ABSTRACT
Overview In 1827, the French mathematician Jean-Baptiste Joseph Fourier (1768-1830) published a method for solving systems of linear inequalities. This publication is usually seen as the first account on linear optimization. In 1939, the Russian mathematician Leonid V. Kantorovich (1912-1986) gave linear optimization formulations of resource allocation problems. Around the same time, the Dutch economist Tjalling C. Koopmans (1910-1985) formulated linear optimization models for problems arising in classical, Walrasian (Léon Walras, 1834-1910), economics. In 1975, both Kantorovich and Koopmans received the Nobel Prize in economic sciences for their work. During World War II, linear optimization models were designed and solved for military planning problems. In 1947, George B. Dantzig (1914-2005) invented, what he called, the simplex algorithm. The discovery of the simplex algorithm coincided with the rise of the computer, making it possible to computerize the calculations, and to use the method for solving large-scale real life problems. Since then, linear optimization has developed rapidly, both in theory and in application. At the end of the 1960’s, the first software packages appeared on the market. Nowadays linear optimization problems with millions of variables and constraints can readily be solved.
