Since 1970s, it has been widely used in the field of enterprise decision-making. With the development of modern public management science and technology, it is the general trend to adopt mathematical analysis methods in the field of public decision-making.
Basic introduction Chinese name: mathematical analysis method category: analysis method basic content: mathematicization and modeling generation: content, application, commonly used mathematical analysis methods, advantages and disadvantages, advantages and disadvantages, content of World War II. Each decision analysis method has its own specific content. The basic contents of mathematical analysis methods are mathematization, modeling and computerization. From a mathematical point of view, many practical means have been found in mathematics, such as linear programming, integer programming, dynamic programming, game theory, queuing theory, inventory model, scheduling model, probability statistics and so on. It plays an important role in promoting quantitative analysis and decision-making. From the point of view of modeling, every mathematical means contains a specific mathematical model to solve decision-making problems, and people can find the answers to the questions they need to know with the help of the model; From the point of view of computerization, people can borrow an electronic computer as a fast logical calculation tool to shorten the time to solve problems and enhance the accuracy of prediction. These "three modernizations" are interrelated, and their combination has greatly changed the technology and method of decision-making. The central content of mathematical analysis is to establish a mathematical model that is suitable for decision-making and decision-making objectives and reflects the relationship between things. The core of this model is to express the relationship between variables by mathematical methods, and to express the relationship between variables and goals by mathematical relations. If an electronic computer is used, these mathematical models are programmed in the language of the computer, and then the program models are input into the electronic computer, and accurate data and conclusions are obtained through computer operation. At present, many commonly used mathematical analysis methods have been compiled into computer programs for decision makers to call at any time. How to use mathematical analysis in decision-making depends on the specific situation. Mastering the quantitative relationship is the premise of applying mathematical analysis. If decision-makers and related experts can grasp the quantitative relationship of decision-making objects and use mathematical analysis to make predictions and decisions, it will be fast, efficient, accurate and reliable. Which mathematical analysis method is adopted in decision-making practice is related to the nature and characteristics of the decision-making problem, which mainly includes three factors: first, the number of variables contained in the problem itself; Second, the uncertainty of the decision-making environment; Third, the influence of time factors. The difference of these three factors leads to different types of decision-making and requires different mathematical tools. For example, for univariate static deterministic decision-making, the classical extreme value principle in arithmetic, basic algebra and calculus is generally adopted; For multivariable static deterministic decision-making, matrix algebra, linear programming, nonlinear programming and other methods are generally used. For univariate static probability decision-making, the basic principle of probability theory should be adopted; For multivariate static probability decision-making, multivariate statistical analysis should be adopted; For univariate dynamic deterministic decision-making, differential equations should be adopted; For multivariable dynamic deterministic decision-making, dynamic programming and automatic control theory should be adopted; For univariate dynamic probability decision-making, inventory theory, queuing theory and Markov equation should be adopted; For multivariable dynamic probability decision-making, complex stochastic process theory should be adopted; Wait a minute. Common mathematical analysis methods 1. Linear programming; 2. breakeven analysis; 3. Plan evaluation method; 4. Income matrix decision-making; 5. Queuing model; 6. Other methods. (1) and other possible methods; (2) Take the large and medium as the solution (optimistic method); (3) start from a small place (pessimistic method); (4) optimistic coefficient method; (5) Savage method (the method of taking the minimum regret value). The reason why the mathematical analysis method of advantages and disadvantages is widely used in management decision-making is determined by its advantages. The main manifestations are as follows: under certain conditions, mathematical analysis methods can make decision-making work based on science; Mathematical analysis can make complex mathematical procedures simple and clear, which is conducive to improving decision-making efficiency; In related network systems, managers can solve complex problems with the help of mathematical analysis methods; Linear programming, decision tree and other methods are conducive to formulating the steps of a series of activities, understanding the relationship between various activities, and thus achieving scientific decision-making; A good mathematical model diagram is helpful for decision makers to see all kinds of causal relationships at a glance and correct their prejudice against some problems; Wait a minute. The mathematical analysis method of shortcomings is not perfect, and there are limitations in application, mainly as follows: 1. Mathematical models themselves may not well reflect the related problems in reality, because many mathematical models are based on assumptions that are not necessarily correct, and in real life, not all problems can be expressed by numbers. Therefore, the mathematical analysis method is not suitable for all decision-making problems or all aspects of a decision-making problem. 2. If we rely too much on mathematical models for decision-making activities, we must train a group of talents engaged in the design and application of mathematical models, but these professionals are difficult to play their roles in other aspects.