In
mathematics and economics, transportation theory or transport theory is a name given to the study of optimal
transport
Transport (in British English), or transportation (in American English), is the intentional movement of humans, animals, and goods from one location to another. Modes of transport include air, land ( rail and road), water, cable, pipel ...
ation and
allocation of resources
In economics, resource allocation is the assignment of available resources to various uses. In the context of an entire economy, resources can be allocated by various means, such as markets, or planning.
In project management, resource allocation ...
. The problem was formalized by the French
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
Gaspard Monge
Gaspard Monge, Comte de Péluse (9 May 1746 – 28 July 1818) was a French mathematician, commonly presented as the inventor of descriptive geometry, (the mathematical basis of) technical drawing, and the father of differential geometry. Duri ...
in 1781.
[G. Monge. ''Mémoire sur la théorie des déblais et des remblais. Histoire de l’Académie Royale des Sciences de Paris, avec les Mémoires de Mathématique et de Physique pour la même année'', pages 666–704, 1781.]
In the 1920s A.N. Tolstoi was one of the first to study the transportation problem
mathematically
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
. In 1930, in the collection ''Transportation Planning Volume I'' for the National Commissariat of Transportation of the Soviet Union, he published a paper "Methods of Finding the Minimal Kilometrage in Cargo-transportation in space".
Major advances were made in the field during World War II by the
Soviet
The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen national ...
mathematician and economist
Leonid Kantorovich
Leonid Vitalyevich Kantorovich ( rus, Леони́д Вита́льевич Канторо́вич, , p=lʲɪɐˈnʲit vʲɪˈtalʲjɪvʲɪtɕ kəntɐˈrovʲɪtɕ, a=Ru-Leonid_Vitaliyevich_Kantorovich.ogg; 19 January 19127 April 1986) was a Sovie ...
.
[L. Kantorovich. ''On the translocation of masses.'' C.R. (Doklady) Acad. Sci. URSS (N.S.), 37:199–201, 1942.] Consequently, the problem as it is stated is sometimes known as the Monge–Kantorovich transportation problem.
The
linear programming
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is ...
formulation of the transportation problem is also known as the
Hitchcock
Sir Alfred Joseph Hitchcock (13 August 1899 – 29 April 1980) was an English filmmaker. He is widely regarded as one of the most influential figures in the history of cinema. In a career spanning six decades, he directed over 50 featur ...
–