# Operations Research

Operations research or operational research (OR) is an interdisciplinary branch of mathematics which uses methods like mathematical modeling, statistics, and algorithms to arrive at optimal or good decisions in complex problems which are concerned with optimizing the maxima (profit, faster assembly line, greater crop yield, higher bandwidth, etc) or minima (cost loss, lowering of risk, etc) of some objective function. The eventual intention behind using operations research is to elicit a best possible solution to a problem mathematically, which improves or optimizes the performance of the system.

Optimization aims to find the minimum (or maximum) value of an objective function subject to constraints that represent user preferences and/or limitations imposed by the nature of the question at hand. Research in optimization involves the analysis of such mathematical problems and the design of efficient algorithms for solving them. It is therefore no surprise that optimization, while integral to operations research, has become an indispensable tool in other areas such as statistics, machine learning, computer vision, and computational biology, just to name a few. Optimization technologies are shining examples of how deep mathematical techniques help to provide concrete computational tools for solving a diverse suite of problems.

This book is intended for both mathematics students and also for those interested in the subject from a management point of view.

## Table of contents edit

- Decision Making Environments
- Linear Programming
- Graphical LP solution
- The Simplex Method of solving LPP
- Sensitivity analysis
- Duality

- Transportation and Assignment Problem
- Five Element Theory
- Game Theory
- Sequencing Problem
- Queuing Theory
- Replacement Problems
- Project Management
- Network Models
- Markov Models
- Neural Networks

## Resources edit

*Operations Research*, by Hamdy Taha.- Real cases of using Operations Research