Linear Programming deals with the problem of minimizing or maximizing a linear function in the presence of linear inequalities. Since the development of the simplex method by George B. Dantzig in 1947, linear programming has been extensively used in the military, industrial, governmental, and urban planning fields, among others. The popularity of linear programming can be attributed to many factors including its ability to model large and complex problems, and the ability of the users to solve large problems in a reasonable amount of time by the use of the simplex method and computers.

During and after World War II it became evident that planning and coordi nation among various projects and the efficient utilization of scarce resources were essential. Intensive work by the U. S. Air Force team SCOOP (Scientific Computation of Optimum Programs) began in June 1947. As a result, the simplex method was developed by George B. Dantzig by the end of summer 1947. Interest in linear programming spread quickly among economists, mathematicians, statisticians, and government institutions. In the summer of 1949 a conference on linear programming was held under the sponsorship of the Cowles Commission for Research in Economics. The papers presented at that conference were later collected in 1951 by Т. C. Koopmans into the book Activity Analysis of Production and Allocation.

Since the development of the simplex method many people have contributed to the growth of linear programming by developing its mathematical theory, devising efficient computational methods and codes, exploring new applications, and by their use of linear programming as an aiding tool for solving more complex problems, for instance, discrete programs, nonlinear programs, combi natorial problems, stochastic programming problems, and problems of optimal control.