EVOLUTION OF LINEAR PROGRAMMING COMPUTING TECHNIQUES.

While the linear programming concept and the formulation of a specific model have value in themselves, the technique would fall short of its promise without efficient computing procedures. The simplex method has proved to be the most successful approach but it still leaves a wide range for detailed algorithms. At first, the method was applied by hand or with the aid of punched-card equipment. With the advent of internally-stored-program computers, automatic routines were designed. However, the early machines were adequate only for small problems and the original simplex method was not efficient for many LP models. A program of development was started at RAND to provide better computing techniques. Using first the IBM Model II CEC, then the 701 and now the 704, general LP routines of considerable power and flexibility have been developed. Future improvements will probably be possible only from higher level abstractions which take advantage of structure in the model matrix or which produce more efficient forms of the inverse of a sparse matrix. [ABSTRACT FROM AUTHOR]