The New Logics For Linear Programming Problems

Abstract

This monograph proposes two new logics for LP problems, namely i) choosing optimal active constraints and non-zero variables, ii) pro- duction of the adding constraint (CONAD). Direct Approach Method, Simplex Method, and Revised Simplex Method are modified based on these new logics. The present modifications provide many advantages, such as the reductions of the computing time and size of dimension, no degeneracy troubles, and less possibility to meet unbounded and no - feasible Solutions. A short historical brief survey of the solution methods, main fea- tures of advanced Computer codes of LP, and a variety of special topics in solution ways are also presented. The proposed Direct Approach Method and Simplex Method have been demonstrated by several numerical examples. The similar demonstration can be made for the proposed Revised Simplex Method also.