 3.7, 20, 0.4, 10, 21.5, 0.5, 1, 31, 196 }),
("Pears (can)", "No. 2 1/2", 20.4, new double[] { 3.0, 8, 0.3, 8, 0.8, 0.8, 0.8, 5, 81 }),
("Pineapple (can)", "No. 2 1/2", 21.3, new double[] { 2.4, 16, 0.4, 8, 2, 2.8, 0.8, 7, 399 }),
("Asparagus (can)", "No. 2", 27.7, new double[] { 0.4, 33, 0.3, 12, 16.3, 1.4, 2.1, 17, 272 }),
("Green Beans (can)", "No. 2", 10, new double[] { 1.0, 54, 2, 65, 53.9, 1.6, 4.3, 32, 431 }),
("Pork and Beans (can)", "16 oz.", 7.1, new double[] { 7.5, 364, 4, 134, 3.5, 8.3, 7.7, 56, 0 }),
("Corn (can)", "No. 2", 10.4, new double[] { 5.2, 136, 0.2, 16, 12, 1.6, 2.7, 42, 218 }),
("Peas (can)", "No. 2", 13.8, new double[] { 2.3, 136, 0.6, 45, 34.9, 4.9, 2.5, 37, 370 }),
("Tomatoes (can)", "No. 2", 8.6, new double[] { 1.3, 63, 0.7, 38, 53.2, 3.4, 2.5, 36, 1253 }),
("Tomato Soup (can)", "10 1/2 oz.", 7.6, new double[] { 1.6, 71, 0.6, 43, 57.9, 3.5, 2.4, 67, 862 }),
("Peaches, Dried", "1 lb.", 15.7, new double[] { 8.5, 87, 1.7, 173, 86.8, 1.2, 4.3, 55, 57 }),
("Prunes, Dried", "1 lb.", 9, new double[] { 12.8, 99, 2.5, 154, 85.7, 3.9, 4.3, 65, 257 }),
("Raisins, Dried", "15 oz.", 9.4, new double[] { 13.5, 104, 2.5, 136, 4.5, 6.3, 1.4, 24, 136 }),
("Peas, Dried", "1 lb.", 7.9, new double[] { 20.0, 1367, 4.2, 345, 2.9, 28.7, 18.4, 162, 0 }),
("Lima Beans, Dried", "1 lb.", 8.9, new double[] { 17.4, 1055, 3.7, 459, 5.1, 26.9, 38.2, 93, 0 }),
("Navy Beans, Dried", "1 lb.", 5.9, new double[] { 26.9, 1691, 11.4, 792, 0, 38.4, 24.6, 217, 0 }),
("Coffee", "1 lb.", 22.4, new double[] { 0, 0, 0, 0, 0, 4, 5.1, 50, 0 }),
("Tea", "1/4 lb.", 17.4, new double[] { 0, 0, 0, 0, 0, 0, 2.3, 42, 0 }),
("Cocoa", "8 oz.", 8.6, new double[] { 8.7, 237, 3, 72, 0, 2, 11.9, 40, 0 }),
("Chocolate", "8 oz.", 16.2, new double[] { 8.0, 77, 1.3, 39, 0, 0.9, 3.4, 14, 0 }),
("Sugar", "10 lb.", 51.7, new double[] { 34.9, 0, 0, 0, 0, 0, 0, 0, 0 }),
("Corn Syrup", "24 oz.", 13.7, new double[] { 14.7, 0, 0.5, 74, 0, 0, 0, 5, 0 }),
("Molasses", "18 oz.", 13.6, new double[] { 9.0, 0, 10.3, 244, 0, 1.9, 7.5, 146, 0 }),
("Strawberry Preserves", "1 lb.", 20.5, new double[] { 6.4, 11, 0.4, 7, 0.2, 0.2, 0.4, 3, 0 })
};
LP ソルバーを宣言する
次のコードは、MPsolver ラッパーをインスタンス化します。
Python
# Instantiate a Glop solver and naming it.
solver = pywraplp.Solver.CreateSolver("GLOP")
if not solver:
return
C++
// Create the linear solver with the GLOP backend.
std::unique_ptr<MPSolver> solver(MPSolver::CreateSolver("GLOP"));
Java
// Create the linear solver with the GLOP backend.
MPSolver solver = MPSolver.createSolver("GLOP");
if (solver == null) {
System.out.println("Could not create solver GLOP");
return;
}
C#
// Create the linear solver with the GLOP backend.
Solver solver = Solver.CreateSolver("GLOP");
if (solver is null)
{
return;
}
変数を作成する
次のコードは、問題の変数を作成します。
Python
# Declare an array to hold our variables.
foods = [solver.NumVar(0.0, solver.infinity(), item[0]) for item in data]
print("Number of variables =", solver.NumVariables())
C++
std::vector<MPVariable*> foods;
const double infinity = solver->infinity();
for (const Commodity& commodity : data) {
foods.push_back(solver->MakeNumVar(0.0, infinity, commodity.name));
}
LOG(INFO) << "Number of variables = " << solver->NumVariables();
Java
double infinity = java.lang.Double.POSITIVE_INFINITY;
List<MPVariable> foods = new ArrayList<>();
for (int i = 0; i < data.size(); ++i) {
foods.add(solver.makeNumVar(0.0, infinity, (String) data.get(i)[0]));
}
System.out.println("Number of variables = " + solver.numVariables());
C#
List<Variable> foods = new List<Variable>();
for (int i = 0; i < data.Length; ++i)
{
foods.Add(solver.MakeNumVar(0.0, double.PositiveInfinity, data[i].Name));
}
Console.WriteLine($"Number of variables = {solver.NumVariables()}");
MakeNumVar メソッドは、テーブルの行ごとに 1 つの変数 food[i] を作成します。前述のように、栄養データは 1 ドルあたりのデータであるため、food[i] は商品 i に費やす金額です。
制約を定義する
スティグラー ダイエットの制約により、すべての食品から得られる栄養素の合計量が、各栄養素の最小要件以上であることが要件となっています。次に、これらの制約を、配列 data と nutrients、および変数 food[i] を含む不等式として記述します。
まず、食品 j によって提供される 1 ドルあたりの栄養素 i の量は data[j][i+3] です（栄養素のデータは data の 4 列目から始まるため、列のインデックスに 3 が追加されます）。食品 j に費やす金額が food[j] であるため、食品 j によって提供される栄養素 i の量は\(data[j][i+3] \cdot food[j]\)になります。最後に、栄養素 i の最小要件は nutrients[i][1] であるため、制約 i を次のように記述できます。
\(
\sum_{j} data[j][i+3] \cdot food[j] \geq nutrients[i][1] \;\;\;\;\; (1)
\)
次のコードで、これらの制約を定義しています。
Python
# 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 constraints =", solver.NumConstraints())
C++
// Create the constraints, one per nutrient.
std::vector<MPConstraint*> constraints;
for (std::size_t i = 0; i < nutrients.size(); ++i) {
constraints.push_back(
solver->MakeRowConstraint(nutrients[i].second, infinity));
for (std::size_t j = 0; j < data.size(); ++j) {
constraints.back()->SetCoefficient(foods[j], data[j].nutrients[i]);
}
}
LOG(INFO) << "Number of constraints = " << solver->NumConstraints();
Java
MPConstraint[] constraints = new MPConstraint[nutrients.size()];
for (int i = 0; i < nutrients.size(); ++i) {
constraints[i] = solver.makeConstraint(
(double) nutrients.get(i)[1], infinity, (String) nutrients.get(i)[0]);
for (int j = 0; j < data.size(); ++j) {
constraints[i].setCoefficient(foods.get(j), ((double[]) data.get(j)[3])[i]);
}
// constraints.add(constraint);
}
System.out.println("Number of constraints = " + solver.numConstraints());
C#
List<Constraint> constraints = new List<Constraint>();
for (int i = 0; i < nutrients.Length; ++i)
{
Constraint constraint =
solver.MakeConstraint(nutrients[i].Value, double.PositiveInfinity, nutrients[i].Name);
for (int j = 0; j < data.Length; ++j)
{
constraint.SetCoefficient(foods[j], data[j].Nutrients[i]);
}
constraints.Add(constraint);
}
Console.WriteLine($"Number of constraints = {solver.NumConstraints()}");
Python メソッド Constraint（C++ メソッド MakeRowConstraint に対応）は、問題の制約を作成します。i ごとに、constraint(nutrients[i][1], solver.infinity)
これにより、変数 food[j]（次に定義）の線形組み合わせが nutrients[i][1] 以上という制約が作成されます。一次式の係数は、SetCoefficient メソッドで次のように定義されます。SetCoefficient(food[j], data[j][i+3]
これにより、food[j] の係数が data[j][i+3] に設定されます。
これらをすべてまとめると、コードは上記（1）で表される制約を定義します。
目標を作成する
次のコードは、問題の目的関数を定義します。
Python
# Objective function: Minimize the sum of (price-normalized) foods.
objective = solver.Objective()
for food in foods:
objective.SetCoefficient(food, 1)
objective.SetMinimization()
C++
MPObjective* const objective = solver->MutableObjective();
for (size_t i = 0; i < data.size(); ++i) {
objective->SetCoefficient(foods[i], 1);
}
objective->SetMinimization();
Java
MPObjective objective = solver.objective();
for (int i = 0; i < data.size(); ++i) {
objective.setCoefficient(foods.get(i), 1);
}
objective.setMinimization();
C#
Objective objective = solver.Objective();
for (int i = 0; i < data.Length; ++i)
{
objective.SetCoefficient(foods[i], 1);
}
objective.SetMinimization();
目的関数は食品の総費用であり、変数 food[i] の合計です。
SetCoefficient メソッドは、目的関数の係数を設定します。この場合は、すべて 1 です。最後に、SetMinimization はこれを最小化の問題であると宣言しています。
ソルバーを呼び出す
次のコードはソルバーを呼び出します。
Python
print(f"Solving with {solver.SolverVersion()}")
status = solver.Solve()
C++
const MPSolver::ResultStatus result_status = solver->Solve();
Java
final MPSolver.ResultStatus resultStatus = solver.solve();
C#
Solver.ResultStatus resultStatus = solver.Solve();
Glop は、一般的なコンピュータの問題を 300 ミリ秒未満で解決します。
解答を表示する
次のコードは解答を示しています。
Python
# Check that the problem has an optimal solution.
if status != solver.OPTIMAL:
print("The problem does not have an optimal solution!")
if status == solver.FEASIBLE:
print("A potentially suboptimal solution was found.")
else:
print("The solver could not solve the problem.")
exit(1)
# Display the amounts (in dollars) to purchase of each food.
nutrients_result = [0] * len(nutrients)
print("\nAnnual Foods:")
for i, food in enumerate(foods):
if food.solution_value() > 0.0:
print("{}: ${}".format(data[i][0], 365.0 * food.solution_value()))
for j, _ in enumerate(nutrients):
nutrients_result[j] += data[i][j + 3] * food.solution_value()
print("\nOptimal annual price: ${:.4f}".format(365.0 * objective.Value()))
print("\nNutrients per day:")
for i, nutrient in enumerate(nutrients):
print(
"{}: {:.2f} (min {})".format(nutrient[0], nutrients_result[i], nutrient[1])
)
C++
// Check that the problem has an optimal solution.
if (result_status != MPSolver::OPTIMAL) {
LOG(INFO) << "The problem does not have an optimal solution!";
if (result_status == MPSolver::FEASIBLE) {
LOG(INFO) << "A potentially suboptimal solution was found";
} else {
LOG(INFO) << "The solver could not solve the problem.";
return;
}
}
std::vector<double> nutrients_result(nutrients.size());
LOG(INFO) << "";
LOG(INFO) << "Annual Foods:";
for (std::size_t i = 0; i < data.size(); ++i) {
if (foods[i]->solution_value() > 0.0) {
LOG(INFO) << data[i].name << ": $"
<< std::to_string(365. * foods[i]->solution_value());
for (std::size_t j = 0; j < nutrients.size(); ++j) {
nutrients_result[j] +=
data[i].nutrients[j] * foods[i]->solution_value();
}
}
}
LOG(INFO) << "";
LOG(INFO) << "Optimal annual price: $"
<< std::to_string(365. * objective->Value());
LOG(INFO) << "";
LOG(INFO) << "Nutrients per day:";
for (std::size_t i = 0; i < nutrients.size(); ++i) {
LOG(INFO) << nutrients[i].first << ": "
<< std::to_string(nutrients_result[i]) << " (min "
<< std::to_string(nutrients[i].second) << ")";
}
Java
// Check that the problem has an optimal solution.
if (resultStatus != MPSolver.ResultStatus.OPTIMAL) {
System.err.println("The problem does not have an optimal solution!");
if (resultStatus == MPSolver.ResultStatus.FEASIBLE) {
System.err.println("A potentially suboptimal solution was found.");
} else {
System.err.println("The solver could not solve the problem.");
return;
}
}
// Display the amounts (in dollars) to purchase of each food.
double[] nutrientsResult = new double[nutrients.size()];
System.out.println("\nAnnual Foods:");
for (int i = 0; i < foods.size(); ++i) {
if (foods.get(i).solutionValue() > 0.0) {
System.out.println((String) data.get(i)[0] + ": $" + 365 * foods.get(i).solutionValue());
for (int j = 0; j < nutrients.size(); ++j) {
nutrientsResult[j] += ((double[]) data.get(i)[3])[j] * foods.get(i).solutionValue();
}
}
}
System.out.println("\nOptimal annual price: $" + 365 * objective.value());
System.out.println("\nNutrients per day:");
for (int i = 0; i < nutrients.size(); ++i) {
System.out.println(
nutrients.get(i)[0] + ": " + nutrientsResult[i] + " (min " + nutrients.get(i)[1] + ")");
}
C#
// Check that the problem has an optimal solution.
if (resultStatus != Solver.ResultStatus.OPTIMAL)
{
Console.WriteLine("The problem does not have an optimal solution!");
if (resultStatus == Solver.ResultStatus.FEASIBLE)
{
Console.WriteLine("A potentially suboptimal solution was found.");
}
else
{
Console.WriteLine("The solver could not solve the problem.");
return;
}
}
// Display the amounts (in dollars) to purchase of each food.
double[] nutrientsResult = new double[nutrients.Length];
Console.WriteLine("\nAnnual Foods:");
for (int i = 0; i < foods.Count; ++i)
{
if (foods[i].SolutionValue() > 0.0)
{
Console.WriteLine($"{data[i].Name}: ${365 * foods[i].SolutionValue():N2}");
for (int j = 0; j < nutrients.Length; ++j)
{
nutrientsResult[j] += data[i].Nutrients[j] * foods[i].SolutionValue();
}
}
}
Console.WriteLine($"\nOptimal annual price: ${365 * objective.Value():N2}");
Console.WriteLine("\nNutrients per day:");
for (int i = 0; i < nutrients.Length; ++i)
{
Console.WriteLine($"{nutrients[i].Name}: {nutrientsResult[i]:N2} (min {nutrients[i].Value})");
}
プログラムの出力は以下のとおりです。
make rpy_stigler_diet "/usr/bin/python3.11" ortools/linear_solver/samples/stigler_diet.py Number of variables = 77 Number of constraints = 9 Annual Foods: Wheat Flour (Enriched): $10.774457511918223 Liver (Beef): $0.6907834111074193 Cabbage: $4.093268864842877 Spinach: $1.8277960703546996 Navy Beans, Dried: $22.275425687243036 Optimal annual price: $39.6617 Nutrients per day: Calories (kcal): 3.00 (min 3) Protein (g): 147.41 (min 70) Calcium (g): 0.80 (min 0.8) Iron (mg): 60.47 (min 12) Vitamin A (KIU): 5.00 (min 5) Vitamin B1 (mg): 4.12 (min 1.8) Vitamin B2 (mg): 2.70 (min 2.7) Niacin (mg): 27.32 (min 18) Vitamin C (mg): 75.00 (min 75) Advanced usage: Problem solved in 1 milliseconds Problem solved in 14 iterations
プログラムのコード全体
スティグラー・ダイエット・プログラムのコード全体を以下に示します。
Python
"""The Stigler diet problem.
A description of the problem can be found here:
https://en.wikipedia.org/wiki/Stigler_diet.
"""
from ortools.linear_solver import pywraplp
def main():
"""Entry point of the program."""
# Instantiate the data problem.
# 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 = [
# fmt: off
['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],
# fmt: on
]
# Instantiate a Glop solver and naming it.
solver = pywraplp.Solver.CreateSolver("GLOP")
if not solver:
return
# Declare an array to hold our variables.
foods = [solver.NumVar(0.0, solver.infinity(), item[0]) for item in data]
print("Number of variables =", solver.NumVariables())
# 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 constraints =", solver.NumConstraints())
# Objective function: Minimize the sum of (price-normalized) foods.
objective = solver.Objective()
for food in foods:
objective.SetCoefficient(food, 1)
objective.SetMinimization()
print(f"Solving with {solver.SolverVersion()}")
status = solver.Solve()
# Check that the problem has an optimal solution.
if status != solver.OPTIMAL:
print("The problem does not have an optimal solution!")
if status == solver.FEASIBLE:
print("A potentially suboptimal solution was found.")
else:
print("The solver could not solve the problem.")
exit(1)
# Display the amounts (in dollars) to purchase of each food.
nutrients_result = [0] * len(nutrients)
print("\nAnnual Foods:")
for i, food in enumerate(foods):
if food.solution_value() > 0.0:
print("{}: ${}".format(data[i][0], 365.0 * food.solution_value()))
for j, _ in enumerate(nutrients):
nutrients_result[j] += data[i][j + 3] * food.solution_value()
print("\nOptimal annual price: ${:.4f}".format(365.0 * objective.Value()))
print("\nNutrients per day:")
for i, nutrient in enumerate(nutrients):
print(
"{}: {:.2f} (min {})".format(nutrient[0], nutrients_result[i], nutrient[1])
)
print("\nAdvanced usage:")
print(f"Problem solved in {solver.wall_time():d} milliseconds")
print(f"Problem solved in {solver.iterations():d} iterations")
if __name__ == "__main__":
main()
C++
// The Stigler diet problem.
#include <array>
#include <memory>
#include <string>
#include <utility> // std::pair
#include <vector>
#include "absl/flags/flag.h"
#include "absl/log/flags.h"
#include "ortools/base/init_google.h"
#include "ortools/base/logging.h"
#include "ortools/linear_solver/linear_solver.h"
namespace operations_research {
void StiglerDiet() {
// Nutrient minimums.
const std::vector<std::pair<std::string, double>> nutrients = {
{"Calories (kcal)", 3.0}, {"Protein (g)", 70.0},
{"Calcium (g)", 0.8}, {"Iron (mg)", 12.0},
{"Vitamin A (kIU)", 5.0}, {"Vitamin B1 (mg)", 1.8},
{"Vitamin B2 (mg)", 2.7}, {"Niacin (mg)", 18.0},
{"Vitamin C (mg)", 75.0}};
struct Commodity {
std::string name; //!< Commodity name
std::string unit; //!< Unit
double price; //!< 1939 price per unit (cents)
//! Calories (kcal),
//! Protein (g),
//! Calcium (g),
//! Iron (mg),
//! Vitamin A (kIU),
//! Vitamin B1 (mg),
//! Vitamin B2 (mg),
//! Niacin (mg),
//! Vitamin C (mg)
std::array<double, 9> nutrients;
};
std::vector<Commodity> 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}}};
// Create the linear solver with the GLOP backend.
std::unique_ptr<MPSolver> solver(MPSolver::CreateSolver("GLOP"));
std::vector<MPVariable*> foods;
const double infinity = solver->infinity();
for (const Commodity& commodity : data) {
foods.push_back(solver->MakeNumVar(0.0, infinity, commodity.name));
}
LOG(INFO) << "Number of variables = " << solver->NumVariables();
// Create the constraints, one per nutrient.
std::vector<MPConstraint*> constraints;
for (std::size_t i = 0; i < nutrients.size(); ++i) {
constraints.push_back(
solver->MakeRowConstraint(nutrients[i].second, infinity));
for (std::size_t j = 0; j < data.size(); ++j) {
constraints.back()->SetCoefficient(foods[j], data[j].nutrients[i]);
}
}
LOG(INFO) << "Number of constraints = " << solver->NumConstraints();
MPObjective* const objective = solver->MutableObjective();
for (size_t i = 0; i < data.size(); ++i) {
objective->SetCoefficient(foods[i], 1);
}
objective->SetMinimization();
const MPSolver::ResultStatus result_status = solver->Solve();
// Check that the problem has an optimal solution.
if (result_status != MPSolver::OPTIMAL) {
LOG(INFO) << "The problem does not have an optimal solution!";
if (result_status == MPSolver::FEASIBLE) {
LOG(INFO) << "A potentially suboptimal solution was found";
} else {
LOG(INFO) << "The solver could not solve the problem.";
return;
}
}
std::vector<double> nutrients_result(nutrients.size());
LOG(INFO) << "";
LOG(INFO) << "Annual Foods:";
for (std::size_t i = 0; i < data.size(); ++i) {
if (foods[i]->solution_value() > 0.0) {
LOG(INFO) << data[i].name << ": $"
<< std::to_string(365. * foods[i]->solution_value());
for (std::size_t j = 0; j < nutrients.size(); ++j) {
nutrients_result[j] +=
data[i].nutrients[j] * foods[i]->solution_value();
}
}
}
LOG(INFO) << "";
LOG(INFO) << "Optimal annual price: $"
<< std::to_string(365. * objective->Value());
LOG(INFO) << "";
LOG(INFO) << "Nutrients per day:";
for (std::size_t i = 0; i < nutrients.size(); ++i) {
LOG(INFO) << nutrients[i].first << ": "
<< std::to_string(nutrients_result[i]) << " (min "
<< std::to_string(nutrients[i].second) << ")";
}
LOG(INFO) << "";
LOG(INFO) << "Advanced usage:";
LOG(INFO) << "Problem solved in " << solver->wall_time() << " milliseconds";
LOG(INFO) << "Problem solved in " << solver->iterations() << " iterations";
}
} // namespace operations_research
int main(int argc, char** argv) {
InitGoogle(argv[0], &argc, &argv, true);
absl::SetFlag(&FLAGS_stderrthreshold, 0);
operations_research::StiglerDiet();
return EXIT_SUCCESS;
}
Java
// The Stigler diet problem.
package com.google.ortools.linearsolver.samples;
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.util.ArrayList;
import java.util.List;
/** Stigler diet example. */
public final class StiglerDiet {
public static void main(String[] args) {
Loader.loadNativeLibraries();
// Nutrient minimums.
List<Object[]> nutrients = new ArrayList<>();
nutrients.add(new Object[] {"Calories (kcal)", 3.0});
nutrients.add(new Object[] {"Protein (g)", 70.0});
nutrients.add(new Object[] {"Calcium (g)", 0.8});
nutrients.add(new Object[] {"Iron (mg)", 12.0});
nutrients.add(new Object[] {"Vitamin A (kIU)", 5.0});
nutrients.add(new Object[] {"Vitamin B1 (mg)", 1.8});
nutrients.add(new Object[] {"Vitamin B2 (mg)", 2.7});
nutrients.add(new Object[] {"Niacin (mg)", 18.0});
nutrients.add(new Object[] {"Vitamin C (mg)", 75.0});
List<Object[]> data = new ArrayList<>();
data.add(new Object[] {"Wheat Flour (Enriched)", "10 lb.", 36,
new double[] {44.7, 1411, 2, 365, 0, 55.4, 33.3, 441, 0}});
data.add(new Object[] {
"Macaroni", "1 lb.", 14.1, new double[] {11.6, 418, 0.7, 54, 0, 3.2, 1.9, 68, 0}});
data.add(new Object[] {"Wheat Cereal (Enriched)", "28 oz.", 24.2,
new double[] {11.8, 377, 14.4, 175, 0, 14.4, 8.8, 114, 0}});
data.add(new Object[] {
"Corn Flakes", "8 oz.", 7.1, new double[] {11.4, 252, 0.1, 56, 0, 13.5, 2.3, 68, 0}});
data.add(new Object[] {
"Corn Meal", "1 lb.", 4.6, new double[] {36.0, 897, 1.7, 99, 30.9, 17.4, 7.9, 106, 0}});
data.add(new Object[] {
"Hominy Grits", "24 oz.", 8.5, new double[] {28.6, 680, 0.8, 80, 0, 10.6, 1.6, 110, 0}});
data.add(
new Object[] {"Rice", "1 lb.", 7.5, new double[] {21.2, 460, 0.6, 41, 0, 2, 4.8, 60, 0}});
data.add(new Object[] {
"Rolled Oats", "1 lb.", 7.1, new double[] {25.3, 907, 5.1, 341, 0, 37.1, 8.9, 64, 0}});
data.add(new Object[] {"White Bread (Enriched)", "1 lb.", 7.9,
new double[] {15.0, 488, 2.5, 115, 0, 13.8, 8.5, 126, 0}});
data.add(new Object[] {"Whole Wheat Bread", "1 lb.", 9.1,
new double[] {12.2, 484, 2.7, 125, 0, 13.9, 6.4, 160, 0}});
data.add(new Object[] {
"Rye Bread", "1 lb.", 9.1, new double[] {12.4, 439, 1.1, 82, 0, 9.9, 3, 66, 0}});
data.add(new Object[] {
"Pound Cake", "1 lb.", 24.8, new double[] {8.0, 130, 0.4, 31, 18.9, 2.8, 3, 17, 0}});
data.add(new Object[] {
"Soda Crackers", "1 lb.", 15.1, new double[] {12.5, 288, 0.5, 50, 0, 0, 0, 0, 0}});
data.add(
new Object[] {"Milk", "1 qt.", 11, new double[] {6.1, 310, 10.5, 18, 16.8, 4, 16, 7, 177}});
data.add(new Object[] {"Evaporated Milk (can)", "14.5 oz.", 6.7,
new double[] {8.4, 422, 15.1, 9, 26, 3, 23.5, 11, 60}});
data.add(
new Object[] {"Butter", "1 lb.", 30.8, new double[] {10.8, 9, 0.2, 3, 44.2, 0, 0.2, 2, 0}});
data.add(new Object[] {
"Oleomargarine", "1 lb.", 16.1, new double[] {20.6, 17, 0.6, 6, 55.8, 0.2, 0, 0, 0}});
data.add(new Object[] {
"Eggs", "1 doz.", 32.6, new double[] {2.9, 238, 1.0, 52, 18.6, 2.8, 6.5, 1, 0}});
data.add(new Object[] {"Cheese (Cheddar)", "1 lb.", 24.2,
new double[] {7.4, 448, 16.4, 19, 28.1, 0.8, 10.3, 4, 0}});
data.add(new Object[] {
"Cream", "1/2 pt.", 14.1, new double[] {3.5, 49, 1.7, 3, 16.9, 0.6, 2.5, 0, 17}});
data.add(new Object[] {
"Peanut Butter", "1 lb.", 17.9, new double[] {15.7, 661, 1.0, 48, 0, 9.6, 8.1, 471, 0}});
data.add(new Object[] {
"Mayonnaise", "1/2 pt.", 16.7, new double[] {8.6, 18, 0.2, 8, 2.7, 0.4, 0.5, 0, 0}});
data.add(new Object[] {"Crisco", "1 lb.", 20.3, new double[] {20.1, 0, 0, 0, 0, 0, 0, 0, 0}});
data.add(new Object[] {"Lard", "1 lb.", 9.8, new double[] {41.7, 0, 0, 0, 0.2, 0, 0.5, 5, 0}});
data.add(new Object[] {
"Sirloin Steak", "1 lb.", 39.6, new double[] {2.9, 166, 0.1, 34, 0.2, 2.1, 2.9, 69, 0}});
data.add(new Object[] {
"Round Steak", "1 lb.", 36.4, new double[] {2.2, 214, 0.1, 32, 0.4, 2.5, 2.4, 87, 0}});
data.add(
new Object[] {"Rib Roast", "1 lb.", 29.2, new double[] {3.4, 213, 0.1, 33, 0, 0, 2, 0, 0}});
data.add(new Object[] {
"Chuck Roast", "1 lb.", 22.6, new double[] {3.6, 309, 0.2, 46, 0.4, 1, 4, 120, 0}});
data.add(
new Object[] {"Plate", "1 lb.", 14.6, new double[] {8.5, 404, 0.2, 62, 0, 0.9, 0, 0, 0}});
data.add(new Object[] {"Liver (Beef)", "1 lb.", 26.8,
new double[] {2.2, 333, 0.2, 139, 169.2, 6.4, 50.8, 316, 525}});
data.add(new Object[] {
"Leg of Lamb", "1 lb.", 27.6, new double[] {3.1, 245, 0.1, 20, 0, 2.8, 3.9, 86, 0}});
data.add(new Object[] {
"Lamb Chops (Rib)", "1 lb.", 36.6, new double[] {3.3, 140, 0.1, 15, 0, 1.7, 2.7, 54, 0}});
data.add(new Object[] {
"Pork Chops", "1 lb.", 30.7, new double[] {3.5, 196, 0.2, 30, 0, 17.4, 2.7, 60, 0}});
data.add(new Object[] {
"Pork Loin Roast", "1 lb.", 24.2, new double[] {4.4, 249, 0.3, 37, 0, 18.2, 3.6, 79, 0}});
data.add(new Object[] {
"Bacon", "1 lb.", 25.6, new double[] {10.4, 152, 0.2, 23, 0, 1.8, 1.8, 71, 0}});
data.add(new Object[] {
"Ham, smoked", "1 lb.", 27.4, new double[] {6.7, 212, 0.2, 31, 0, 9.9, 3.3, 50, 0}});
data.add(new Object[] {
"Salt Pork", "1 lb.", 16, new double[] {18.8, 164, 0.1, 26, 0, 1.4, 1.8, 0, 0}});
data.add(new Object[] {"Roasting Chicken", "1 lb.", 30.3,
new double[] {1.8, 184, 0.1, 30, 0.1, 0.9, 1.8, 68, 46}});
data.add(new Object[] {
"Veal Cutlets", "1 lb.", 42.3, new double[] {1.7, 156, 0.1, 24, 0, 1.4, 2.4, 57, 0}});
data.add(new Object[] {
"Salmon, Pink (can)", "16 oz.", 13, new double[] {5.8, 705, 6.8, 45, 3.5, 1, 4.9, 209, 0}});
data.add(new Object[] {
"Apples", "1 lb.", 4.4, new double[] {5.8, 27, 0.5, 36, 7.3, 3.6, 2.7, 5, 544}});
data.add(new Object[] {
"Bananas", "1 lb.", 6.1, new double[] {4.9, 60, 0.4, 30, 17.4, 2.5, 3.5, 28, 498}});
data.add(
new Object[] {"Lemons", "1 doz.", 26, new double[] {1.0, 21, 0.5, 14, 0, 0.5, 0, 4, 952}});
data.add(new Object[] {
"Oranges", "1 doz.", 30.9, new double[] {2.2, 40, 1.1, 18, 11.1, 3.6, 1.3, 10, 1998}});
data.add(new Object[] {
"Green Beans", "1 lb.", 7.1, new double[] {2.4, 138, 3.7, 80, 69, 4.3, 5.8, 37, 862}});
data.add(new Object[] {
"Cabbage", "1 lb.", 3.7, new double[] {2.6, 125, 4.0, 36, 7.2, 9, 4.5, 26, 5369}});
data.add(new Object[] {
"Carrots", "1 bunch", 4.7, new double[] {2.7, 73, 2.8, 43, 188.5, 6.1, 4.3, 89, 608}});
data.add(new Object[] {
"Celery", "1 stalk", 7.3, new double[] {0.9, 51, 3.0, 23, 0.9, 1.4, 1.4, 9, 313}});
data.add(new Object[] {
"Lettuce", "1 head", 8.2, new double[] {0.4, 27, 1.1, 22, 112.4, 1.8, 3.4, 11, 449}});
data.add(new Object[] {
"Onions", "1 lb.", 3.6, new double[] {5.8, 166, 3.8, 59, 16.6, 4.7, 5.9, 21, 1184}});
data.add(new Object[] {
"Potatoes", "15 lb.", 34, new double[] {14.3, 336, 1.8, 118, 6.7, 29.4, 7.1, 198, 2522}});
data.add(new Object[] {
"Spinach", "1 lb.", 8.1, new double[] {1.1, 106, 0, 138, 918.4, 5.7, 13.8, 33, 2755}});
data.add(new Object[] {"Sweet Potatoes", "1 lb.", 5.1,
new double[] {9.6, 138, 2.7, 54, 290.7, 8.4, 5.4, 83, 1912}});
data.add(new Object[] {"Peaches (can)", "No. 2 1/2", 16.8,
new double[] {3.7, 20, 0.4, 10, 21.5, 0.5, 1, 31, 196}});
data.add(new Object[] {
"Pears (can)", "No. 2 1/2", 20.4, new double[] {3.0, 8, 0.3, 8, 0.8, 0.8, 0.8, 5, 81}});
data.add(new Object[] {
"Pineapple (can)", "No. 2 1/2", 21.3, new double[] {2.4, 16, 0.4, 8, 2, 2.8, 0.8, 7, 399}});
data.add(new Object[] {"Asparagus (can)", "No. 2", 27.7,
new double[] {0.4, 33, 0.3, 12, 16.3, 1.4, 2.1, 17, 272}});
data.add(new Object[] {
"Green Beans (can)", "No. 2", 10, new double[] {1.0, 54, 2, 65, 53.9, 1.6, 4.3, 32, 431}});
data.add(new Object[] {"Pork and Beans (can)", "16 oz.", 7.1,
new double[] {7.5, 364, 4, 134, 3.5, 8.3, 7.7, 56, 0}});
data.add(new Object[] {
"Corn (can)", "No. 2", 10.4, new double[] {5.2, 136, 0.2, 16, 12, 1.6, 2.7, 42, 218}});
data.add(new Object[] {
"Peas (can)", "No. 2", 13.8, new double[] {2.3, 136, 0.6, 45, 34.9, 4.9, 2.5, 37, 370}});
data.add(new Object[] {
"Tomatoes (can)", "No. 2", 8.6, new double[] {1.3, 63, 0.7, 38, 53.2, 3.4, 2.5, 36, 1253}});
data.add(new Object[] {"Tomato Soup (can)", "10 1/2 oz.", 7.6,
new double[] {1.6, 71, 0.6, 43, 57.9, 3.5, 2.4, 67, 862}});
data.add(new Object[] {
"Peaches, Dried", "1 lb.", 15.7, new double[] {8.5, 87, 1.7, 173, 86.8, 1.2, 4.3, 55, 57}});
data.add(new Object[] {
"Prunes, Dried", "1 lb.", 9, new double[] {12.8, 99, 2.5, 154, 85.7, 3.9, 4.3, 65, 257}});
data.add(new Object[] {"Raisins, Dried", "15 oz.", 9.4,
new double[] {13.5, 104, 2.5, 136, 4.5, 6.3, 1.4, 24, 136}});
data.add(new Object[] {
"Peas, Dried", "1 lb.", 7.9, new double[] {20.0, 1367, 4.2, 345, 2.9, 28.7, 18.4, 162, 0}});
data.add(new Object[] {"Lima Beans, Dried", "1 lb.", 8.9,
new double[] {17.4, 1055, 3.7, 459, 5.1, 26.9, 38.2, 93, 0}});
data.add(new Object[] {"Navy Beans, Dried", "1 lb.", 5.9,
new double[] {26.9, 1691, 11.4, 792, 0, 38.4, 24.6, 217, 0}});
data.add(new Object[] {"Coffee", "1 lb.", 22.4, new double[] {0, 0, 0, 0, 0, 4, 5.1, 50, 0}});
data.add(new Object[] {"Tea", "1/4 lb.", 17.4, new double[] {0, 0, 0, 0, 0, 0, 2.3, 42, 0}});
data.add(
new Object[] {"Cocoa", "8 oz.", 8.6, new double[] {8.7, 237, 3, 72, 0, 2, 11.9, 40, 0}});
data.add(new Object[] {
"Chocolate", "8 oz.", 16.2, new double[] {8.0, 77, 1.3, 39, 0, 0.9, 3.4, 14, 0}});
data.add(new Object[] {"Sugar", "10 lb.", 51.7, new double[] {34.9, 0, 0, 0, 0, 0, 0, 0, 0}});
data.add(new Object[] {
"Corn Syrup", "24 oz.", 13.7, new double[] {14.7, 0, 0.5, 74, 0, 0, 0, 5, 0}});
data.add(new Object[] {
"Molasses", "18 oz.", 13.6, new double[] {9.0, 0, 10.3, 244, 0, 1.9, 7.5, 146, 0}});
data.add(new Object[] {"Strawberry Preserves", "1 lb.", 20.5,
new double[] {6.4, 11, 0.4, 7, 0.2, 0.2, 0.4, 3, 0}});
// Create the linear solver with the GLOP backend.
MPSolver solver = MPSolver.createSolver("GLOP");
if (solver == null) {
System.out.println("Could not create solver GLOP");
return;
}
double infinity = java.lang.Double.POSITIVE_INFINITY;
List<MPVariable> foods = new ArrayList<>();
for (int i = 0; i < data.size(); ++i) {
foods.add(solver.makeNumVar(0.0, infinity, (String) data.get(i)[0]));
}
System.out.println("Number of variables = " + solver.numVariables());
MPConstraint[] constraints = new MPConstraint[nutrients.size()];
for (int i = 0; i < nutrients.size(); ++i) {
constraints[i] = solver.makeConstraint(
(double) nutrients.get(i)[1], infinity, (String) nutrients.get(i)[0]);
for (int j = 0; j < data.size(); ++j) {
constraints[i].setCoefficient(foods.get(j), ((double[]) data.get(j)[3])[i]);
}
// constraints.add(constraint);
}
System.out.println("Number of constraints = " + solver.numConstraints());
MPObjective objective = solver.objective();
for (int i = 0; i < data.size(); ++i) {
objective.setCoefficient(foods.get(i), 1);
}
objective.setMinimization();
final MPSolver.ResultStatus resultStatus = solver.solve();
// Check that the problem has an optimal solution.
if (resultStatus != MPSolver.ResultStatus.OPTIMAL) {
System.err.println("The problem does not have an optimal solution!");
if (resultStatus == MPSolver.ResultStatus.FEASIBLE) {
System.err.println("A potentially suboptimal solution was found.");
} else {
System.err.println("The solver could not solve the problem.");
return;
}
}
// Display the amounts (in dollars) to purchase of each food.
double[] nutrientsResult = new double[nutrients.size()];
System.out.println("\nAnnual Foods:");
for (int i = 0; i < foods.size(); ++i) {
if (foods.get(i).solutionValue() > 0.0) {
System.out.println((String) data.get(i)[0] + ": $" + 365 * foods.get(i).solutionValue());
for (int j = 0; j < nutrients.size(); ++j) {
nutrientsResult[j] += ((double[]) data.get(i)[3])[j] * foods.get(i).solutionValue();
}
}
}
System.out.println("\nOptimal annual price: $" + 365 * objective.value());
System.out.println("\nNutrients per day:");
for (int i = 0; i < nutrients.size(); ++i) {
System.out.println(
nutrients.get(i)[0] + ": " + nutrientsResult[i] + " (min " + nutrients.get(i)[1] + ")");
}
System.out.println("\nAdvanced usage:");
System.out.println("Problem solved in " + solver.wallTime() + " milliseconds");
System.out.println("Problem solved in " + solver.iterations() + " iterations");
}
private StiglerDiet() {}
}
C#
// The Stigler diet problem.
using System;
using System.Collections.Generic;
using Google.OrTools.LinearSolver;
public class StiglerDiet
{
static void Main()
{
// Nutrient minimums.
(String Name, double Value)[] nutrients =
new[] { ("Calories (kcal)", 3.0), ("Protein (g)", 70.0), ("Calcium (g)", 0.8),
("Iron (mg)", 12.0), ("Vitamin A (kIU)", 5.0), ("Vitamin B1 (mg)", 1.8),
("Vitamin B2 (mg)", 2.7), ("Niacin (mg)", 18.0), ("Vitamin C (mg)", 75.0) };
(String Name, String Unit, double Price, double[] Nutrients)[] data = new[] {
("Wheat Flour (Enriched)", "10 lb.", 36, new double[] { 44.7, 1411, 2, 365, 0, 55.4, 33.3, 441, 0 }),
("Macaroni", "1 lb.", 14.1, new double[] { 11.6, 418, 0.7, 54, 0, 3.2, 1.9, 68, 0 }),
("Wheat Cereal (Enriched)", "28 oz.", 24.2, new double[] { 11.8, 377, 14.4, 175, 0, 14.4, 8.8, 114, 0 }),
("Corn Flakes", "8 oz.", 7.1, new double[] { 11.4, 252, 0.1, 56, 0, 13.5, 2.3, 68, 0 }),
("Corn Meal", "1 lb.", 4.6, new double[] { 36.0, 897, 1.7, 99, 30.9, 17.4, 7.9, 106, 0 }),
("Hominy Grits", "24 oz.", 8.5, new double[] { 28.6, 680, 0.8, 80, 0, 10.6, 1.6, 110, 0 }),
("Rice", "1 lb.", 7.5, new double[] { 21.2, 460, 0.6, 41, 0, 2, 4.8, 60, 0 }),
("Rolled Oats", "1 lb.", 7.1, new double[] { 25.3, 907, 5.1, 341, 0, 37.1, 8.9, 64, 0 }),
("White Bread (Enriched)", "1 lb.", 7.9, new double[] { 15.0, 488, 2.5, 115, 0, 13.8, 8.5, 126, 0 }),
("Whole Wheat Bread", "1 lb.", 9.1, new double[] { 12.2, 484, 2.7, 125, 0, 13.9, 6.4, 160, 0 }),
("Rye Bread", "1 lb.", 9.1, new double[] { 12.4, 439, 1.1, 82, 0, 9.9, 3, 66, 0 }),
("Pound Cake", "1 lb.", 24.8, new double[] { 8.0, 130, 0.4, 31, 18.9, 2.8, 3, 17, 0 }),
("Soda Crackers", "1 lb.", 15.1, new double[] { 12.5, 288, 0.5, 50, 0, 0, 0, 0, 0 }),
("Milk", "1 qt.", 11, new double[] { 6.1, 310, 10.5, 18, 16.8, 4, 16, 7, 177 }),
("Evaporated Milk (can)", "14.5 oz.", 6.7, new double[] { 8.4, 422, 15.1, 9, 26, 3, 23.5, 11, 60 }),
("Butter", "1 lb.", 30.8, new double[] { 10.8, 9, 0.2, 3, 44.2, 0, 0.2, 2, 0 }),
("Oleomargarine", "1 lb.", 16.1, new double[] { 20.6, 17, 0.6, 6, 55.8, 0.2, 0, 0, 0 }),
("Eggs", "1 doz.", 32.6, new double[] { 2.9, 238, 1.0, 52, 18.6, 2.8, 6.5, 1, 0 }),
("Cheese (Cheddar)", "1 lb.", 24.2, new double[] { 7.4, 448, 16.4, 19, 28.1, 0.8, 10.3, 4, 0 }),
("Cream", "1/2 pt.", 14.1, new double[] { 3.5, 49, 1.7, 3, 16.9, 0.6, 2.5, 0, 17 }),
("Peanut Butter", "1 lb.", 17.9, new double[] { 15.7, 661, 1.0, 48, 0, 9.6, 8.1, 471, 0 }),
("Mayonnaise", "1/2 pt.", 16.7, new double[] { 8.6, 18, 0.2, 8, 2.7, 0.4, 0.5, 0, 0 }),
("Crisco", "1 lb.", 20.3, new double[] { 20.1, 0, 0, 0, 0, 0, 0, 0, 0 }),
("Lard", "1 lb.", 9.8, new double[] { 41.7, 0, 0, 0, 0.2, 0, 0.5, 5, 0 }),
("Sirloin Steak", "1 lb.", 39.6, new double[] { 2.9, 166, 0.1, 34, 0.2, 2.1, 2.9, 69, 0 }),
("Round Steak", "1 lb.", 36.4, new double[] { 2.2, 214, 0.1, 32, 0.4, 2.5, 2.4, 87, 0 }),
("Rib Roast", "1 lb.", 29.2, new double[] { 3.4, 213, 0.1, 33, 0, 0, 2, 0, 0 }),
("Chuck Roast", "1 lb.", 22.6, new double[] { 3.6, 309, 0.2, 46, 0.4, 1, 4, 120, 0 }),
("Plate", "1 lb.", 14.6, new double[] { 8.5, 404, 0.2, 62, 0, 0.9, 0, 0, 0 }),
("Liver (Beef)", "1 lb.", 26.8, new double[] { 2.2, 333, 0.2, 139, 169.2, 6.4, 50.8, 316, 525 }),
("Leg of Lamb", "1 lb.", 27.6, new double[] { 3.1, 245, 0.1, 20, 0, 2.8, 3.9, 86, 0 }),
("Lamb Chops (Rib)", "1 lb.", 36.6, new double[] { 3.3, 140, 0.1, 15, 0, 1.7, 2.7, 54, 0 }),
("Pork Chops", "1 lb.", 30.7, new double[] { 3.5, 196, 0.2, 30, 0, 17.4, 2.7, 60, 0 }),
("Pork Loin Roast", "1 lb.", 24.2, new double[] { 4.4, 249, 0.3, 37, 0, 18.2, 3.6, 79, 0 }),
("Bacon", "1 lb.", 25.6, new double[] { 10.4, 152, 0.2, 23, 0, 1.8, 1.8, 71, 0 }),
("Ham, smoked", "1 lb.", 27.4, new double[] { 6.7, 212, 0.2, 31, 0, 9.9, 3.3, 50, 0 }),
("Salt Pork", "1 lb.", 16, new double[] { 18.8, 164, 0.1, 26, 0, 1.4, 1.8, 0, 0 }),
("Roasting Chicken", "1 lb.", 30.3, new double[] { 1.8, 184, 0.1, 30, 0.1, 0.9, 1.8, 68, 46 }),
("Veal Cutlets", "1 lb.", 42.3, new double[] { 1.7, 156, 0.1, 24, 0, 1.4, 2.4, 57, 0 }),
("Salmon, Pink (can)", "16 oz.", 13, new double[] { 5.8, 705, 6.8, 45, 3.5, 1, 4.9, 209, 0 }),
("Apples", "1 lb.", 4.4, new double[] { 5.8, 27, 0.5, 36, 7.3, 3.6, 2.7, 5, 544 }),
("Bananas", "1 lb.", 6.1, new double[] { 4.9, 60, 0.4, 30, 17.4, 2.5, 3.5, 28, 498 }),
("Lemons", "1 doz.", 26, new double[] { 1.0, 21, 0.5, 14, 0, 0.5, 0, 4, 952 }),
("Oranges", "1 doz.", 30.9, new double[] { 2.2, 40, 1.1, 18, 11.1, 3.6, 1.3, 10, 1998 }),
("Green Beans", "1 lb.", 7.1, new double[] { 2.4, 138, 3.7, 80, 69, 4.3, 5.8, 37, 862 }),
("Cabbage", "1 lb.", 3.7, new double[] { 2.6, 125, 4.0, 36, 7.2, 9, 4.5, 26, 5369 }),
("Carrots", "1 bunch", 4.7, new double[] { 2.7, 73, 2.8, 43, 188.5, 6.1, 4.3, 89, 608 }),
("Celery", "1 stalk", 7.3, new double[] { 0.9, 51, 3.0, 23, 0.9, 1.4, 1.4, 9, 313 }),
("Lettuce", "1 head", 8.2, new double[] { 0.4, 27, 1.1, 22, 112.4, 1.8, 3.4, 11, 449 }),
("Onions", "1 lb.", 3.6, new double[] { 5.8, 166, 3.8, 59, 16.6, 4.7, 5.9, 21, 1184 }),
("Potatoes", "15 lb.", 34, new double[] { 14.3, 336, 1.8, 118, 6.7, 29.4, 7.1, 198, 2522 }),
("Spinach", "1 lb.", 8.1, new double[] { 1.1, 106, 0, 138, 918.4, 5.7, 13.8, 33, 2755 }),
("Sweet Potatoes", "1 lb.", 5.1, new double[] { 9.6, 138, 2.7, 54, 290.7, 8.4, 5.4, 83, 1912 }),
("Peaches (can)", "No. 2 1/2", 16.8, new double[] { 3.7, 20, 0.4, 10, 21.5, 0.5, 1, 31, 196 }),
("Pears (can)", "No. 2 1/2", 20.4, new double[] { 3.0, 8, 0.3, 8, 0.8, 0.8, 0.8, 5, 81 }),
("Pineapple (can)", "No. 2 1/2", 21.3, new double[] { 2.4, 16, 0.4, 8, 2, 2.8, 0.8, 7, 399 }),
("Asparagus (can)", "No. 2", 27.7, new double[] { 0.4, 33, 0.3, 12, 16.3, 1.4, 2.1, 17, 272 }),
("Green Beans (can)", "No. 2", 10, new double[] { 1.0, 54, 2, 65, 53.9, 1.6, 4.3, 32, 431 }),
("Pork and Beans (can)", "16 oz.", 7.1, new double[] { 7.5, 364, 4, 134, 3.5, 8.3, 7.7, 56, 0 }),
("Corn (can)", "No. 2", 10.4, new double[] { 5.2, 136, 0.2, 16, 12, 1.6, 2.7, 42, 218 }),
("Peas (can)", "No. 2", 13.8, new double[] { 2.3, 136, 0.6, 45, 34.9, 4.9, 2.5, 37, 370 }),
("Tomatoes (can)", "No. 2", 8.6, new double[] { 1.3, 63, 0.7, 38, 53.2, 3.4, 2.5, 36, 1253 }),
("Tomato Soup (can)", "10 1/2 oz.", 7.6, new double[] { 1.6, 71, 0.6, 43, 57.9, 3.5, 2.4, 67, 862 }),
("Peaches, Dried", "1 lb.", 15.7, new double[] { 8.5, 87, 1.7, 173, 86.8, 1.2, 4.3, 55, 57 }),
("Prunes, Dried", "1 lb.", 9, new double[] { 12.8, 99, 2.5, 154, 85.7, 3.9, 4.3, 65, 257 }),
("Raisins, Dried", "15 oz.", 9.4, new double[] { 13.5, 104, 2.5, 136, 4.5, 6.3, 1.4, 24, 136 }),
("Peas, Dried", "1 lb.", 7.9, new double[] { 20.0, 1367, 4.2, 345, 2.9, 28.7, 18.4, 162, 0 }),
("Lima Beans, Dried", "1 lb.", 8.9, new double[] { 17.4, 1055, 3.7, 459, 5.1, 26.9, 38.2, 93, 0 }),
("Navy Beans, Dried", "1 lb.", 5.9, new double[] { 26.9, 1691, 11.4, 792, 0, 38.4, 24.6, 217, 0 }),
("Coffee", "1 lb.", 22.4, new double[] { 0, 0, 0, 0, 0, 4, 5.1, 50, 0 }),
("Tea", "1/4 lb.", 17.4, new double[] { 0, 0, 0, 0, 0, 0, 2.3, 42, 0 }),
("Cocoa", "8 oz.", 8.6, new double[] { 8.7, 237, 3, 72, 0, 2, 11.9, 40, 0 }),
("Chocolate", "8 oz.", 16.2, new double[] { 8.0, 77, 1.3, 39, 0, 0.9, 3.4, 14, 0 }),
("Sugar", "10 lb.", 51.7, new double[] { 34.9, 0, 0, 0, 0, 0, 0, 0, 0 }),
("Corn Syrup", "24 oz.", 13.7, new double[] { 14.7, 0, 0.5, 74, 0, 0, 0, 5, 0 }),
("Molasses", "18 oz.", 13.6, new double[] { 9.0, 0, 10.3, 244, 0, 1.9, 7.5, 146, 0 }),
("Strawberry Preserves", "1 lb.", 20.5, new double[] { 6.4, 11, 0.4, 7, 0.2, 0.2, 0.4, 3, 0 })
};
// Create the linear solver with the GLOP backend.
Solver solver = Solver.CreateSolver("GLOP");
if (solver is null)
{
return;
}
List<Variable> foods = new List<Variable>();
for (int i = 0; i < data.Length; ++i)
{
foods.Add(solver.MakeNumVar(0.0, double.PositiveInfinity, data[i].Name));
}
Console.WriteLine($"Number of variables = {solver.NumVariables()}");
List<Constraint> constraints = new List<Constraint>();
for (int i = 0; i < nutrients.Length; ++i)
{
Constraint constraint =
solver.MakeConstraint(nutrients[i].Value, double.PositiveInfinity, nutrients[i].Name);
for (int j = 0; j < data.Length; ++j)
{
constraint.SetCoefficient(foods[j], data[j].Nutrients[i]);
}
constraints.Add(constraint);
}
Console.WriteLine($"Number of constraints = {solver.NumConstraints()}");
Objective objective = solver.Objective();
for (int i = 0; i < data.Length; ++i)
{
objective.SetCoefficient(foods[i], 1);
}
objective.SetMinimization();
Solver.ResultStatus resultStatus = solver.Solve();
// Check that the problem has an optimal solution.
if (resultStatus != Solver.ResultStatus.OPTIMAL)
{
Console.WriteLine("The problem does not have an optimal solution!");
if (resultStatus == Solver.ResultStatus.FEASIBLE)
{
Console.WriteLine("A potentially suboptimal solution was found.");
}
else
{
Console.WriteLine("The solver could not solve the problem.");
return;
}
}
// Display the amounts (in dollars) to purchase of each food.
double[] nutrientsResult = new double[nutrients.Length];
Console.WriteLine("\nAnnual Foods:");
for (int i = 0; i < foods.Count; ++i)
{
if (foods[i].SolutionValue() > 0.0)
{
Console.WriteLine($"{data[i].Name}: ${365 * foods[i].SolutionValue():N2}");
for (int j = 0; j < nutrients.Length; ++j)
{
nutrientsResult[j] += data[i].Nutrients[j] * foods[i].SolutionValue();
}
}
}
Console.WriteLine($"\nOptimal annual price: ${365 * objective.Value():N2}");
Console.WriteLine("\nNutrients per day:");
for (int i = 0; i < nutrients.Length; ++i)
{
Console.WriteLine($"{nutrients[i].Name}: {nutrientsResult[i]:N2} (min {nutrients[i].Value})");
}
Console.WriteLine("\nAdvanced usage:");
Console.WriteLine($"Problem solved in {solver.WallTime()} milliseconds");
Console.WriteLine($"Problem solved in {solver.Iterations()} iterations");
}
}