During the Warring States Period in China, there was a horse race that was passed down from generation to generation. I believe everyone knows that this is a horse race in Tian Ji. The story of horse racing in Tianji shows that under the existing conditions, the best results will be achieved through planning and arrangement. So planning and arrangement are very important.
It is generally believed that operational research is a branch of modern applied mathematics, which mainly refines some general operational research problems in production, management and other events, and then solves them by mathematical methods. The former provides models, while the latter provides theories and methods.
The idea of operational research has existed since ancient times. If we want to defeat the enemy, we must make the best plan to deal with the enemy on the basis of understanding the situation of both sides. This is the saying that "strategic planning wins a thousand miles".
However, as a mathematical discipline, it is too late to solve the selection and arrangement of the optimal method by pure mathematics. It can also be said that operational research is a branch that began to rise in the 1940s.
Operational research mainly studies the planning and management problems that can be expressed quantitatively in economic activities and military activities. Of course, with the development of objective reality, many contents of operational research not only study economic and military activities, but also go deep into daily life. Operations research can get various results through mathematical analysis and operation according to the requirements of the problem, and finally put forward a comprehensive and reasonable arrangement, which has achieved the best results.
As a discipline used to solve practical problems, operational research generally has the following steps when dealing with various problems: determining goals, making plans, establishing models and making solutions.
Although it is unlikely that operational research can deal with large-scale objects, some abstract models have been formed in the development of operational research, which can be applied to solve large-scale practical problems.
With the development of science and technology and production, operational research has penetrated into many fields and played an increasingly important role. Operational research itself is also developing constantly, and now it is a mathematics department including several branches, such as: mathematical programming (including linear programming; Nonlinear programming; Integer programming; Combinatorial planning, graph theory, network flow, decision analysis, queuing theory, reliability mathematics theory, inventory theory, game theory, search theory, simulation and so on.
The application field of operational research is very wide, which has penetrated into service, inventory, search, population, confrontation, control, timetable, resource allocation, site selection, energy, design, production, reliability and so on.
Operational research is a hard subject in soft science, which has the properties of logical mathematics and mathematical logic. It is the basic theory and indispensable method, means and tool in systems engineering and modern management science. Operational research has been applied to various management projects and plays an important role in modernization.
[Edit this paragraph] The history of operational research
As a modern science, operational research was first developed in Britain and the United States during the Second World War. Some scholars describe operational research as a scientific means to make decisions on various operations of organizational systems. In their basic works, P.M.Morse and G.E.Kimball defined operational research as: "Operational research belongs to the field of management, and uses mathematical methods to make overall plans for problems that need to be managed. The applied science of decision making. " Another founder of operations research defines operations research as "a scientific method that people who manage systems must use to obtain the optimal solution about system operation." It uses many mathematical tools (including probability statistics, mathematical analysis, linear algebra, etc. ) and logical judgment method to study the organization and management, planning and scheduling of people, money and things in the system. In order to maximize the benefits.
The origin of modern operational research can be traced back to decades ago, when scientific means were first tried in the management of some organizations. However, it is generally believed that the activities of operational research began with military tasks in the early days of World War II. At that time, there was an urgent need to effectively allocate scarce resources to various military operations and activities in each operation. Therefore, the military administration of the United States and a large number of scientists later called for scientific means to deal with strategic and tactical issues. In fact, this requires them to learn all kinds of (military) operations. These groups of scientists are the earliest operation teams.
During World War II, OR successfully solved many important operational problems, which showed the great material strength of science and paved the way for the later development of OR.
When the post-war industry resumed its prosperity, people realized that these problems were basically similar to those faced in the war, because the complexity and specialization of the organization were getting higher and higher, but the realistic environment was different. As a result, operational research penetrated into industrial and commercial enterprises and other departments, and was widely used after the 1950s. The in-depth study and application of the application mechanism of system configuration, convergence and competition formed a set of relatively complete theories. Such as planning theory, queuing theory, storage theory, decision theory and so on. Due to the maturity of its theory, the advent of electronic computers has greatly promoted the development of operational research. Many countries in the world have established specialized societies specializing in this field and related activities. On 1952, the United States established the Institute of Operations Research and published the magazine of Operations Research. Other countries in the world have also established operational research societies and journals, 65438.
[Edit this paragraph] Characteristics of operational research
The characteristics of operational research are: 1. Operational research has been widely used in the overall coordination of industrial and commercial enterprises, military departments, civil affairs and other research institutions, so its application is not limited by industries and departments; 2. Operational research not only carries out creative scientific research on various operations, but also involves the actual management of organizations. It has strong practicability, and should eventually provide constructive suggestions to decision makers and receive practical results; 3. It aims at overall optimization, and tries to solve the conflict of interests among all departments of the system in the best way from the perspective of the system. It can also be regarded as an optimization technology, providing optimization methods to solve various problems.
[Edit this paragraph] Research methods of operational research
The research methods of operational research are as follows: 1. Extract essential elements from real life situations to build a mathematical model, so as to seek solutions related to the goals of decision makers; 2. Explore the structure of the solution and deduce the solution process of the system; 3. Seek the optimal solution of the system from the feasible scheme.
[Edit this paragraph] The specific content of operational research
The specific contents of operational research include: planning theory (including linear programming, nonlinear programming, integer programming and dynamic programming), graph theory, decision theory, game theory, queuing theory, storage theory, reliability theory and so on.
Planning theory
Mathematical programming, that is, the above planning theory, is an important branch of operational research. As early as 1939, H.B.Kahtopob of the Soviet Union and F.L.Hitchcock of the United States first studied and applied linear programming methods in production organization management and transportation planning. 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 perfection 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 computers. From the scope, it can be as small as a team's planning arrangement, as large as the whole department, and even the optimization scheme analysis of the national economic plan. All of them are useful, with 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 was not only in theory and method, but also in
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 arrangement scheme under given conditions and according to certain metrics. It can be expressed as a problem of finding the maximum and minimum values 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, the objective function and constraint conditions of modern mathematical programming are very complex, which requires some accurate numerical solutions, so the research of algorithms is particularly valued.