# Operation Research and Historical Development in Optimizations

## Operation Research

Operation Research aims to provide a framework to model complex decision-making problems that arise in engineering, business & analytics, and the mathematical sciences and investigates methods for analyzing and solving them.

The most common solution techniques include mathematical optimization, simulation, queuing theory, Markov decision process, and data analysis, all of which use mathematical models to describe the system.

### Definitions

i) Operation Research (OR) is the art of winning the war without actually fighting.

ii) OR is a scientific approach to problem-solving for executive management.

iii) OR is a systematic method-oriented study of the basic structure characteristics, functions, and relationships of an organization to provide the executive and a sound, scientific basis for decision-making.

iv) OR is the art of giving bad answers to problems to which otherwise worse answers are given.

v) OR is a scientific method of providing executives with a quantitative basis for decisions regarding the operations under their control.

### Historical Development of Operation Research

#### i) Issac Newton (1642-1727)

It is the development of differential calculus methods of optimization.

#### ii) Joseph-Louis Language (1736-1813)

Calculus of variations, minimization of functionals, methods of optimization for constrained problems.

#### iii) Augustin-Louis Cauchy (1789-1857)

Solution by direct substitution, steepest descent method for unconstrained optimization.

#### iv) George Bernard Dantizing (1914-2005)

Linear Programming and Simplex Method (1947)

#### v) Albert William Tucker (1905-1995)

Necessary and sufficient conditions for the optimal solutions of programming problems, non-linear programming.

#### OR

i) The main origin of operation research was during the second world war. At that time the military management in England called upon a team of scientists to study the strategic & tactical problems related to air and lead defense of the country.

ii) Their mission was to formulate specific proposals and plans for aiding the decisions on optimal utilization of scare military resources and efforts and to implement the decisions effectively.

iii) The OR team was not actually engaged in military operations and in fighting the war. They were only advisors and significantly instrumental in winning the war to the extent that the scientific and systematic approaches involves in Operation Research provided good intellectual support to the strategic initiatives of the military commands.

iv) Hence OR can be associated with: "An art of winning the war without actually fighting it".

v) As the name implies "Operation Research" was invented because the team was dealing with research on (military) operations.

vi) The work of OR teams was given various names in the United States: Operational Analysis, Operation Evaluation, Operation Research, System Analysis, System Evaluation, System Research, and Management Science.