Effect of seven steps approach on simplex method to optimize the mathematical manipulation

Abstract

The Simplex method is the most popular and successful method for solving linear programs. The objective function of linear programming problem (LPP) involves in the maximization and minimization problem with the set of linear equalities and inequalities constraints. There are different methods to solve LPP, such as simplex, dual-simplex, Big-M and two phase method. In this paper, an approach is presented to solve LPP with new seven steps process by choosing “key element rule” which is still widely used and remains important in practice. We propose a new technique i.e. seven step process in LPP for the simplex, dual-simplex, Big-M and two phase methods to get the solution with complexity reduction. The complexity reduction is done by eliminating the number of elementary row transformation operation in simplex tableau of identity matrix. By the proposed technique elementary transformation of operation has completely avoided and we can achieve the results in considerable duration.