Brief History Role of Mathematical Models

Model Building

Model Types

Linear Programming

Queuing Theory

Psychology of Queuing

Queuing Systems & Formula

Network Routing

Inventory and Yield Management

Simulation

Multi-Attribute Utility Theory (MAUT)

Integer Programming

Decision Analysis – Decision Trees

Operations research (OR) is a scientific approach to analyzing problems and making decisions. OR professionals aim to provide rational bases for decision making by seeking to understand and structure complex situations and to use this understanding to predict system behavior and improve system performance. Much of this work is done using analytical and numerical techniques to develop and manipulate mathematical and computer models of organizational systems composed of people, machines, and procedures. The field of Operations Research (called operational research in Great Britain) has its roots in the years just prior to World War II as the British prepared for the anticipated air war. In 1937 field tests started on what was later to be called radar. In 1938 experiments began to explore how the information provided by radar should be used to direct deployment and use of fighter planes. Until this time, the word experiment conjured up the picture of a scientist carrying out a controlled experiment in a laboratory. In contrast, the multi-disciplinary team of scientists working on this radar-fighter plane project studied the actual operating conditions of these new devices and designed experiments in the field of operations and the new term operations research was born. The team's goal was to derive an understanding of the operations of the complete system of equipment, people, and environmental conditions (e.g. weather, nighttime) and then improve upon it. Their work was an important factor in winning the Battle of Britain and operations research eventually spread to all of the military services. Several of the leaders of this effort were Nobel laureates in their original fields of study. Similar groups of interdisciplinary scientists were later established in the US at the various branches of the armed services. They worked to protect convoys, search for enemy convoys, enhance anti-submarine warfare and improve the effectiveness of bombers. Common elements of their many studies were: data collection, direct observation of operations, a mathematical model, recommendations for improvements and feedback on the impact of the changes. It was this emphasis on seeing how things actually operated in the real-world and applying a scientific approach to improving performance that gave rise to the term operations research. Currently, every branch of the military has its own operations research group that includes both military and civilian personnel. They play a key role in both long-term strategy and weapons development, as well as directing the logistics of actions such as Operation Desert Storm. In addition, the National Security Agency has its own Center for Operations Research. In the 1950s operations research evolved into a profession with the formation of national societies, establishment of journals and academic departments in universities. The use of operations research expanded beyond the military to include both private companies and other governmental organizations. The petrochemical industry was one of the first to broadly embrace operations research to improve the performance of plants, develop natural resources and plan strategy. Today, operations research plays important roles in a variety of industries such as: airline - scheduling planes and crews, pricing tickets, taking reservations, and planning the size of the fleet,

pharmaceutical - R& D management,

logistics companies - routing and planning,

financial services - credit scoring, marketing, and internal operations,

lumber and wood products - managing forests and cutting timber,

local government - deployment of emergency services, and

policy studies and regulation - environmental pollution, air traffic safety, AIDS, and criminal justice policy. As the field evolved, the core moved away from interdisciplinary teams to a focus on the development of mathematical models that can be used to model, improve, and even optimize real-world systems. These mathematical models include both deterministic models such as mathematical programming, routing or network flows and probabilistic models such as queuing, simulation and decision trees. These mathematical modeling techniques form the core curriculum of masters degree and doctoral programs in operations research which can be found in either engineering or business schools. Most mathematics departments also offer one or more introductory operations research courses at the junior or senior undergraduate level.