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. A mathematical model is an abstract model that uses mathematical language to describe the behaviour of a system. ... A graph of a normal bell curve showing statistics used in educational assessment and comparing various grading methods. ... Flowcharts are often used to represent algorithms. ... A graph illustrating local min/max and global min/max points In mathematics, maxima and minima, also known as extrema, are points in the domain of a function at which the function takes the largest (maximum), or smallest (minimum) value either within a given neighbourhood (local extrema), or on the... A graph illustrating local min/max and global min/max points In mathematics, maxima and minima, also known as extrema, are points in the domain of a function at which the function takes the largest (maximum), or smallest (minimum) value either within a given neighbourhood (local extrema), or on the...

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. Management science, or MS, is the discipline of using mathematics, and other analytical methods, to help make better business decisions. ... Management (from Old French ménagement the art of conducting, directing, from Latin manu agere to lead by the hand) characterises the process of leading and directing all or part of an organization, often a business, through the deployment and manipulation of resources (human, financial, material, intellectual or intangible). ...

Operations research also closely relates to Industrial engineering. Industrial engineering takes more of an engineering point of view, and industrial engineers typically consider OR techniques to be a major part of their toolset. This article needs additional references or sources to facilitate its verification. ...

Some of the primary tools used by operations researchers are statistics, optimization, stochastics, queueing 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. A graph of a normal bell curve showing statistics used in educational assessment and comparing various grading methods. ... In mathematics, the term optimization, or mathematical programming, refers to the study of problems in which one seeks to minimize or maximize a real function by systematically choosing the values of real or integer variables from within an allowed set. ... In the mathematics of probability, a stochastic process can be thought of as a random function. ... Queueing theory (also commonly spelled queuing theory) is the mathematical study of waiting lines (or queues). ... Game theory is often described as a branch of applied mathematics and economics that studies situations where multiple players make decisions in an attempt to maximize their returns. ... A pictorial representation of a graph In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. ... Decision analysis (DA) is the discipline comprising the philosophy, theory, methodology, and professional practice necessary to address important decisions in a formal manner. ... This article is about the general term. ... Computer science, or computing science, is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ...

Operations research is distinguished by its ability to look at and improve 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
  • project tasks
  • network data traffic: these are known as queuing models or queuing 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. This article or section does not cite any references or sources. ... A telecommunications network is a network of telecommunications links arranged so that messages may be passed from one part of the network to another over multiple links. ... The abbreviation QOS could refer to one of several things: Quality of service, a measure of the reliability of a computer network Queen of the South F.C., a Scottish football club Quarterdeck Office Systems, a software company that is now part of Symantec This is a disambiguation page &#8212... Quality of Experience (QoE), In business terminology QoE is also known as Quality of User Experience, and is a subjective measure of a customers experiences with a vendor. ... An integrated circuit (IC) is a thin chip consisting of at least two interconnected semiconductor devices, mainly transistors, as well as passive components like resistors. ... Manufacturing (from Latin manu factura, making by hand) is the use of tools and labor to make things for use or sale. ... A supply chain, logistics network, or supply network is a coordinated system of organizations, people, activities, information and resources involved in moving a product or service in physical or virtual manner from supplier to customer. ... Freight is a term used to classify the transportation of cargo and is typically a commercial process. ... Less-Than-Truckload (LTL) shipping is the transportation of relatively small freight. ... An intermodal train carrying both shipping containers and highway semi-trailers in piggyback service, on flatcars, passes through the Cajon Pass in February, 1995. ... Look up scheduling in Wiktionary, the free dictionary. ... Project Management is the discipline of organizing and managing resources (e. ... Evidence-based policy is the idea that all public policy should be informed by rigorously established objective evidence. ...

History

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 (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. Combatants Allied powers: China France Great Britain Soviet Union United States and others Axis powers: Germany Italy Japan and others Commanders Chiang Kai-shek Charles de Gaulle Winston Churchill Joseph Stalin Franklin Roosevelt Adolf Hitler Benito Mussolini Hideki Tōjō Casualties Military dead: 17,000,000 Civilian dead: 33,000... Patrick Maynard Stuart Blackett, Baron Blackett (November 18, 1897—July 13, 1974) was a British experimental physicist known for his work on cloud chambers, cosmic rays, and paleomagnetism. ... Conrad Hal Waddington (1905 — 1975), known to his friends as Wad, was a developmental biologist, paleontologist, geneticist, embryologist and philosopher. ... Sir Owen Haddon Wansbrough-Jones KBE, CB (born 1906, Long Stratton, Norfolk, England, died 1983, Long Stratton), was a leading academic chemist and soldier whose career included serving as Chief Scientist to the British Ministry of Supply. ... Frank Yates Frank Yates (1902 - 1994) was one of the pioneers of 20th century statistics. ... George Bernard Dantzig (8 November 1914 – 13 May 2005) was a mathematician who introduced the simplex algorithm and is considered the Father of linear programming. He was the recipient of many honors, including the National Medal of Science in 1975, the John von Neumann Theory Prize in 1974. ... Look up Logistics in Wiktionary, the free dictionary. ...

World War II

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 clearly showed that:^{[citation needed]} A convoy is a group of vehicles traveling together for mutual support. ... This article does not cite any references or sources. ... Cargo ship or freighter is any sort of ship that carries goods and materials from one port to another. ... U-boat is also a nickname for some diesel locomotives built by GE; see List of GE locomotives October 1939. ...

• Large convoys were more efficient
• The probability of detection by U-boat was statistically unrelated to the size of the convoy
• Slow convoys were at greater risk (though considered overall, large convoys were still to be preferred)

In another piece of work, Blackett's team analysed a report of a survey carried out by RAF Bomber Command.^{[citation needed]} 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. Bomber Command badge RAF Bomber Command was the organisation that controlled the RAFs bomber forces. ... Branch insignia of the U.S. Army Air Defense Artillery, representing a missile surmounting two crossed field guns The U.S. Army Air Defense Artillery was changed from Anti-Aircraft Artillery (part of the Field Artillery), into a separate branch on On 20 June 1968. ...

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.^{[citation needed]} Something is counter-intuitive if it does not seem likely to be true using the tool of human intuition or gut-feeling to perceive reality. ...

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.[1] The Kammhuber Line was the name given to the German night air defense system established in July 1940 by Colonel Josef Kammhuber. ... A map of part of the Kammhuber Line showing the belt and nightfighter boxes through which the bomber stream flew The bomber stream was a tactic developed by the Royal Air Force (RAF) Bomber Command to overwhelm the German aerial defences of the Kammhuber Line during World War II. The...

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. Main Building - The Headquarters of the Ministry of Defence, Whitehall, Westminster, London Tri-service badge of the UK armed forces The Ministry of Defence (MoD) is the United Kingdom government department responsible for implementation of government defence policy and the headquarters of the UK military. ...

The profession of operations research

Societies

The International Federation of Operational Research Societies (IFORS) is an umbrella organization for operations research societies worldwide. Significant among these are the Institute for Operations Research and the Management Sciences (INFORMS) and the Operational Research Society (ORS). EURO is the association of European Operational Research Societies (EURO). CORS is the Canadian Operations Research Society (CORS). ASOR is the Australian Society for Operations Research (ASOR). MORS is the Military Operations Research Society (MORS)--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 (ORSNZ). ORSP is the Operations Research Society of the Philippines (ORSP), ORSI the Operational Research Society of India (ORSI) and ORSSA the Operations Research Society of South Africa (ORSSA). An umbrella organization is an association of (often related, industry-specific) institutions, who work together formally to coordinate activities or pool resources. ... INFORMS is The Institute for Operations Research and the Management Sciences. ...

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. INFORMS Journals include Decision Analysis, Information Systems Research, INFORMS Journal on Computing, Interfaces, Management Science, Manufacturing & Service Operations Management, Marketing Science, Mathematics of OR, Operations Research, Organization Science, Transportation Science, and the open access journal INFORMS Transactions on Education.

The European Journal of Operational Research (EJOR) was 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. Year 1975 (MCMLXXV) was a common year starting on Wednesday (link will display full calendar) of the Gregorian calendar. ... Year 2004 (MMIV) was a leap year starting on Thursday of the Gregorian calendar. ...

The Journal of The Operational Research Society (JORS) is an official journal of The OR Society.

INFOR Journal is published and sponsored by the Canadian Operational Research Society.

Opsearch is an official journal of the Operational Research Society of India.

TOP[2] is an official journal of the Spanish Society of Statistics and Operations Research.

Textbooks

• Ecker, Joseph G. and Kupferschmid, Michael "Introduction to Operations Research", Krieger Pub Co ISBN 0-89464-576-5
• Hillier, Frederick S. and Lieberman, Gerald J. "Introduction to Operations Research", McGraw-Hill : Boston MA. Eighth edition. International edition. (2005) ISBN 0-07-321114-1
• Taha, Hamdy A. "Operations Research: An Introduction", Prentice Hall. Eighth edition. (2006). ISBN-10: 0131889230 ISBN 978-0131889231.
• Winston, Wayne "Operations Research: Applications and Algorithms". Duxbury Press; 4th. Edition. (2003) ISBN-10: 0534380581 ISBN 978-0534380588

See also

INFORMS is The Institute for Operations Research and the Management Sciences. ... Anthony Stafford Beer (September 25, 1926 - August 23, 2002) was a British theorist, academic, and consultant, best known for his work in the fields of operational research and management cybernetics. ... George Bernard Dantzig (8 November 1914 – 13 May 2005) was a mathematician who introduced the simplex algorithm and is considered the Father of linear programming. He was the recipient of many honors, including the National Medal of Science in 1975, the John von Neumann Theory Prize in 1974. ... Management science, or MS, is the discipline of using mathematics, and other analytical methods, to help make better business decisions. ... Systems thinking is an approach to integration that is based on the belief that the component parts of a system will act differently when isolated from the systems environment or other parts of the system. ... This article does not cite its references or sources. ... In mathematics, the term optimization, or mathematical programming, refers to the study of problems in which one seeks to minimize or maximize a real function by systematically choosing the values of real or integer variables from within an allowed set. ... In mathematics, linear programming (LP) problems involve the optimization of a linear objective function, subject to linear equality and inequality constraints. ... In mathematics and computer science, dynamic programming is a method of solving problems exhibiting the properties of overlapping subproblems and optimal substructure (described below) that takes much less time than naive methods. ... Managerial economics (also called business economics), is a branch of economics that applies microeconomic analysis to specific business decisions. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... This article is about the general term. ... System Dynamics is an approach to understanding the behaviour of complex systems over time. ... Decision analysis (DA) is the discipline comprising the philosophy, theory, methodology, and professional practice necessary to address important decisions in a formal manner. ... Optimal Maintenance is the discipline within Operations Research concerned with maintaining a system in a manner that maximizes profit or minimizes cost. ... This article needs additional references or sources to facilitate its verification. ... Look up scheduling in Wiktionary, the free dictionary. ... In the mathematics of probability, a stochastic process can be thought of as a random function. ... Morphological analysis (or General Morphological Analysis) is a method developed by Fritz Zwicky (1967, 1969) for exploring all the possible solutions to a multi-dimensional, non-quantified problem complex. ... Search Based Software Engineering (SBSE) is an approach to apply metaheuristic search techniques like genetic algorithms, simulated annealing and tabu search to software engineering problems. ... A real option is the right and the obligation, to undertake some business decision, typically the option to make a capital investment. ...

References