The specific contents of operational research include: planning theory (including linear programming, nonlinear programming, integer programming and dynamic programming), inventory theory, graph theory, decision theory, game theory, queuing theory, reliability theory and so on. As early as 1939, H.B.Kahtopob of the Soviet Union and F.L.Hitchcock of the United States first studied and applied the linear programming method in production organization management and transportation scheme formulation. 1947, Danziger and others put forward the simplex method for solving linear programming problems, which laid the foundation for linear programming theory and calculation. In particular, the emergence and improvement of electronic computers have made the planning theory develop rapidly. From the optimization of solving technical problems to the departments of industry, agriculture, commerce, transportation and decision analysis, thousands of large-scale linear programming problems with constraints and variables can be handled by electronic computers. From the scope, it is useful from the planning arrangement of a team, to the whole department, and even to the analysis of the optimal plan of the national economic plan. It has the characteristics of strong adaptability, wide application and simple calculation technology. The basic work of nonlinear programming was completed by H.W. Kuhn and A.W. Tucker in 195 1 year. By the 1970s, mathematical programming had further developed in theory and method, as well as in the depth and breadth of its application.

The research object of mathematical planning is the arrangement and evaluation in planning management. The main problem to be solved is to find the optimal scheme of arrangement according to a certain measurement index under given conditions. It can be expressed as the problem of finding the minimum value of a function under constraints.

Mathematical programming is essentially different from the classical problem of seeking extreme value. Classical methods can only deal with simple expressions and simple constraints. However, in modern mathematical programming, the objective function and constraints of the problem are very complex, and some accurate numerical solutions are needed, so the research on the algorithm is particularly valued.

The simplest problem here is linear programming. If the constraint and objective function are linear, it is called linear programming. To solve linear programming problems, linear equations should be solved theoretically, so the method of solving linear equations and the knowledge of determinant and matrix are very necessary tools in linear programming.

The emergence of linear programming and its solution-simplex method has greatly promoted the development of operational research. Many practical problems can be solved by linear programming, and simplex method is an effective algorithm, and the emergence of computers makes the solution of some large and complex practical problems become a reality.

Nonlinear programming is the further development and continuation of linear programming. Many practical problems, such as design problems and economic balance problems, belong to the category of nonlinear programming. Nonlinear programming not only expands the application scope of mathematical programming, but also raises many basic theoretical problems for mathematicians, which makes convex analysis and numerical analysis in mathematics develop. There is also a time-related planning problem called "dynamic planning". In recent years, it has become an important tool commonly used in optimal control problems in engineering control, technical physics and communication. Queuing theory is also called stochastic service system theory. At the beginning of the 20th century, Danish engineer Erlang began to study the efficiency of telephone exchange. In World War II, in order to estimate the capacity of airport runway, it was further developed, and its corresponding discipline renewal theory and reliability theory were also developed.

After 1909, Danish telephone engineer A.K.Erlang began to study the queuing problem in a more general way, and achieved some important results. 1949 or so, started the research on machine management, land and air transportation, etc. After 195 1 year, the theoretical work has made new progress and gradually laid the theoretical foundation of modern random service system. Queuing theory mainly studies the queue length, waiting time and service provided by various systems in order to obtain better service. It is a theory to study the phenomenon of random aggregation and dispersion of systems.

Queuing theory is also called stochastic service system theory. The purpose of its research is to answer the question of how to improve the service objects of service institutions or organizations and make some indicators reach the optimal level. For example, how many docks should a port have and how many maintenance personnel should a factory have.

Because queuing phenomenon is a random phenomenon, probability theory is mainly used as the main tool to study queuing phenomenon. In addition, there are differential and differential equations. Queuing theory describes the image of the object it wants to study when customers come to the service desk to ask for reception. If the service desk is occupied by other customers, there will be a queue. On the other hand, the service desk is sometimes idle and sometimes busy. It is necessary to obtain the probability distribution of customer waiting time and queue length by mathematical method.

Queuing theory is widely used in daily life, such as the regulation of reservoir water volume, the arrangement of production line, the dispatching of railway approach, the design of power grid and so on. Game theory is also called game theory. The aforementioned horse racing in Tian Ji is a typical game theory problem. As a branch of operational research, the development of game theory is only a few decades. Von Neumann, a mathematician who systematically founded this subject.

At first, the study of game theory by mathematical methods began with chess, aiming at how to determine the winning algorithm. Because this is a problem of studying the conflict between the two sides and winning countermeasures, this subject has very important applications in the military. Mathematicians have also studied the fighting and tracking between mines and ships, fighters and bombers, and put forward a mathematical theory that both sides can make decisions independently. With the further development of artificial intelligence research, more and more new requirements are put forward for game theory. Decision theory studies decision-making problems. The so-called decision-making is the process of choosing the best scheme scientifically with the help of certain theories, methods and tools according to objective possibilities. Decision problem consists of decision maker and decision domain, and decision domain consists of decision space, state space and result function. The science of studying decision theory and method is decision science. The problems to be solved in decision-making are various, and there are different classification methods from different angles. According to the certainty of the natural state faced by decision makers, it can be divided into: deterministic decision-making, decision-making under uncertainty and risky decision-making; According to the number of objectives on which decisions are based, they can be divided into: single-objective decision-making and multi-objective decision-making; According to the nature of decision-making problems, it can be divided into: strategic decision-making and strategic decision-making, and various types of decision-making problems according to different standards. Different decision-making methods should be adopted for different types of decision-making problems. The basic steps of decision-making are: (1) determine the problem and put forward the decision-making goal; (2) Discover, explore and draw up various feasible schemes; (3) Choose the most satisfactory scheme from various feasible schemes; (4) the implementation and feedback of the decision, in order to seek the dynamic optimization of the decision.

If the other side of the decision-maker is also a person (a person or a group of people) and both sides want to win, this competitive decision-making is called game decision-making or game decision-making. The three basic elements that constitute the problem of countermeasures are: players, strategies and the gains and losses of a game of countermeasures. Game problems can generally be divided into finite zero-sum two-person game, position game, continuous game, multiplayer game and differential game. Search theory is a branch of operational research that emerged because of the need of war in the Second World War. This paper mainly studies the theory and method of how to design and find the optimal scheme of a certain target and implement it under the condition of limited resources and detection means. In World War II, the allied air force and navy were born in the process of studying how to identify the submarine activities, fleet transportation and force deployment of the Axis countries. Search theory has also made many achievements in practical application. For example, in the 1960s, the United States successfully searched for the nuclear submarines "oil tankers" and "scorpions" missing in the Atlantic Ocean and the hydrogen bombs missing in the Mediterranean Sea.