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.