Linear Programming is a mathematical optimization framework involving optimizing a linear multivariable function over a Polyhedral set, which is a convex set and can be bounded (a polytope) or unbounded (having a direction of unboundedness)

Operations research is a collection of mathematical and statistical methodologies that assist in quantitative analysis of many scenarios that arise in operations, be in manufacturing or some other domain...linear programming is useful in handling certain types of operations research problems, but in addition to Linear programming, other mathematical methodologies also play role in operations research, for example Markov chains and processes, Bayesian inference and other mathematical programming methods such as goal programming, stochastic programming, Quadratic programming and Integer Linear programming.

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This book / textbook

"Introduction to operations research / by Frederick S. Hillier, Gerald J. Lieberman"

already has at least 11 editions over the last 50 years.

'Table of contents' of one edition can be seen here

https://catdir.loc.gov/catdir/toc/ecip0827/2008039045.html

with 28 chapters covering various topics in Operations Research (OR). However, the term 'linear programming' (LP) can be seen only in 4-5-or-6 chapters out of the total 28 chapters.

Therefore, LP is just a subset of OR.

Operations Research is a wider branch of mathematics, which involves linear and nonlinear optimization, managing stocks of goods, etc.

Linear Programming is a branch of Operations Research, which deals with optimizing problems that are linear in nature.

research.Certainly a special case of operations research, but we cannot say for sure that it is broader than mathematics.

Operational Research uses "scientific" techniques (mainly mathematics, statistics and computing) to help people make decisions. Applications are in business, healthcare, defence and so on. Commonly used techniques include optimisation, simulation and stochastic modelling. Linear programming is just one specific optimisation technique.

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Please excuse my English. I think the question should be changed.

OR emerged with computers and disintegrated with the growth of computer resources. Markov chains or stochastic analysis are applied to problems beyond OR. New theories such as Complexity Theory, Algorithm Theory, AI, Combinatorial Optimization... are not included in OR. But Complexity theory is necessary when analyzing and comparing solution methods.

So I would like to ask, what unites LP (in all variants and applications), Game Theory, Statistical Analysis, etc. into a single field, so called OR?

Alexander Lipovetsky - Your English is OK but your answer sucks. OR has not "disintegrated". It is more active today than ever and includes linear programming as part of the techniques used for it. Markov chains and stochastic analsyses are also a part of OR techniques. You are just WRONG that the "new theories" you list are not included in OR. Please stop misinforming the world with such. Please figure out what OR is before slamming it, misrepresenting it, and just showing your lack of knowledge about it and lack of initiative to go read a book about it and learn before trying to show your ass to the public. UGhhhhhhh

Alexander Lipovetsky : I'm not sure what you mean by "OR emerged with computers". OR was created in 1937, just before the start of the second world war. See for example this webpage and paper:

https://www.britannica.com/topic/operations-research/History

https://www.sciencedirect.com/science/article/abs/pii/S0160932705001134

Adam N. Letchford, you are absolutely correct in assuming that 'Operational research was, in fact, born of radar' (1937). However, 'operations research is not a science itself but rather the application of science to the solution of managerial and administrative problems...'

Surely you know how the definition and content of the field has changed. OR has now become an amalgamation of various sciences.

LP appeared in 1939 (Kantorovich) and 1942 (T. K. Koopmans). LP immediately showed effectiveness in planning. But its real application began with the advent of computers after 1945. These dates are important. But fundamentally, the development of computers today has reached AI and Big Data. Perhaps we should define what we are discussing, theory or skills of using OR.

David F. Rogers LP is to OR, just like electrical physics is to electrician skills.

And if I'm wrong, please tell me which is more effective - one of the interior-point method or the ellipsoid method? Or maybe you could more easily tell me how Markov chains are used in the Chapman-Kolmogorov equation.

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Thanks@