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Mathematical Theories in Management
1. Management science is a phrase intended to represent a common and mutually accepted norm on the part of a number of scientific disciplines with the study and solution of the problems management. World War II and the period after saw a great increase of interest on the part of the plied scientist in the management problems of the military and of the industrial firms. The management sciences are bound together by more than a common intellectual interest. They also are a common philosophy of method: namely the need for more rigorous analysis of the complied problems of management. This need can often be satisfied by the use of the mathematics or carefully controlled observation and experiment.
2. Interest in the mathematics of management increased tremendously after World War II, although a number of notable treaties had appeared before. This interest resulted in new fields of mathematical research, fields whose titles reflect the potential application to management problems: Inventory theory. Waiting Line or Queuing theory, Linear and Nonlinear programming, Dynamic Programming, Game theory. Inventory theory provides a language for describing the state of a system that is subject to a pattern of demand and has available resources for building up supplies. The demands may be probabilistic and may vary in kind. The replenishment may be subject to delays and uncertainties. This inventory theory may be applied to many problems where the term «inventory» would be normally used, such as planning of personnel assignments, parking facilities and cash flows.
3. Waiting Line theory we know as Queuing theory is the language of a system of service units. It describes customers to arrive for service, it shows how service meets their requirements in terms of average service time and variations in service time. That is, how long the customer may and have to wait, how long the service unit may be idle.
4. Linear Programming is a language of activities that describes how these activities utilise their resources in order to accomplish certain prescribed tasks. It also describes how these activities operate within limitation of time and space. The term «linear» reflects the fact that the basic descriptions have to take a form of linear algebraic equations or inequations. Now linear programming permits a relaxation of this requirement. The language of linear programming is astonishingly versatile. In addition to its obvious use in the planning of production schedules, it has been employed in such areas as military logistics, transportation and traffic, personnel assignments and salary´ levels.
5. Dynamic Programming of the maximization theory expresses in the language and permits one to maximize over a whole series of states where each state depends on decisions that have been made in earlier states. This language allows one to state in rigorous terms the period-by-period consequences of decisions and to calculate the desirability of incurring temporary losses.
6. Game theory is a language for describing competitive strategies when the opponents are able to influence the probability of success of the other «players» under prescribed rules, and can form situation to threat the activities of others. This language therefore will be well adapted to the study of competition. But its applications have not been extensive because in many realistic problems it is difficult to ascertain what the players really want and the rules that govern their plays. In addition to these languages, the following can also be mentioned: theories of search, replacement, communication, information and decision making. All these languages enable the scientist to state in rigorous terms the nature of the problem as he sees it and the consequences of alternative decisions even when situation is extremely complicated.