® A linear programming problem is one that is concerned with finding the optimal value (maximum or minimum) of a linear function of several variables (called objective function) subject to the conditions that the variables are non-negative and satisfy a set of linear inequalities (called linear constraints ). Variables are sometimes called decision variables and are non-negative. Historical Note In the World War II, when the war operations had to be planned to economise expenditure, maximise damage to the enemy, linear programming problems came to the forefront. The first problem in linear programming was formulated in by the Russian mathematician, L.
Kantorovich and the American economist, F. L. Hitchcock, LINEAR PROGRAMMING both of whom worked at it independently of each other. This was the well known transportation problem .
In , an English economist, G.Stigler, described yet another linear programming problem – that of determining an optimal diet . In , the American economist, G. B. Dantzig suggested an efficient method known as the simplex method which is an iterative procedure to solve any linear programming problem in a finite number of steps.
L. Katorovich and American mathematical economist, T. C. Koopmans were awarded the nobel prize in the year in economics for their pioneering work in linear programming.
With the advent of computers and the necessary softwares, it has become possible to apply linear programming model to increasingly complex problems in many areas.