Article
Article
Linear programming
Article By:
Johnson, Ellis L. School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia.
Cottle, Richard W. Department of Management Science and Engineering, Huang Engineering Center, Stanford University, Stanford, California.
Last reviewed:January 2020
DOI:https://doi.org/10.1036/1097-8542.384200
An area of mathematics concerned with the minimization (or maximization) of a linear function of several variables subject to linear equations and inequalities. Linear programming developed from three main areas: transportation problems, game theory, and input-output models. Work on all these areas took place before and during World War II, with independent major contributions by L. V. Kantorovich, J. von Neumann, W. Leontief, and T. C. Koopmans. The subject in its present form was created in 1947, when G. B. Dantzig defined the general model and proposed the first, and still the most widely used, algorithm for its solution: the simplex method.
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