 | This article may require cleanup to meet Wikipedia's quality standards. The specific problem is: Some of the mathematical notation is abominably badly typeset, and some that is typeset well has horribly inefficient code (probably someone unskilled in TeX used one of those software packages that write your code for you. (June 2022) |
In mathematics and economics, transportation theory or transport theory is a name given to the study of optimal transportation and allocation of resources. The problem was formalized by the French mathematician Gaspard Monge in 1781.[1]
In the 1920s A.N. Tolstoi was one of the first to study the transportation problem mathematically. 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".[2][3]
Major advances were made in the field during World War II by the Soviet mathematician and economist Leonid Kantorovich.[4] Consequently, the problem as it is stated is sometimes known as the Monge–Kantorovich transportation problem.[5] The linear programming formulation of the transportation problem is also known as the Hitchcock–Koopmans transportation problem.[6]
- ^ 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.
- ^ Schrijver, Alexander, Combinatorial Optimization, Berlin; New York : Springer, 2003. ISBN 3540443894. Cf. p. 362
- ^ Ivor Grattan-Guinness, Ivor, Companion encyclopedia of the history and philosophy of the mathematical sciences, Volume 1, JHU Press, 2003. Cf. p.831
- ^ L. Kantorovich. On the translocation of masses. C.R. (Doklady) Acad. Sci. URSS (N.S.), 37:199–201, 1942.
- ^ Cédric Villani (2003). Topics in Optimal Transportation. American Mathematical Soc. p. 66. ISBN 978-0-8218-3312-4.
- ^ Singiresu S. Rao (2009). Engineering Optimization: Theory and Practice (4th ed.). John Wiley & Sons. p. 221. ISBN 978-0-470-18352-6.