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Operations research
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From Wikipedia, the free encyclopedia
Discipline concerning the application of advanced analytical methods
Not to be confused with Operations management or Operational analysis.<br>For the academic journal, see Operations Research (journal).
The examples and perspective in this article may not represent a worldwide view of the subject . The specific issue is: US perspective completely neglected, George Dantzig gets a passing mention only You may improve this article, discuss the issue on the talk page, or create a new article, as appropriate. (December 2020) (Learn how and when to remove this message)
Operations research (British English: operational research ), often shortened to the initialism OR , is a branch of applied mathematics that deals with the development and application of analytical methods to improve management and decision-making.[1][2] The term management science is occasionally used as a synonym.[3]
Employing techniques from other mathematical sciences, such as modeling, statistics, and optimization, operations research arrives at optimal or near-optimal solutions to decision-making problems. Because of its emphasis on practical applications, operations research has overlapped with many other disciplines, notably industrial engineering. Operations research is often concerned with determining the extreme values of some real-world objective: the maximum (of profit, performance, or yield) or minimum (of loss, risk, or cost). Originating in military efforts before World War II, its techniques have grown to concern problems in a variety of industries.[4]
Overview<br>[edit]
Operations research (OR) encompasses the development and the use of a wide range of problem-solving techniques and methods applied in the pursuit of improved decision-making and efficiency, such as simulation, mathematical optimization, queueing theory and other stochastic-process models, Markov decision processes, econometric methods, data envelopment analysis, ordinal priority approach, neural networks, expert systems, decision analysis, and the analytic hierarchy process.[5] Nearly all of these techniques involve the construction of mathematical models that attempt to describe the system. Because of the computational and statistical nature of most of these fields, OR also has strong ties to computer science and analytics. Operational researchers faced with a new problem must determine which of these techniques are most appropriate given the nature of the system, the goals for improvement, and constraints on time and computing power, or develop a new technique specific to the problem at hand (and, afterwards, to that type of problem).
The major sub-disciplines (but not limited to) in modern operational research, as identified by the journal Operations Research[6] and The Journal of the Operational Research Society [7] are:
Computing and information technologies
Financial engineering
Manufacturing, service sciences, and supply chain management
Policy modeling and public sector work
Revenue management
Simulation
Stochastic models
Transportation theory
Game theory for strategies
Linear programming
Nonlinear programming
Integer programming in NP-complete problem specially for 0-1 integer linear programming for binary
Dynamic programming in Aerospace engineering and Economics
Information theory used in Cryptography, Quantum computing
Quadratic programming for solutions of Quadratic equation and Quadratic function
History<br>[edit]
In the decades after the two World Wars, the tools of operations research were more widely applied to problems in business, industry, and society. Since that time, operational research has expanded into a field widely used in industries ranging from petrochemicals to airlines, finance, logistics, and government, with a focus on the development of mathematical models that can be used to analyze and optimize sometimes complex systems, and it has become an area of active academic and industrial research.[4]
Historical origins<br>[edit]
In the 17th century, mathematicians Blaise Pascal and Christiaan Huygens solved problems involving sometimes complex decisions (problem of points) by using game-theoretic ideas and expected values; others, such as Pierre de Fermat and Jacob Bernoulli, solved these types of problems using combinatorial reasoning instead.[8] Charles...