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

1. Decision Making Environments
   1. Certainty, uncertainty and risk situations
   2. Uses of decision trees
   3. Managerial decision making
2. Linear Programming
   1. Graphical LP solution
   2. The Simplex Method of solving LPP
   3. Sensitivity analysis
   4. Duality
3. Transportation and Assignment Problem
   1. Methods of solving the TP problem
   2. Assignment model and its applications
4. Five Element Theory
5. Game Theory
   1. Concept of a game
   2. Two person zero-sum game
   3. Pure and mixed strategy games
   4. Saddle point, Odds method
   5. Dominance method and graphical method for solving mixed strategy game
6. Sequencing Problem
   1. Johnson's algorithm for n jobs and 2 or 3 machines
   2. Jobs and m machines problem
7. Queuing Theory
   1. Characteristics of M/M/1 Queue model
   2. Application of Poisson and Exponential distribution in estimating arrival and service rate
   3. Application of Queue model for better service to the customers
8. Replacement Problems
   1. Replacement of assets that deteriorate with time
   2. Replacement of items that deteriorate suddenly
9. Project Management
   1. Rules for drawing the network diagram
   2. Applications of CPM and PERT techniques in project planning and control
   3. Crashing and resource leveling of operations
   4. Simulation and its uses in Queuing theory and materials management
10. Network Models
11. Markov Models
12. Neural Networks

Resources

• Operations Research, by Hamdy Taha.
• Real cases of using Operations Research

See also

• Graph Theory