## History

*George Dantzig, founder of Linear Programming* [1]

The 1940s was a time of innovation and reformation of how products were made, both to make things more efficient and to make a better-quality product. The second world war was going on at the time and the army needed a way to plan expenditures and returns in order to reduce costs and increase losses for the enemy. George B. Dantzig is the founder of the simplex method of linear programming, but it was kept secret and was not published until 1947 since it was being used as a war-time strategy. But once it was released, many industries also found the method to be highly valuable. Another person who played a key role in the development of linear programming is John von Neumann, who developed the theory of the duality and Leonid Kantorovich, a Russian mathematician who used similar techniques in economics before Dantzig and won the Nobel prize in 1975 in economics. [2]

Dantzig's original example of finding the best assignment of 70 people to 70 jobs emphasizes the praticality of linear programming. The computing power required to test all possible combinations to select the best assignment is quite large. However, it takes only a moment to find the optimum solution by modeling problem as a linear program and applying the simplex algorithm. The theory behind linear programming is to drastically reduce the number of possible optimal solutions that must be checked. [2]

In the years from the time when it was first proposed in 1947 by Dantzig, linear programming and its many forms have come into wide use worldwide. LP has become popular in academic circles, for decision scientists (operations researchers and management scientists), as well as numerical analysts, mathematicians, and economists who have written hundreds of books and many more papers on the subject. Though it is so common now, it was unknown to the public prior to 1947. Actually, several researchers developed the idea in the past. Fourier in 1823 and the well-known Belgian mathematician de la VallĂ©e Poussin in 1911 each wrote a paper describing today's linear programming methods, but it never made its way into mainstream use. A paper by Hitchcock in 1941 on a transportation problem was also overlooked until the late 1940s and early 1950s. It seems the reason linear programming failed to catch on in the past was lack of interest in optimizing. [3]

"Linear programming can be viewed as part of a great revolutionary development which has given mankind the ability to state general goals and to lay out a path of detailed decisions to take in order to 'best' achieve its goals when faced with practical situations of great complexity. Our tools for doing this are ways to formulate real-world problems in detailed mathematical terms (models), techniques for solving the models (algorithms), and engines for executing the steps of algorithms (computers and software)." [Quote from 3]