A Pivot Rule for Maximization Degeneracy Problems of Simplex Method for Linear Programming Problems

Abstract

The simplex algorithm is a powerful technique, widely used to find the optimal solution of linear programming problems. Pivot rule is the most important first step of the simplex algorithm in the maximization degeneracy problems of LP for selecting the entering variable/work column (to obtain the smallest ratios) and after than leaving variable for pivot equation. The selection of an effective pivot rule leads the smallest number of iterations of the optimal solution of L.P. The selecting of most negative number (for entering variable) in the maximization problems is known as G.B Dantzig's pivot rule. The purpose of this paper is to model an algorithm that improves in the entering and leaving variable for the maximization degeneracy problems of LP. In this article, we have introduced a powerful technique for pivot rule which reduces the number of iterations to obtain the optimal solution as compare to Dantzig’s pivot rule. This article gives better concept of selection the entering variable as well leaving variable. This article also gives a helpful imminent into the unique and constructive performance of the proposed method by coverage computational experiments.