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diff --git a/glpk-5.0/examples/stigler.mod b/glpk-5.0/examples/stigler.mod new file mode 100644 index 0000000..20c5d9d --- /dev/null +++ b/glpk-5.0/examples/stigler.mod @@ -0,0 +1,411 @@ +/* STIGLER, original Stigler's 1939 diet problem */ + +/* The Stigler Diet is an optimization problem named for George Stigler, + a 1982 Nobel Laureate in economics, who posed the following problem: + For a moderately active man weighing 154 pounds, how much of each of + 77 foods should be eaten on a daily basis so that the man's intake of + nine nutrients will be at least equal to the recommended dietary + allowances (RDSs) suggested by the National Research Council in 1943, + with the cost of the diet being minimal? + + The nutrient RDAs required to be met in Stigler's experiment were + calories, protein, calcium, iron, vitamin A, thiamine, riboflavin, + niacin, and ascorbic acid. The result was an annual budget allocated + to foods such as evaporated milk, cabbage, dried navy beans, and beef + liver at a cost of approximately $0.11 a day in 1939 U.S. dollars. + + While the name "Stigler Diet" was applied after the experiment by + outsiders, according to Stigler, "No one recommends these diets for + anyone, let alone everyone." The Stigler diet has been much ridiculed + for its lack of variety and palatability, however his methodology has + received praise and is considered to be some of the earliest work in + linear programming. + + The Stigler diet question is a linear programming problem. Lacking + any sophisticated method of solving such a problem, Stigler was + forced to utilize heuristic methods in order to find a solution. The + diet question originally asked in which quantities a 154 pound male + would have to consume 77 different foods in order to fulfill the + recommended intake of 9 different nutrients while keeping expense at + a minimum. Through "trial and error, mathematical insight and + agility," Stigler was able to eliminate 62 of the foods from the + original 77 (these foods were removed based because they lacked + nutrients in comparison to the remaining 15). From the reduced list, + Stigler calculated the required amounts of each of the remaining 15 + foods to arrive at a cost-minimizing solution to his question. + According to Stigler's calculations, the annual cost of his solution + was $39.93 in 1939 dollars. When corrected for inflation using the + consumer price index, the cost of the diet in 2005 dollars is + $561.43. The specific combination of foods and quantities is as + follows: + + Stigler's 1939 Diet + + Food Annual Quantities Annual Cost + ---------------- ----------------- ----------- + Wheat Flour 370 lb. $13.33 + Evaporated Milk 57 cans 3.84 + Cabbage 111 lb. 4.11 + Spinach 23 lb. 1.85 + Dried Navy Beans 285 lb. 16.80 + ---------------------------------------------- + Total Annual Cost $39.93 + + The 9 nutrients that Stigler's diet took into consideration and their + respective recommended daily amounts were: + + Table of nutrients considered in Stigler's diet + + Nutrient Daily Recommended Intake + ------------------------- ------------------------ + Calories 3,000 Calories + Protein 70 grams + Calcium .8 grams + Iron 12 milligrams + Vitamin A 5,000 IU + Thiamine (Vitamin B1) 1.8 milligrams + Riboflavin (Vitamin B2) 2.7 milligrams + Niacin 18 milligrams + Ascorbic Acid (Vitamin C) 75 milligrams + + Seven years after Stigler made his initial estimates, the development + of George Dantzig's Simplex algorithm made it possible to solve the + problem without relying on heuristic methods. The exact value was + determined to be $39.69 (using the original 1939 data). Dantzig's + algorithm describes a method of traversing the vertices of a polytope + of N+1 dimensions in order to find the optimal solution to a specific + situation. + + (From Wikipedia, the free encyclopedia.) */ + +/* Translated from GAMS by Andrew Makhorin <mao@gnu.org>. + + For the original GAMS model stigler1939.gms see [3]. + + References: + + 1. George J. Stigler, "The Cost of Subsistence," J. Farm Econ. 27, + 1945, pp. 303-14. + + 2. National Research Council, "Recommended Daily Allowances," Reprint + and Circular Series No. 115, January, 1943. + + 3. Erwin Kalvelagen, "Model building with GAMS," Chapter 2, "Building + linear programming models," pp. 128-34. */ + +set C; +/* commodities */ + +check card(C) = 77; +/* there must be 77 commodities */ + +set N; +/* nutrients */ + +param data{c in C, {"price", "weight"} union N}; +/* nutritive values per dollar of expenditure */ + +param allowance{n in N}; +/* recommended daily allowance for a moderately active man */ + +var x{c in C}, >= 0; +/* dollars of food to be purchased daily */ + +s.t. nb{n in N}: sum{c in C} data[c,n] * x[c] >= allowance[n]; +/* nutrient balance */ + +minimize cost: sum{c in C} x[c]; +/* total food bill */ + +solve; + +param days := 365.25; +/* days in a year */ + +param commodity{c in C}, symbolic; + +param unit{c in C}, symbolic; + +printf "\n"; +printf "MINIMUM COST ANNUAL DIET\n"; +printf "\n"; +printf " Commodity Unit Quantity Cost \n"; +printf "------------------------- ---------- ---------- ----------\n"; +printf{c in C: x[c] != 0} "%-25s %10s %10.2f $%7.2f\n", commodity[c], + unit[c], 100 * days * x[c] / data[c,"price"], days * x[c]; +printf " -----------------\n"; +printf " Total: $%7.2f\n", + days * sum{c in C} x[c]; +printf "\n"; + +data; + +param : C : commodity unit := +flour "Wheat Flour (Enriched)" "10 lb." +macaroni "Macaroni" "1 lb." +cereal "Wheat Cereal (Enriched)" "28 oz." +cornflakes "Corn Flakes" "8 oz." +cornmeal "Corn Meal" "1 lb." +grits "Hominy Grits" "24 oz." +rice "Rice" "1 lb." +oats "Rolled Oats" "1 lb." +whitebread "White Bread (Enriched)" "1 lb." +wheatbread "Whole Wheat Bread" "1 lb." +ryebread "Rye Bread" "1 lb." +poundcake "Pound Cake" "1 lb." +crackers "Soda Crackers" "1 lb." +milk "Milk" "1 qt." +evapmild "Evaporated Milk (can)" "14.5 oz." +butter "Butter" "1 lb." +margarine "Oleomargarine" "1 lb." +eggs "Eggs" "1 doz." +cheese "Cheese (Cheddar)" "1 lb." +cream "Cream" "1/2 pt." +peanutbutter "Peanut Butter" "1 lb." +mayonnaise "Mayonnaise" "1/2 pt." +crisco "Crisco" "1 lb." +lard "Lard" "1 lb." +sirloinsteak "Sirloin Steak" "1 lb." +roundsteak "Round Steak" "1 lb." +ribroast "Rib Roast" "1 lb." +chuckroast "Chuck Roast" "1 lb." +plate "Plate" "1 lb." +liver "Liver (Beef)" "1 lb." +lambleg "Leg of Lamb" "1 lb." +lambchops "Lamb Chops (Rib)" "1 lb." +porkchops "Pork Chops" "1 lb." +porkroast "Pork Loin Roast" "1 lb." +bacon "Bacon" "1 lb." +ham "Ham - smoked" "1 lb." +saltpork "Salt Pork" "1 lb." +chicken "Roasting Chicken" "1 lb." +veal "Veal Cutlets" "1 lb." +salmon "Salmon, Pink (can)" "16 oz." +apples "Apples" "1 lb." +bananas "Bananas" "1 lb." +lemons "Lemons" "1 doz." +oranges "Oranges" "1 doz." +greenbeans "Green Beans" "1 lb." +cabbage "Cabbage" "1 lb." +carrots "Carrots" "1 bunch" +celery "Celery" "1 stalk" +lettuce "Lettuce" "1 head" +onions "Onions" "1 lb." +potatoes "Potatoes" "15 lb." +spinach "Spinach" "1 lb." +sweetpotato "Sweet Potatoes" "1 lb." +peaches "Peaches (can)" "No. 2 1/2" +pears "Pears (can)" "No. 2 1/2" +pineapple "Pineapple (can)" "No. 2 1/2" +asparagus "Asparagus (can)" "No. 2" +cannedgrbn "Grean Beans (can)" "No. 2" +porkbeans "Pork and Beans (can)" "16 oz." +corn "Corn (can)" "No. 2" +peas "Peas (can)" "No. 2" +tomatoes "Tomatoes (can)" "No. 2" +tomatosoup "Tomato Soup (can)" "10 1/2 oz." +driedpeach "Peaches, Dried" "1 lb." +prunes "Prunes, Dried" "1 lb." +raisins "Raisins, Dried" "15 oz." +driedpeas "Peas, Dried" "1 lb." +limabeans "Lima Beans, Dried" "1 lb." +navybeans "Navy Beans, Dried" "1 lb." +coffee "Coffee" "1 lb." +tea "Tea" "1/4 lb." +cocoa "Cocoa" "8 oz." +chocolate "Chocolate" "8 oz." +sugar "Sugar" "10 lb." +cornsirup "Corn Sirup" "24 oz." +molasses "Molasses" "18 oz." +strawberry "Strawberry Preserve" "1 lb." +; + +set N := +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 */ +; + +param data +: price weight calories protein calcium iron := +# aug. 15 edible +# 1939 per $1 +# (cents) (grams) (1000) (grams) (grams) (mg.) +flour 36.0 12600 44.7 1411 2.0 365 +macaroni 14.1 3217 11.6 418 .7 54 +cereal 24.2 3280 11.8 377 14.4 175 +cornflakes 7.1 3194 11.4 252 .1 56 +cornmeal 4.6 9861 36.0 897 1.7 99 +grits 8.5 8005 28.6 680 .8 80 +rice 7.5 6048 21.2 460 .6 41 +oats 7.1 6389 25.3 907 5.1 341 +whitebread 7.9 5742 15.6 488 2.5 115 +wheatbread 9.1 4985 12.2 484 2.7 125 +ryebread 9.2 4930 12.4 439 1.1 82 +poundcake 24.8 1829 8.0 130 .4 31 +crackers 15.1 3004 12.5 288 .5 50 +milk 11.0 8867 6.1 310 10.5 18 +evapmild 6.7 6035 8.4 422 15.1 9 +butter 20.8 1473 10.8 9 .2 3 +margarine 16.1 2817 20.6 17 .6 6 +eggs 32.6 1857 2.9 238 1.0 52 +cheese 24.2 1874 7.4 448 16.4 19 +cream 14.1 1689 3.5 49 1.7 3 +peanutbutter 17.9 2534 15.7 661 1.0 48 +mayonnaise 16.7 1198 8.6 18 .2 8 +crisco 20.3 2234 20.1 0 .0 0 +lard 9.8 4628 41.7 0 .0 0 +sirloinsteak 39.6 1145 2.9 166 .1 34 +roundsteak 36.4 1246 2.2 214 .1 32 +ribroast 29.2 1553 3.4 213 .1 33 +chuckroast 22.6 2007 3.6 309 .2 46 +plate 14.6 3107 8.5 404 .2 62 +liver 26.8 1692 2.2 333 .2 139 +lambleg 27.6 1643 3.1 245 .1 20 +lambchops 36.6 1239 3.3 140 .1 15 +porkchops 30.7 1477 3.5 196 .2 80 +porkroast 24.2 1874 4.4 249 .3 37 +bacon 25.6 1772 10.4 152 .2 23 +ham 27.4 1655 6.7 212 .2 31 +saltpork 16.0 2835 18.8 164 .1 26 +chicken 30.3 1497 1.8 184 .1 30 +veal 42.3 1072 1.7 156 .1 24 +salmon 13.0 3489 5.8 705 6.8 45 +apples 4.4 9072 5.8 27 .5 36 +bananas 6.1 4982 4.9 60 .4 30 +lemons 26.0 2380 1.0 21 .5 14 +oranges 30.9 4439 2.2 40 1.1 18 +greenbeans 7.1 5750 2.4 138 3.7 80 +cabbage 3.7 8949 2.6 125 4.0 36 +carrots 4.7 6080 2.7 73 2.8 43 +celery 7.3 3915 .9 51 3.0 23 +lettuce 8.2 2247 .4 27 1.1 22 +onions 3.6 11844 5.8 166 3.8 59 +potatoes 34.0 16810 14.3 336 1.8 118 +spinach 8.1 4592 1.1 106 .0 138 +sweetpotato 5.1 7649 9.6 138 2.7 54 +peaches 16.8 4894 3.7 20 .4 10 +pears 20.4 4030 3.0 8 .3 8 +pineapple 21.3 3993 2.4 16 .4 8 +asparagus 27.7 1945 .4 33 .3 12 +cannedgrbn 10.0 5386 1.0 54 2.0 65 +porkbeans 7.1 6389 7.5 364 4.0 134 +corn 10.4 5452 5.2 136 .2 16 +peas 13.8 4109 2.3 136 .6 45 +tomatoes 8.6 6263 1.3 63 .7 38 +tomatosoup 7.6 3917 1.6 71 .6 43 +driedpeach 15.7 2889 8.5 87 1.7 173 +prunes 9.0 4284 12.8 99 2.5 154 +raisins 9.4 4524 13.5 104 2.5 136 +driedpeas 7.9 5742 20.0 1367 4.2 345 +limabeans 8.9 5097 17.4 1055 3.7 459 +navybeans 5.9 7688 26.9 1691 11.4 792 +coffee 22.4 2025 .0 0 .0 0 +tea 17.4 652 .0 0 .0 0 +cocoa 8.6 2637 8.7 237 3.0 72 +chocolate 16.2 1400 8.0 77 1.3 39 +sugar 51.7 8773 34.9 0 .0 0 +cornsirup 13.7 4996 14.7 0 .5 74 +molasses 13.6 3752 9.0 0 10.3 244 +strawberry 20.5 2213 6.4 11 .4 7 + +: vitaminA thiamine riboflavin niacin ascorbicAcid := +# (1000 IU) (mg.) (mg.) (mg.) (mg.) +flour .0 55.4 33.3 441 0 +macaroni .0 3.2 1.9 68 0 +cereal .0 14.4 8.8 114 0 +cornflakes .0 13.5 2.3 68 0 +cornmeal 30.9 17.4 7.9 106 0 +grits .0 10.6 1.6 110 0 +rice .0 2.0 4.8 60 0 +oats .0 37.1 8.9 64 0 +whitebread .0 13.8 8.5 126 0 +wheatbread .0 13.9 6.4 160 0 +ryebread .0 9.9 3.0 66 0 +poundcake 18.9 2.8 3.0 17 0 +crackers .0 .0 .0 0 0 +milk 16.8 4.0 16.0 7 177 +evapmild 26.0 3.0 23.5 11 60 +butter 44.2 .0 .2 2 0 +margarine 55.8 .2 .0 0 0 +eggs 18.6 2.8 6.5 1 0 +cheese 28.1 .8 10.3 4 0 +cream 16.9 .6 2.5 0 17 +peanutbutter .0 9.6 8.1 471 0 +mayonnaise 2.7 .4 .5 0 0 +crisco .0 .0 .0 0 0 +lard .2 .0 .5 5 0 +sirloinsteak .2 2.1 2.9 69 0 +roundsteak .4 2.5 2.4 87 0 +ribroast .0 .0 2.0 0 0 +chuckroast .4 1.0 4.0 120 0 +plate .0 .9 .0 0 0 +liver 169.2 6.4 50.8 316 525 +lambleg .0 2.8 3.0 86 0 +lambchops .0 1.7 2.7 54 0 +porkchops .0 17.4 2.7 60 0 +porkroast .0 18.2 3.6 79 0 +bacon .0 1.8 1.8 71 0 +ham .0 9.9 3.3 50 0 +saltpork .0 1.4 1.8 0 0 +chicken .1 .9 1.8 68 46 +veal .0 1.4 2.4 57 0 +salmon 3.5 1.0 4.9 209 0 +apples 7.3 3.6 2.7 5 544 +bananas 17.4 2.5 3.5 28 498 +lemons .0 .5 .0 4 952 +oranges 11.1 3.6 1.3 10 1993 +greenbeans 69.0 4.3 5.8 37 862 +cabbage 7.2 9.0 4.5 26 5369 +carrots 188.5 6.1 4.3 89 608 +celery .9 1.4 1.4 9 313 +lettuce 112.4 1.8 3.4 11 449 +onions 16.6 4.7 5.9 21 1184 +potatoes 6.7 29.4 7.1 198 2522 +spinach 918.4 5.7 13.8 33 2755 +sweetpotato 290.7 8.4 5.4 83 1912 +peaches 21.5 .5 1.0 31 196 +pears .8 .8 .8 5 81 +pineapple 2.0 2.8 .8 7 399 +asparagus 16.3 1.4 2.1 17 272 +cannedgrbn 53.9 1.6 4.3 32 431 +porkbeans 3.5 8.3 7.7 56 0 +corn 12.0 1.6 2.7 42 218 +peas 34.9 4.9 2.5 37 370 +tomatoes 53.2 3.4 2.5 36 1253 +tomatosoup 57.9 3.5 2.4 67 862 +driedpeach 86.8 1.2 4.3 55 57 +prunes 85.7 3.9 4.3 65 257 +raisins 4.5 6.3 1.4 24 136 +driedpeas 2.9 28.7 18.4 162 0 +limabeans 5.1 26.9 38.2 93 0 +navybeans .0 38.4 24.6 217 0 +coffee .0 4.0 5.1 50 0 +tea .0 .0 2.3 42 0 +cocoa .0 2.0 11.9 40 0 +chocolate .0 .9 3.4 14 0 +sugar .0 .0 .0 0 0 +cornsirup .0 .0 .0 5 0 +molasses .0 1.9 7.5 146 0 +strawberry .2 .2 .4 3 0 +; + +param allowance := +calories 3 +protein 70 +calcium .8 +iron 12 +vitaminA 5 +thiamine 1.8 +riboflavin 2.7 +niacin 18 +ascorbicAcid 75 +; + +end; |