Stigler diet
Encyclopedia
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 (RDAs) 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
.
Linear Programming Problem
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 $561.43http://eh.net/hmit. The specific combination of foods and quantities is as follows:
The 9 nutrients that Stigler's diet took into consideration and their respective recommended daily amounts were:
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.
Optimization (mathematics)
In mathematics, computational science, or management science, mathematical optimization refers to the selection of a best element from some set of available alternatives....
problem named for George Stigler
George Stigler
George Joseph Stigler was a U.S. economist. He won the Nobel Memorial Prize in Economic Sciences in 1982, and was a key leader of the Chicago School of Economics, along with his close friend Milton Friedman....
, 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 (RDAs) 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
Protein
Proteins are biochemical compounds consisting of one or more polypeptides typically folded into a globular or fibrous form, facilitating a biological function. A polypeptide is a single linear polymer chain of amino acids bonded together by peptide bonds between the carboxyl and amino groups of...
, calcium
Calcium
Calcium is the chemical element with the symbol Ca and atomic number 20. It has an atomic mass of 40.078 amu. Calcium is a soft gray alkaline earth metal, and is the fifth-most-abundant element by mass in the Earth's crust...
, iron
Iron
Iron is a chemical element with the symbol Fe and atomic number 26. It is a metal in the first transition series. It is the most common element forming the planet Earth as a whole, forming much of Earth's outer and inner core. It is the fourth most common element in the Earth's crust...
, vitamin A
Vitamin A
Vitamin A is a vitamin that is needed by the retina of the eye in the form of a specific metabolite, the light-absorbing molecule retinal, that is necessary for both low-light and color vision...
, thiamine
Thiamine
Thiamine or thiamin or vitamin B1 , named as the "thio-vitamine" is a water-soluble vitamin of the B complex. First named aneurin for the detrimental neurological effects if not present in the diet, it was eventually assigned the generic descriptor name vitamin B1. Its phosphate derivatives are...
, riboflavin
Riboflavin
Riboflavin, also known as vitamin B2 or additive E101, is an easily absorbed micronutrient with a key role in maintaining health in humans and animals. It is the central component of the cofactors FAD and FMN, and is therefore required by all flavoproteins. As such, vitamin B2 is required for a...
, niacin
Niacin
"Niacin" redirects here. For the neo-fusion band, see Niacin .Niacin is an organic compound with the formula and, depending on the definition used, one of the forty to eighty essential human nutrients.Niacin is one of five vitamins associated with a pandemic deficiency disease: niacin deficiency...
, and ascorbic acid
Ascorbic acid
Ascorbic acid is a naturally occurring organic compound with antioxidant properties. It is a white solid, but impure samples can appear yellowish. It dissolves well in water to give mildly acidic solutions. Ascorbic acid is one form of vitamin C. The name is derived from a- and scorbutus , the...
. 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
Linear programming
Linear programming is a mathematical method for determining a way to achieve the best outcome in a given mathematical model for some list of requirements represented as linear relationships...
.
Linear Programming Problem
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
Consumer price index
A consumer price index measures changes in the price level of consumer goods and services purchased by households. The CPI, in the United States is defined by the Bureau of Labor Statistics as "a measure of the average change over time in the prices paid by urban consumers for a market basket of...
, the cost of the diet in 2005 dollars is $561.43http://eh.net/hmit. The specific combination of foods and quantities is as follows:
| 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:
| 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
George Dantzig
George Bernard Dantzig was an American mathematical scientist who made important contributions to operations research, computer science, economics, and statistics....
's Simplex algorithm
Simplex algorithm
In mathematical optimization, Dantzig's simplex algorithm is a popular algorithm for linear programming. The journal Computing in Science and Engineering listed it as one of the top 10 algorithms of the twentieth century....
made it possible to solve the problem without relying on heuristic
Heuristic
Heuristic refers to experience-based techniques for problem solving, learning, and discovery. Heuristic methods are used to speed up the process of finding a satisfactory solution, where an exhaustive search is impractical...
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
Polytope
In elementary geometry, a polytope is a geometric object with flat sides, which exists in any general number of dimensions. A polygon is a polytope in two dimensions, a polyhedron in three dimensions, and so on in higher dimensions...
of N+1 dimensions in order to find the optimal solution to a specific situation.