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. P.M. Morse and G.E. kimball define operational research as: "Operational research is an applied science, which uses mathematical methods to make overall planning and decision on problems that need to be managed in the management field." Another founder of operations research defines operations research as "a scientific method that people who manage systems must use in order 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 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 study various (military) actions. These groups of scientists are the earliest operation teams.
During the Second World War, 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. Therefore, operational research penetrated into industrial and commercial enterprises and other departments, and was widely used after the 1950s. The application mechanism of system configuration, aggregation, decentralization and competition is deeply studied and applied, and a set of relatively complete theories is formed, such as planning theory, queuing theory, storage theory and decision theory. Due to the maturity of its theory, the advent of electronic computers has greatly promoted the development of operational research, and many countries in the world have established specialized societies specializing in this field and related activities. The American Society for Operations Research was established in 1952.
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 be regarded as an optimization technology to find the optimal solution and the best action plan for the studied problem, which provides an optimization method to solve various problems.
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.
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.
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. Computers can be used to deal with thousands of large-scale linear programming problems with constraints and variables, from the optimization of solving technical problems to the departments of industry, agriculture, commerce, transportation and decision analysis. 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.
Graph theory is an ancient and very active branch, which is the basis of network technology. The founder of graph theory is mathematician Euler. 1736, he published his first paper on graph theory, which solved the famous problem of the Seven Bridges in Konigsberg. After a hundred years, Kirchhoff first applied graph theory to analyze power grid in 1847, thus introducing graph theory into the field of engineering technology. Since 1950s, graph theory has been further developed. Using graphs to describe complex and huge engineering systems and management problems can solve many optimization problems in engineering design and management decision-making, such as the shortest time, shortest distance and lowest cost to complete engineering tasks. Graph theory has been paid more and more attention by mathematics, engineering technology and management.
Queuing theory is also called stochastic service system theory. 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.
Reliability theory is a theory that studies system faults to improve system reliability. The systems studied by reliability theory are generally divided into two categories: (1) unrepairable systems, such as missiles, whose parameters are life and reliability; (2) The important parameter of repairable system, such as general electromechanical equipment, is effectiveness, and its value is the ratio of normal working time to normal working time plus accident repair time.
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, risky decision-making and decision-making under uncertainty; 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. At present, game problems can be generally divided into finite zero-sum two-person game, position game, continuous game, multiplayer game and differential game.
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.