# Operations research

#### Background to the schools Wikipedia

Operations Research (OR) in the US, and Operational Research in the UK, is an interdisciplinary branch of applied 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.

## Overview

The terms operations research and management science are often used synonymously. When a distinction is drawn, management science generally implies a closer relationship to the problems of business management. Operations research also closely relates to Industrial engineering. Industrial engineering takes more of an engineering point of view, and industrial engineers typically consider Operations Research (OR) techniques to be a major part of their toolset.

Some of the primary tools used by operations researchers are statistics, optimization, stochastics, queuing theory, game theory, graph theory, decision analysis, and simulation. Because of the computational nature of these fields, OR also has ties to computer science, and operations researchers regularly use custom-written or off-the-shelf software.

Operations research is distinguished by its frequent use to examine an entire system, rather than concentrating only on specific elements (though this is often done as well). An operations researcher faced with a new problem is expected to determine which techniques are most appropriate given the nature of the system, the goals for improvement, and constraints on time and computing power. For this and other reasons, the human element of OR is vital. Like any other tools, OR techniques cannot solve problems by themselves.

Scope of operations research

A few examples of applications in which operations research is currently used include:

• designing the layout of a factory for efficient flow of materials
• constructing a telecommunications network at low cost while still guaranteeing QoS (quality of service) or QoE (Quality of Experience) if particular connections become very busy or get damaged
• road traffic management and 'one way' street allocations i.e. allocation problems.
• determining the routes of school buses (or city buses) so that as few buses are needed as possible
• designing the layout of a computer chip to reduce manufacturing time (therefore reducing cost)
• managing the flow of raw materials and products in a supply chain based on uncertain demand for the finished products
• efficient messaging and customer response tactics
• roboticizing or automating human-driven operations processes
• globalizing operations processes in order to take advantage of cheaper materials, labor, land or other productivity inputs
• managing freight transportation and delivery systems (Examples: LTL Shipping, intermodal freight transport)
• scheduling:
• personnel staffing
• manufacturing steps
• network data traffic: these are known as queueing models or queueing systems.
• sports events and their television coverage
• blending of raw materials in oil refineries

Operations research is also used extensively in government where evidence-based policy is used.

## History

Some say that Charles Babbage (1791-1871) is the "father of operations research" because his research into the cost of transportation and sorting of mail led to England's universal " Penny Post" in 1840. The modern field of operations research arose during World War II. Scientists in the United Kingdom including Patrick Blackett, Cecil Gordon, C. H. Waddington, Owen Wansbrough-Jones and Frank Yates, and in the United States with George Dantzig looked for ways to make better decisions in such areas as logistics and training schedules. After the war it began to be applied to similar problems in industry.

Blackett's team made a number of crucial analyses which aided the war effort. Britain introduced the convoy system to reduce shipping losses, but while the principle of using warships to accompany merchant ships was generally accepted, it was unclear whether it was better for convoys to be small or large. Convoys travel at the speed of the slowest member, so small convoys can travel faster. It was also argued that small convoys would be harder for German U-boats to detect. On the other hand, large convoys could deploy more warships against an attacker. Blackett's staff showed that the losses suffered by convoys depended largely on the number of escort vessels present, rather than on the overall size of the convoy. Their conclusion, therefore, was that a few large convoys are more defensible than many small ones.

In another piece of work, Blackett's team analysed a report of a survey carried out by RAF Bomber Command. For the survey, Bomber Command inspected all bombers returning from bombing raids over Germany over a particular period. All damage inflicted by German air defenses was noted and the recommendation was given that armour be added in the most heavily damaged areas. Their suggestion to remove some of the crew so that an aircraft loss would result in fewer personnel loss was rejected by RAF command. Blackett's team instead made the surprising and counter-intuitive recommendation that the armour be placed in the areas which were completely untouched by damage, according to the survey. They reasoned that the survey was biased, since it only included aircraft that successfully came back from Germany. The untouched areas were probably vital areas, which, if hit, would result in the loss of the aircraft.

When the Germans organised their air defences into the Kammhuber Line, it was realised that if the RAF bombers were to fly in a bomber stream they could overwhelm the night fighters who flew in individual cells directed to their targets by ground controllers. It was then a matter of calculating the statistical loss from collisions against the statistical loss from night fighters to calculate how close the bombers should fly to minimise RAF losses.

It is known as "operational research" in the United Kingdom ("operational analysis" within the UK military and UK Ministry of Defence, where OR stands for "Operational Requirement") and as "operations research" in most other English-speaking countries, though OR is a common abbreviation everywhere. With expanded techniques and growing awareness, OR is no longer limited to only operations, and the proliferation of computer data collection has relieved analysts of much of the more mundane research. But the OR analyst must still know how a system operates, and learn to perform even more sophisticated research than ever before. In every sense the name OR still applies, more than a half century later.

## Societies and journals

Societies

The International Federation of Operational Research Societies is an umbrella organization for operations research societies worldwide. Significant among these are the:

• Institute for Operations Research and the Management Sciences (INFORMS)
• Operational Research Society.
• EURO is the association of European Operational Research Societies.
• CORS is the Canadian Operations Research Society.
• ASOR is the Australian Society for Operations Research.
• MORS is the Military Operations Research Society: based in the United States since 1966 with the objective of enhancing the quality and usefulness of military operations research analysis in support of defense decisions.
• ORSNZ is the Operations Research Society of New Zealand.
• ORSP is the Operations Research Society of the Philippines
• ORSI the Operational Research Society of India. and
• ORSSA the Operations Research Society of South Africa.

In 2004 INFORMS began an initiative to better market the OR profession, including a website entitled The Science of Better which provides an introduction to OR and examples of successful applications of OR to industrial problems.

Journals

INFORMS publishes 12 scholarly journals about operations research, including the Top 2 journals in their class, according to 2005 Journal Citation Reports. include:

• Decision Analysis,
• Information Systems Research,
• INFORMS Journal on Computing,
• Interfaces,
• Management Science,
• Manufacturing & Service Operations Management,
• Marketing Science,
• Mathematics of Operations Research,
• Operations Research,
• Organization Science,
• Transportation Science, and
• INFORMS Transactions on Education: open access journal.
Other journals
• European Journal of Operational Research (EJOR): Founded in 1975 and is presently by far the largest Operational Research journal in the world with its around 9,000 pages of published papers per year. In 2004, its total number of cites was the second largest amongst Operational Research and Management Science journals.
• Journal of The Operational Research Society (JORS): is an official journal of The OR Society.
• INFOR Journal: published and sponsored by the Canadian Operational Research Society.
• Opsearch: official journal of the Operational Research Society of India.
• TOP: Official journal of the Spanish Society of Statistics and Operations Research.
• JDMS: The Journal of Defense Modeling and Simulation: Applications, Methodology, Technology. Quarterly journal devoted to advancing the science of modeling and simulation as it relates to the military and defense.