Operations research (OR) is a scientific discipline concerned with the development and application of optimization methods based on mathematical modeling and various heuristic approaches.
Operations research methods are applied in situations where a purposeful undertaking needs to be organized and can be carried out in more than one way — that is, where a decision must be chosen from a number of possible alternatives. Each alternative has certain advantages and disadvantages, and given the prevailing circumstances, it is not immediately clear which alternative is preferable and why.
The goal of operations research is to provide a preliminary quantitative justification for optimal decisions, grounded in a measure of effectiveness. The actual making of the decision lies outside the scope of operations research and falls within the competence of the responsible decision-maker (DM).
Operations research methods are effective for well-structured problems. Well-structured (or well-formalizable) problems admit a quantitative formulation; their most essential dependencies are expressed by formal models and represented in symbolic form, where the symbols take numerical values. The methodology of operations research, in addition to computation, pays close attention to the process of problem formulation, the choice of mathematical models, and the interpretation and comprehension of the computational results.
Much of the work in operations research is based on mathematical programming methods. Unlike purely mathematical methods, these provide tools for problem formulation, yield a feasible solution region and solution alternatives. Furthermore, a mathematical programming model can account for multiple criteria (in the form of an objective function and constraints), which enhances the objectivity of decision-making.
Alongside the branch oriented toward mathematical programming models, operations research also encompasses methods and models grounded in mathematical statistics and probability theory. The methods of operations research also include game theory, mathematical logic, graph theory, and other methods of discrete mathematics.
As a result, a number of distinct branches of operations research have emerged, each grounded in the application of different methods: inventory control, equipment replacement, resource allocation, and scheduling — that is, problem classes rooted in the principal formulations of mathematical programming — as well as queueing theory, game-theoretic models of conflict and competition, and others.