In the updated study, the minimal annual cost to feed a 25-50 year-old man is $651.27, while for a 25-50 year old female the minimal annual cost is $535.27. The data are corrected to 1998 prices and current recommended dietary allowances (RDAs) and food nutritional content.
Stigler’s Diet Problem is a classic example of a linear program, a mathematical technique used by operations researchers to determine the optimal way of achieving an objective, subject to restrictions. The diet problem, although not effective for producing diets for humans to be followed literally, has proven of great value in determining feed mixes for chickens and cattle, as well as other ingredient mix products such as fertilizers.
"The concept of a minimum cost diet for humans serves as a base line for government funding and school lunch planning," explains Operations Researcher Saul I. Gass of the Robert H. Smith School of Business at the University of Maryland College Park.
Diet problems that trace their development to the original study include the Thrifty Food Plan, a subsistence dietary approach developed by the United States Department of Agriculture (USDA) Agricultural Research Service to determine the number of food stamps issued to Food Stamp Program recipients; and the rules imposed by the USDA on school dieticians and related diet/menu software to ensure that public-school students receive nutritious school lunches.
Operations Research Milestone
The economist George Stigler posed and solved what became know as Stigler’s Diet Problem in 1945. The solution of this problem helped to show that linear programming, a dazzling but untested theory developed in 1947 for solving complex military problems, would work in practice.
Extensions of linear programming have led to billions of dollars of revenue and savings across a large number of industries, says Prof. Gass.
Computation Time Slashed
The researchers updated the original data to reflect price changes, revised values of the RDA’s, and current evaluations of the nutrient content of the 77 foods chosen by Stigler. The updated problem shows that the optimal solution diet for a 25-50 year old man consists, on a daily basis, of 1.31 cups of wheat flour, 1.32 cups of rolled oats, 16 fluid ounces of milk, 3.86 tablespoons of peanut butter, 7.28 tablespoons of lard, 0.0108 ounces of beef liver, 1.77 bananas, 0.0824 of an orange, 0.707 cup of shredded cabbage, 0.314 of a carrot, 0.387 of a potato, and 0.53 cup of pork and beans. The daily cost of this diet is $1.78.
The optimal solution diet for a 25-50 year old woman consists, on a daily basis, of 1.13 cups of wheat flour, 1.61 cups of rolled oats, 16.7 fluid ounces of milk, 3.31 tablespoons of peanut butter, 2.59 tablespoons of lard, 0.00724 ounces of beef liver, 1.2 bananas, 0.234 of an orange, 0.561 cup of shredded cabbage, 0.219 of a carrot, 0.384 of a potato, and 0.297 cup of pork and beans. The daily cost of this diet is $1.47.
Both diets provides servings from all six food groups established by the USDA: 1) fats, oils, and sweets group; 2) milk group; 3) meats and beans group; 4) vegetable group; 5) fruit group; and 6) grain product group. The foods in common between the 1945 and the current studies are wheat flour, beef liver, cabbage, and potatoes. The upper limit for manganese was exceeded. Male and female minimum requirements for polyunsaturated fatty acids and copper were not satisfied with the diets. In addition, the male minimum requirement for carbohydrates was not met.
The new nutrient content was taken from the 1998 edition of "Bowes and Church’s Food Values of Portions Commonly Use," by J A T Pennington, the 17th edition of the reference originally used by Stigler. Most of the data used is traced to USDA handbooks. Because U.S. Department of Labor Statistics include retail prices for only 30 of the 77 foods being studied, the authors based their food prices on April, 1998 data gathered at Giant Foods, the supermarket chain with stores in the Baltimore-Washington area.
Diet and cost are not the only things that have changed since the original study. Before the computer age, it took 120 clerk-days to make the calculations using hand-operated desk calculators. In 1953, the solution to the problem was found and printed by an IBM 701 computer in 12 minutes. Today, in contrast, the diet problem is solved in less than a second on a standard PC.
The study, "Stigler’s Diet Problem Revisited," is by Prof. Gass and Susan Garner Garille, University of Maryland. It will appear in Operations Research, an INFORMS publication. Professor Gass is co-author of "The Encyclopedia of Operations Research and Management Science." He was recently named Dean's Lifetime Achievement Professor by the Smith School.
The Institute for Operations Research and the Management Sciences (INFORMS®) is an international scientific society with 12,000 members, including Nobel Prize laureates, dedicated to applying scientific methods to help improve decision-making, management, and operations. Members of INFORMS work in business, government, and academia. They are represented in fields as diverse as airlines, health care, law enforcement, the military, the stock market, and telecommunications. The INFORMS website is at http://www.informs.org.