Research On Economic Decision-Making Models In Optimization Theory And Methods

Optimization Theory and Methods is the most important subject in application areas, it studies the best method of the decision-making problem. The Input- output model and portfolio investment model are the most important parts in economy. Based on Optimization Theory and Methods, this thesis studies these models.The main content and achievement of this thesis are:In chapter 1, the thesis makes an analysis on feasible Leontief-Model in resources systems, and gets two important theorems and consequents about them. At the same time, it reasons the application of dynamic Leontief-Model in calculation for economy growth rate and output design of the resources systems. Furthermore, it makes instance analysis for the economy forecasting and control of the dynamic Leontief-Model with practical example.From the viewpoint of minimization of the loss of opportunity cost, the thesis analyzes two different rational ranges of variable output corresponding with two different ways by which the production is divided into three intervals in chapter 2. The results show that the rational range of variable output is between the quantity of output when marginal cost is lest of all and the quantity of output which is decided by marginal cost when it equals the expectation price of the product in market.Based on the model of Markowitz's Portfolio Investment: min 1/2WtVW, s.t. Wte = 1, WtE(X) = ?, in chapter 3, the thesis studies the model when the covariance matrices are general symmetric matrices, gets an extension on an important theorem, discusses the solution of the model following two classes of the general symmetric matrices, and gives a method for calculating optimal portfolio.Based on the decision tree method of the portfolio investment, in chapter 4, the thesis proposes the improved decision tree method, and discusses how to use this method to select and rank the alternatives of the portfolio investment.