The Study And Expansion Of Economic Optimized Analysis Metheods

Economic optimized methods and models are parts of the basic contents of Quantitative Economics. As the important methods of studying economic problems in economic, optimized analysis methods enrich and develop the measurement and practice of economic relation from deferent aspects in quantity economics. Since 1940s, economic optimized analysis methods are gradually mature in theory and algorithm and widely applied in practice. But, some optimized analysis methods need further improving to meet practical needs and decrease its artificial and computer measurement.Although many internal and foreign scholars are studying optimized analysis methods (also called sensitivity analysis),the methods of study and starting points of theory are different. On the other hand, theory basis of optimized analysis methods are becoming mature and the various applying software of computer are used, so the study of this theory and measurement is decreasing. The theory and measurement are the basis of application. Therefore there is wide space of the study in this field.Meanwhile, people often meet amount of the undefined such as confusion and randomness in dealing with practical problems. And the problems which these undefined factors bring about can't be well solved by the traditional mathematical methods. As professor Liu Baoding from Qing Hua University pointed out:From the extension of undefined theory, it needs deeper mathematical theory analysis; from the expansion of undefined program model, it needs further study of dynamic program and poly-storied program under undefined circumstance. From the other aspect, it is a challenging question of study to search for optimized conditions or set up duality theory and how to analyzing sensitivity; from the calculation efficiency of undefined program, it needs designing more efficient resolution method based on elicitation method algorithm; from the aspect of application, it is further considered to be applied in model identification, lining system, environment protection,quality control, risk analysis.'It is obvious that fuzzy program theory is an important part of undefined program theory, the deep study of fuzzy program will further enrich the undefined program theory. But, at present, it is rare to study duality theory and KKT condition of fuzzy program, even no progress. Therefore, the study of duality theory of fuzzy linear programming become an important question for study.This paper does two main parts of the work from improving some economic optimization methods.The first part researches the method that finding an initial basic feasible solution by the sensitivity analysis of increasing or decreasing restrains of LP (linear programming) from the optimized analysis method of the linear programming problem. It supplies the sensitivity analysis method by decreasing restrains which is scarcely studied recently, and applies the method to solve the linear programming problem with the upper bounds constraint for the sensitivity analysis. It supplies the method by increasing a special restrain and then removing the restrain to solve the initial basic feasible solution, and applies the thought and the way to simplex method of quadratic programming, improve the algorithm and convergent conditions to obtain the more simple procedure and convergence criterions by this way.The second part researches the duality of LP with fuzzy mathematics. First, it introduces the basic concepts of FLP (fuzzy linear programming) and the relationship between classical L P, generalizes various models of FLP, and summarizes various fuzzy programming models. Secondly, it studies duality theorem of linear programming with fuzzy≤. It gives the dual programming model with fuzzy≤, summarizes the general rule constituting fuzzy dual programming, and proves symmetric fuzzy duality with fuzzy≤.Finally, the important results of classic LP are popularized in FLP with fuzzy coefficient type.This paper is constituted of six chapters.Chapter I Introduction. It discusses domestic and foreign status quo about the optimized analysis and the background and significance of the topics, it introduces the related knowledge about LP and FLP, specifies the ideas, structural arrangements, the major innovation points and the need for the problems deserving further study.Chapter II The sensitivity analysis of increasing or decreasing restrain conditions for LP. The chapter supplies the sensitivity analysis methods of increasing restrain conditions and decreasing restrain conditions based on general sensitivity analysis, especially discusses the optimal solutions method with and without auxiliary variables for LP with decreasing restrain conditions. Finally it solves LP with upper limited variables by the way of increasing or decreasing restrain conditions. ChapterⅢA method of solving basic feasible solution for LP. The chapter first introduces the general method of solving initial basic feasible solution M-Method, Two-Phase Method and the simplified method seeking initial basic feasible solutions. And then it proposes a new method of solving initial basic feasible solutions. The method solves the optimal solutions by iteration by increasing a special restrain, carries out the thought that simplex method for dual all non-positive tests numbers, then get rid of the restrain, as a result, a basic feasible solution can be obtained. Increasing or decreasing restrain can be omitted after the process is simplified. It only makes simplex table for matrix increase several elementary transformation. It proves this method is easy simple and efficient. Finally, it applies the thought way to simplex method of quadratic programming, improving the algorithm and convergent conditions and obtaining the more simple procedure and convergence criterions by this way.Chapter IV FLP and models. The chapter first introduces the basic concepts about FLP and the relationship with classic LP. Secondly, a variety of FLP models are generalized, getting the following models-FLP(Ⅰ-a):≤fuzzy type, FLP(Ⅰ-b):fuzzy object and≤fuzzy type, FLP(Ⅱ-a):fuzzy coefficients of the right side b type, FLP(Ⅱ-b):fuzzy object (?)type, FLP(Ⅱ-c):fuzzy restraint coefficient A,b type and FLP(Ⅱ-d):the whole fuzzy coefficient (?),(?),(?)type. Finally, it introduces the common algorithm for FLP-WERNER symmetric model, Zimmermann symmetric model, the algorithm for FLP (Ⅱ-a) and the possibility of FLP (Ⅱ-d)-type algorithm.Chapter V A study of duality theorem of FLP for fuzzy≤fuzzy type. The chapter studies duality theorem of FLP for fuzzy≤fuzzy type, supplies the relationship model between symmetric and non-symmetric fuzzy duality, and puts forward the method that deriving non-symmetric fuzzy duality by symmetric fuzzy duality and symmetric fuzzy duality by non-symmetric fuzzy duality, summarizes the general rule constituting FLP, and proves symmetric duality theorem for≤fuzzy type.Chapter VI FLP duality theorem for fuzzy coefficient type. The chapter first introduces the definition and the nature of the optimal solution, then introduces the definition and the nature of the optimal solution of DFLP (dual fuzzy linear programming) with fuzzy coefficient type, strong and weak duality theorem. It mainly studies duality theorem for fuzzy coefficient type based on fuzzy relationship, extends classical LP results, and derives and proves FLP duality theorem and the complementary slackness theorem.Innovations of this paper1. Supplies the sensitivity analysis method of decreasing restrains which is few currently for the sensitivity analysis of increasing or decreasing restrains of LP, discuss the optimal solutions method with and without auxiliary variables for LP with decreasing restrain conditions, and illustrate that the method is simple and practical by giving examples.2. Propose a new method of solving initial basic feasible solution. The method solves the optimal solutions by iteration by increasing a special restrain, carries out the thought that simplex method for dual all non-positive tests numbers, then get rid of the restrain, as a result, a basic feasible solution can be obtained. The usage of method doesn't makes increasing or decreasing restraint not limited to the scope of sensitivity analysis, but greatly expanded and become an effective means of dealing with certain issues.3. Propose duality model for duality theorem of FLP with≤type, supplies the general rule of constituting DFLP, and prove symmetric duality theorem for≤type.4. Research duality theorem for FLP with fuzzy coefficient type based on fuzzy relation, extend the important results of classic LP, and derive and prove the symmetric theorem and the complementary slackness theorem of FLP.