Transportation theory (mathematics)

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Transportation theory (mathematics)

In <a href="/en/Mathematics" title="Mathematics" class="wl">mathematics</a> and economics, transportation theory or transport theory is a name given to the study of optimal <a href="/en/Transport" title="Transport" class="wl">transportation</a> and <a href="/en/Resource_allocation" title="Resource allocation" class="wl">allocation of resources</a>. The problem was formalized by the French <a href="/en/Mathematician" title="Mathematician" class="wl">mathematician</a> <a href="/en/Gaspard_Monge" title="Gaspard Monge" class="wl">Gaspard Monge</a> in 1781.<a href="#cite_note-Monge-1" style="counter-reset: mw-Ref 1;">[1]</a>


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In the 1920s A.N. Tolstoi was one of the first to study the transportation problem <a href="/en/Mathematical_model" title="Mathematical model" class="wl">mathematically</a>. 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".<a href="#cite_note-2" style="counter-reset: mw-Ref 2;">[2]</a><a href="#cite_note-3" style="counter-reset: mw-Ref 3;">[3]</a>

Major advances were made in the field during World War II by the <a href="/en/Soviet_Union" title="Soviet Union" class="wl">Soviet</a> mathematician and economist <a href="/en/Leonid_Kantorovich" title="Leonid Kantorovich" class="wl">Leonid Kantorovich</a>.<a href="#cite_note-Kantorovich-4" style="counter-reset: mw-Ref 4;">[4]</a> Consequently, the problem as it is stated is sometimes known as the Monge–Kantorovich transportation problem.<a href="#cite_note-Villani2003-5" style="counter-reset: mw-Ref 5;">[5]</a> The <a href="/en/Linear_programming" title="Linear programming" class="wl">linear programming</a> formulation of the transportation problem is also known as the <a href="/en/Frank_Lauren_Hitchcock" title="Frank Lauren Hitchcock" class="wl">Hitchcock</a>–<a href="/en/Tjalling_Koopmans" title="Tjalling Koopmans" class="wl">Koopmans</a> transportation problem.<a href="#cite_note-RaoRao2009-6" style="counter-reset: mw-Ref 6;">[6]</a>

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. 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". Major advances were made in the field during World War II by the Soviet mathematician and economist Leonid Kantorovich. 