# 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.

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

1. Decision Making Environments

1.1 Certainity, uncertainity and risk situations

1.2 Uses of decision trees

1.3 Managerial decision making

2.4 Duality

3.1 Methods of solving the TP problem

3.2 Assignment model and its applications

4. Game Theory

4.1 Concept of a game

4.2 Two person zero-sum game

4.3 Pure and mixed strategy games

4.5 Dominance method and graphical method for solving mixed strategy game

5. Sequencing Problem

5.1 Johnsons algorithm for n jobs and 2 or 3 machines

5.2 2 jobs and m machines problem

6. Queuing Theory

6.1 Characteristics of M/M/1 Queue model

6.2 Application of Poisson and Exponential distribution in estimating arrival and service rate

6.2 Application of Queue model for better service to the customers

7. Replacement Problems

7.1 Replacement of assets that deteriorate with time

7.2 Replacement of items that deteriorate suddenly

8. Project Management

8.1 Rules for drawing the network diagram

8.2 Applications of CPM and PERT techniques in project plannning and control

8.3 Crashing and resource leveling of operations

8.4 Simulation and its uses in Queuing theory and materials management

9. Network Models