Research And Application On The Simplex Method Of Linear Programming

Since the efficiency of simplex method for solving linear programming problems can be improved, the modified simplex method is proposed for decreasing storage and calculation. While, the solution of the simplex method could start at an initial feasible basis, some artificial variables must be added when there is not an initial feasible basis in the standard form of a linear programming problem.Based on the principle of linear dependence and linear independence of vectors and the iteration essence of the dual simplex method, some researches have been done to modify the simplex method.The major work of this thesis is as follows:First, using the property of linear dependence and linear independence of vectors, the improvement ideal of the modified simplex method has been derived in detail. The key step and some related researches of the modified simplex method are also been summarized in this thesis.Second, based on the thoughts in [17] and [45], we propose a new method combined with the iteration essence of the dual simplex method to avoid artificial variables. The feasibility and effectiveness of the new method are also verified through some numerical examples. The main characteristics of the new method are as follows:(1) artificial variables are not needed;(2) initial feasible basis is not required;(3), the right hand side need not to be non-negative.Third, the sensitivity analysis is one of the most important topics in linear programming and also plays a significant role in production decision. The application of the proposed method on sensitivity analysis provides a reference for related researchers.Last but not least, the feasibility and effectiveness of the proposed method are verified again via the numerical results of blanking issues, continuous investment issues and determination of microbial metabolic pathways by using MATLAB. The numerical results also show the universality of our algorithm in the actual production and daily life.