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Operations research ( en-GB, operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the
initialism An acronym is a word or name formed from the initial components of a longer name or phrase. Acronyms are usually formed from the initial letters of words, as in ''NATO'' (''North Atlantic Treaty Organization''), but sometimes use syllables, as ...
OR, is a discipline that deals with the development and application of analytical methods to improve decision-making. It is considered to be a subfield of mathematical sciences. The term management science is occasionally used as a synonym. Employing techniques from other mathematical sciences, such as modeling,
statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...
, and optimization, operations research arrives at optimal or near-optimal solutions to
decision-making In psychology, decision-making (also spelled decision making and decisionmaking) is regarded as the Cognition, cognitive process resulting in the selection of a belief or a course of action among several possible alternative options. It could be ...
problems. Because of its emphasis on practical applications, operations research has overlap with many other disciplines, notably industrial engineering. Operations research is often concerned with determining the extreme values of some real-world objective: the maximum (of profit, performance, or yield) or minimum (of loss, risk, or cost). Originating in military efforts before World War II, its techniques have grown to concern problems in a variety of industries.


Overview

Operational research (OR) encompasses the development and the use of a wide range of problem-solving techniques and methods applied in the pursuit of improved decision-making and efficiency, such as simulation,
mathematical optimization Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...
, queueing theory and other stochastic-process models, Markov decision processes, econometric methods, data envelopment analysis, ordinal priority approach,
neural networks A neural network is a network or circuit of biological neurons, or, in a modern sense, an artificial neural network, composed of artificial neurons or nodes. Thus, a neural network is either a biological neural network, made up of biological ...
, expert systems, decision analysis, and the analytic hierarchy process. Nearly all of these techniques involve the construction of mathematical models that attempt to describe the system. Because of the computational and statistical nature of most of these fields, OR also has strong ties to computer science and
analytics Analytics is the systematic computational analysis of data or statistics. It is used for the discovery, interpretation, and communication of meaningful patterns in data. It also entails applying data patterns toward effective decision-making. It ...
. Operational researchers faced with a new problem must determine which of these techniques are most appropriate given the nature of the system, the goals for improvement, and constraints on time and computing power, or develop a new technique specific to the problem at hand (and, afterwards, to that type of problem). The major sub-disciplines in modern operational research, as identified by the journal ''Operations Research'', are: * Computing and information technologies * Financial engineering * Manufacturing, service sciences, and
supply chain management In commerce, supply chain management (SCM) is the management of the flow of goods and services including all processes that transform raw materials into final products between businesses and locations. This can include the movement and stor ...
* Policy modeling and public sector work * Revenue management * Simulation *
Stochastic models In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used as mathematical models of systems and phenomena that appea ...
*
Transportation theory (mathematics) In mathematics and economics, transportation theory or transport theory is a name given to the study of optimal transportation and allocation of resources. The problem was formalized by the French mathematician Gaspard Monge in 1781.G. Monge. ''M ...
*
Game theory Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has appli ...
for strategies *
Linear programming Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear function#As a polynomial function, li ...
* Nonlinear programming * Integer programming in
NP-complete problem In computational complexity theory, a problem is NP-complete when: # it is a problem for which the correctness of each solution can be verified quickly (namely, in polynomial time) and a brute-force search algorithm can find a solution by tryi ...
specially for 0-1 integer linear programming for binary * Dynamic programming in
Aerospace engineering Aerospace engineering is the primary field of engineering concerned with the development of aircraft and spacecraft. It has two major and overlapping branches: aeronautical engineering and astronautical engineering. Avionics engineering is si ...
and Economics *
Information theory Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, communication of information. The field was originally established by the works of Harry Nyquist a ...
used in Cryptography,
Quantum computing Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though ...
* Quadratic programming for solutions of Quadratic equation and
Quadratic function In mathematics, a quadratic polynomial is a polynomial of degree two in one or more variables. A quadratic function is the polynomial function defined by a quadratic polynomial. Before 20th century, the distinction was unclear between a polynomial ...


History

In the decades after the two world wars, the tools of operations research were more widely applied to problems in business, industry, and society. Since that time, operational research has expanded into a field widely used in industries ranging from petrochemicals to airlines, finance, logistics, and government, moving to a focus on the development of mathematical models that can be used to analyse and optimize sometimes complex systems, and has become an area of active academic and industrial research.


Historical origins

In the 17th century, mathematicians
Blaise Pascal Blaise Pascal ( , , ; ; 19 June 1623 – 19 August 1662) was a French mathematician, physicist, inventor, philosopher, and Catholic Church, Catholic writer. He was a child prodigy who was educated by his father, a tax collector in Rouen. Pa ...
and
Christiaan Huygens Christiaan Huygens, Lord of Zeelhem, ( , , ; also spelled Huyghens; la, Hugenius; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor, who is regarded as one of the greatest scientists of ...
solved problems involving sometimes complex decisions ( problem of points) by using game-theoretic ideas and
expected values In probability theory, the expected value (also called expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of a l ...
; others, such as Pierre de Fermat and Jacob Bernoulli, solved these types of problems using combinatorial reasoning instead.
Charles Babbage Charles Babbage (; 26 December 1791 – 18 October 1871) was an English polymath. A mathematician, philosopher, inventor and mechanical engineer, Babbage originated the concept of a digital programmable computer. Babbage is considered ...
's research into the cost of transportation and sorting of mail led to England's universal "Penny Post" in 1840, and to studies into the dynamical behaviour of railway vehicles in defence of the GWR's broad gauge. Beginning in the 20th century, study of inventory management could be considered the origin of modern operations research with economic order quantity developed by
Ford W. Harris Ford Whitman Harris (August 8, 1877 – October 27, 1962) was an American production engineer who derived the square-root formula for ordering inventory now known as the economic order quantity, which has appeared in countless academic articles ...
in 1913. Operational research may have originated in the efforts of military planners during World War I (convoy theory and Lanchester's laws). Percy Bridgman brought operational research to bear on problems in physics in the 1920s and would later attempt to extend these to the social sciences. Modern operational research originated at the
Bawdsey Research Station Bawdsey is a village and civil parish in Suffolk, eastern England. Located on the other side of the river Deben from Felixstowe, it had an estimated population of 340 in 2007, reducing to 276 at the Census 2011. Bawdsey Manor is notable as the ...
in the UK in 1937 as the result of an initiative of the station's superintendent, A. P. Rowe and Robert Watson-Watt. Rowe conceived the idea as a means to analyse and improve the working of the UK's early-warning radar system, code-named "
Chain Home Chain Home, or CH for short, was the codename for the ring of coastal Early Warning radar stations built by the Royal Air Force (RAF) before and during the Second World War to detect and track aircraft. Initially known as RDF, and given the off ...
" (CH). Initially, Rowe analysed the operating of the radar equipment and its communication networks, expanding later to include the operating personnel's behaviour. This revealed unappreciated limitations of the CH network and allowed remedial action to be taken. Scientists in the United Kingdom (including
Patrick Blackett Patrick Maynard Stuart Blackett, Baron Blackett (18 November 1897 – 13 July 1974) was a British experimental physicist known for his work on cloud chambers, cosmic rays, and paleomagnetism, winning the Nobel Prize for Physics in 1948. ...
(later Lord Blackett OM PRS),
Cecil Gordon Cecil Gordon (June 21, 1941 – September 19, 2012) was an American stock car racing driver. A competitor in the NASCAR Winston Cup Series between 1968 and 1985, he competed in 449 events without winning a race. NASCAR Career as driver Gordon d ...
, Solly Zuckerman, (later Baron Zuckerman OM, KCB, FRS),
C. H. Waddington Conrad Hal Waddington (8 November 1905 – 26 September 1975) was a British developmental biologist, paleontologist, geneticist, embryologist and philosopher who laid the foundations for systems biology, epigenetics, and evolutionary developme ...
,
Owen Wansbrough-Jones Sir Owen Haddon Wansbrough-Jones KBE, CB (1906, Long Stratton, Norfolk, England – 1983, Long Stratton), was a leading academic chemist and soldier whose career included serving as Chief Scientist to the British Ministry of Supply. Educated at ...
,
Frank Yates Frank Yates FRS (12 May 1902 – 17 June 1994) was one of the pioneers of 20th-century statistics. Biography Yates was born in Manchester, England, the eldest of five children (and only son) of seed merchant Percy Yates and his wife Edith. H ...
,
Jacob Bronowski Jacob Bronowski (18 January 1908 – 22 August 1974) was a Polish-British mathematician and philosopher. He was known to friends and professional colleagues alike by the nickname Bruno. He is best known for developing a humanistic approach to sc ...
and Freeman Dyson), and in the United States ( George Dantzig) looked for ways to make better decisions in such areas as logistics and training schedules.


Second World War

The modern field of operational research arose during World War II. In the World War II era, operational research was defined as "a scientific method of providing executive departments with a quantitative basis for decisions regarding the operations under their control"."Operational Research in the British Army 1939–1945", October 1947, Report C67/3/4/48, UK National Archives file WO291/1301
Quoted on the dust-jacket of: Morse, Philip M, and Kimball, George E, ''Methods of Operation Research'', 1st edition revised, MIT Press & J Wiley, 5th printing, 1954.
Other names for it included operational analysis (UK Ministry of Defence from 1962)UK National Archives Catalogue for WO291
lists a War Office organisation called
Army Operational Research Group Operations research ( en-GB, operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a discipline that deals with the development and application of analytical methods to improve decis ...
(AORG) that existed from 1946 to 1962. "In January 1962 the name was changed to Army Operational Research Establishment (AORE). Following the creation of a unified Ministry of Defence, a tri-service operational research organisation was established: the Defence Operational Research Establishment (DOAE) which was formed in 1965, and it the Army Operational Research Establishment based at West Byfleet."
and quantitative management. During the Second World War close to 1,000 men and women in Britain were engaged in operational research. About 200 operational research scientists worked for the British Army.
Patrick Blackett Patrick Maynard Stuart Blackett, Baron Blackett (18 November 1897 – 13 July 1974) was a British experimental physicist known for his work on cloud chambers, cosmic rays, and paleomagnetism, winning the Nobel Prize for Physics in 1948. ...
worked for several different organizations during the war. Early in the war while working for the
Royal Aircraft Establishment The Royal Aircraft Establishment (RAE) was a British research establishment, known by several different names during its history, that eventually came under the aegis of the Ministry of Defence (United Kingdom), UK Ministry of Defence (MoD), bef ...
(RAE) he set up a team known as the "Circus" which helped to reduce the number of
anti-aircraft artillery Anti-aircraft warfare, counter-air or air defence forces is the battlespace response to aerial warfare, defined by NATO as "all measures designed to nullify or reduce the effectiveness of hostile air action".AAP-6 It includes surface based, ...
rounds needed to shoot down an enemy aircraft from an average of over 20,000 at the start of the Battle of Britain to 4,000 in 1941. In 1941, Blackett moved from the RAE to the Navy, after first working with RAF Coastal Command, in 1941 and then early in 1942 to the
Admiralty Admiralty most often refers to: *Admiralty, Hong Kong * Admiralty (United Kingdom), military department in command of the Royal Navy from 1707 to 1964 *The rank of admiral * Admiralty law Admiralty can also refer to: Buildings *Admiralty, Tr ...
. Blackett's team at Coastal Command's Operational Research Section (CC-ORS) included two future Nobel prize winners and many other people who went on to be pre-eminent in their fields. Freeman Dyson, ''MIT Technology Review'' (1 November 2006)
A Failure of Intelligence: Part I
They undertook a number of crucial analyses that 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 the size of the convoy. Their conclusion was that a few large convoys are more defensible than many small ones. While performing an analysis of the methods used by RAF Coastal Command to hunt and destroy submarines, one of the analysts asked what colour the aircraft were. As most of them were from Bomber Command they were painted black for night-time operations. At the suggestion of CC-ORS a test was run to see if that was the best colour to camouflage the aircraft for daytime operations in the grey North Atlantic skies. Tests showed that aircraft painted white were on average not spotted until they were 20% closer than those painted black. This change indicated that 30% more submarines would be attacked and sunk for the same number of sightings. As a result of these findings Coastal Command changed their aircraft to using white undersurfaces. Other work by the CC-ORS indicated that on average if the trigger depth of aerial-delivered
depth charge A depth charge is an anti-submarine warfare (ASW) weapon. It is intended to destroy a submarine by being dropped into the water nearby and detonating, subjecting the target to a powerful and destructive Shock factor, hydraulic shock. Most depth ...
s were changed from 100 to 25 feet, the kill ratios would go up. The reason was that if a U-boat saw an aircraft only shortly before it arrived over the target then at 100 feet the charges would do no damage (because the U-boat wouldn't have had time to descend as far as 100 feet), and if it saw the aircraft a long way from the target it had time to alter course under water so the chances of it being within the 20-foot kill zone of the charges was small. It was more efficient to attack those submarines close to the surface when the targets' locations were better known than to attempt their destruction at greater depths when their positions could only be guessed. Before the change of settings from 100 to 25 feet, 1% of submerged U-boats were sunk and 14% damaged. After the change, 7% were sunk and 11% damaged; if submarines were caught on the surface but had time to submerge just before being attacked, the numbers rose to 11% sunk and 15% damaged. Blackett observed "there can be few cases where such a great operational gain had been obtained by such a small and simple change of tactics". Bomber Command's Operational Research Section (BC-ORS), analyzed a report of a survey carried out by
RAF Bomber Command RAF Bomber Command controlled the Royal Air Force's bomber forces from 1936 to 1968. Along with the United States Army Air Forces, it played the central role in the strategic bombing of Germany in World War II. From 1942 onward, the British bo ...
. For the survey, Bomber Command inspected all bombers returning from bombing raids over Germany over a particular period. All damage inflicted by German
air defences Anti-aircraft warfare, counter-air or air defence forces is the battlespace response to aerial warfare, defined by NATO as "all measures designed to nullify or reduce the effectiveness of hostile air action".AAP-6 It includes surface based, ...
was noted and the recommendation was given that armour be added in the most heavily damaged areas. This recommendation was not adopted because the fact that the aircraft were able to return with these areas damaged indicated the areas were not vital, and adding armour to non-vital areas where damage is acceptable reduces aircraft performance. Their suggestion to remove some of the crew so that an aircraft loss would result in fewer personnel losses, was also rejected by RAF command. Blackett's team made the logical recommendation that the armour be placed in the areas which were completely untouched by damage in the bombers which returned. They reasoned that the survey was biased, since it only included aircraft that returned to Britain. The areas untouched in returning aircraft were probably vital areas, which, if hit, would result in the loss of the aircraft. This story has been disputed, with a similar damage assessment study completed in the US by the
Statistical Research Group The Statistical Research Group (SRG) was a research group at Columbia University focused on military problems during World War II. Abraham Wald, Allen Wallis, Herbert Solomon, Frederick Mosteller, George Stigler and Milton Friedman were all part o ...
at Columbia University, the result of work done by Abraham Wald. When Germany organized its air defences into the Kammhuber Line, it was realized by the British 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 minimize RAF losses. The "exchange rate" ratio of output to input was a characteristic feature of operational research. By comparing the number of flying hours put in by Allied aircraft to the number of U-boat sightings in a given area, it was possible to redistribute aircraft to more productive patrol areas. Comparison of exchange rates established "effectiveness ratios" useful in planning. The ratio of 60 mines laid per ship sunk was common to several campaigns: German mines in British ports, British mines on German routes, and United States mines in Japanese routes. Operational research doubled the on-target bomb rate of
B-29 The Boeing B-29 Superfortress is an American four-engined propeller-driven heavy bomber, designed by Boeing and flown primarily by the United States during World War II and the Korean War. Named in allusion to its predecessor, the B-17 Fly ...
s bombing Japan from the Marianas Islands by increasing the training ratio from 4 to 10 percent of flying hours; revealed that wolf-packs of three United States submarines were the most effective number to enable all members of the pack to engage targets discovered on their individual patrol stations; revealed that glossy enamel paint was more effective camouflage for night fighters than traditional dull camouflage paint finish, and a smooth paint finish increased airspeed by reducing skin friction. On land, the operational research sections of the Army Operational Research Group (AORG) of the
Ministry of Supply The Ministry of Supply (MoS) was a department of the UK government formed in 1939 to co-ordinate the supply of equipment to all three British armed forces, headed by the Minister of Supply. A separate ministry, however, was responsible for aircr ...
(MoS) were landed in Normandy in 1944, and they followed British forces in the advance across Europe. They analyzed, among other topics, the effectiveness of artillery, aerial bombing and anti-tank shooting.


After World War II

In 1947 under the auspices of the British Association, a symposium was organised in
Dundee Dundee (; sco, Dundee; gd, Dùn Dè or ) is Scotland's fourth-largest city and the 51st-most-populous built-up area in the United Kingdom. The mid-year population estimate for 2016 was , giving Dundee a population density of 2,478/km2 or ...
. In his opening address Watson-Watts offered a definition of the aims of OR: :"to examine quantitatively whether the user organization is getting from the operation of its equipment the best attainable contribution to its overall objective." With expanded techniques and growing awareness of the field at the close of the war, operational research was no longer limited to only operational, but was extended to encompass equipment procurement, training, logistics and infrastructure. Operations Research also grew in many areas other than the military once scientists learned to apply its principles to the civilian sector. With the development of the simplex algorithm for
linear programming Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear function#As a polynomial function, li ...
in 1947 and the development of computers over the next three decades, Operations Research can now solve problems with hundreds of thousands of variables and constraints. Moreover, the large volumes of data required for such problems can be stored and manipulated very efficiently." Much of operations research (modernly known as 'analytics') relies upon stochastic variables and a therefore access to truly random numbers. Fortunately the cybernetics field also required the same level of randomness. The development of increasingly better random number generators has been a boon to both disciplines. Modern applications of operations research include city planning, football strategies, emergency planning, optimizing all facets of industry and economy, and undoubtedly with the likelihood of the inclusion of terrorist attack planning and definitely counter-terrorist attack planning. More recently, the research approach of operations research, which dates back to the 1950s, has been criticized for being collections of mathematical models but lacking an empirical basis of data collection for applications. How to collect data is not presented in the textbooks. Because of the lack of data, there are also no computer applications in the textbooks.


Problems addressed

* critical path analysis or project planning: identifying those processes in a multiple-dependancy project which affect the overall duration of the project *
Floorplanning In electronic design automation, a floorplan of an integrated circuit is a schematics representation of tentative placement of its major functional blocks. In modern electronic design process floorplans are created during the floorplanning de ...
: designing the layout of equipment in a factory or components on a
computer chip An integrated circuit or monolithic integrated circuit (also referred to as an IC, a chip, or a microchip) is a set of electronic circuits on one small flat piece (or "chip") of semiconductor material, usually silicon. Large numbers of tiny ...
to reduce manufacturing time (therefore reducing cost) *
Network optimization Network, networking and networked may refer to: Science and technology * Network theory, the study of graphs as a representation of relations between discrete objects * Network science, an academic field that studies complex networks Mathematics ...
: for instance, setup of telecommunications or power system networks to maintain quality of service during outages * Resource allocation problems * Facility location * Assignment Problems: **
Assignment problem The assignment problem is a fundamental combinatorial optimization problem. In its most general form, the problem is as follows: :The problem instance has a number of ''agents'' and a number of ''tasks''. Any agent can be assigned to perform any ta ...
** Generalized assignment problem **
Quadratic assignment problem The quadratic assignment problem (QAP) is one of the fundamental combinatorial optimization problems in the branch of optimization or operations research in mathematics, from the category of the facilities location problems first introduced by Ko ...
**
Weapon target assignment problem The weapon target assignment problem (WTA) is a class of combinatorial optimization problems present in the fields of optimization and operations research. It consists of finding an optimal assignment of a set of weapons of various types to a set o ...
*
Bayesian search theory Bayesian search theory is the application of Bayesian statistics to the search for lost objects. It has been used several times to find lost sea vessels, for example USS Scorpion (SSN-589), USS ''Scorpion'', and has played a key role in the recover ...
: looking for a target * Optimal search *
Routing Routing is the process of selecting a path for traffic in a network or between or across multiple networks. Broadly, routing is performed in many types of networks, including circuit-switched networks, such as the public switched telephone netw ...
, such as determining the routes of buses so that as few buses are needed as possible *
Supply chain management In commerce, supply chain management (SCM) is the management of the flow of goods and services including all processes that transform raw materials into final products between businesses and locations. This can include the movement and stor ...
: managing the flow of raw materials and products based on uncertain demand for the finished products * Project production activities: managing the flow of work activities in a capital project in response to system variability through operations research tools for variability reduction and buffer allocation using a combination of allocation of capacity, inventory and time * Efficient messaging and customer response tactics * Automation: automating or integrating robotic systems in human-driven operations processes * Globalization: globalizing operations processes in order to take advantage of cheaper materials, labor, land or other productivity inputs * Transportation: managing freight transportation and delivery systems (Examples: LTL shipping, intermodal freight transport, travelling salesman problem,
driver scheduling problem The driver scheduling problem (DSP) is type of problem in operations research and theoretical computer science. The DSP consists of selecting a set of duties (assignments) for the drivers or pilots of vehicles (e.g., buses, trains, boats, or planes ...
) * Scheduling: ** Personnel staffing ** Manufacturing steps ** Project tasks ** Network data traffic: these are known as
queueing model Queueing theory is the mathematical study of waiting lines, or queues. A queueing model is constructed so that queue lengths and waiting time can be predicted. Queueing theory is generally considered a branch of operations research because the ...
s or queueing systems. ** Sports events and their television coverage * Blending of raw materials in oil refineries * Determining optimal prices, in many retail and B2B settings, within the disciplines of
pricing science Pricing science is the application of social and business science methods to the problem of setting prices. Methods include economic modeling, statistics, econometrics, mathematical programming. This discipline had its origins in the development ...
*
Cutting stock problem In operations research, the cutting-stock problem is the problem of cutting standard-sized pieces of stock material, such as paper rolls or sheet metal, into pieces of specified sizes while minimizing material wasted. It is an optimization problem ...
: Cutting small items out of bigger ones. Operational research is also used extensively in government where
evidence-based policy Evidence-based policy is an idea in public policy proposing that policy decisions should be based on, or informed by, rigorously established objective evidence. The implied contrast is with policymaking based on ideology, 'common sense,' anecd ...
is used.


Management science

In 1967 Stafford Beer characterized the field of management science as "the business use of operations research". Like operational research itself, management science (MS) is an interdisciplinary branch of applied mathematics devoted to optimal decision planning, with strong links with economics, business, engineering, and other sciences. It uses various scientific research-based principles, strategies, and analytical methods including
mathematical model A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, ...
ing, statistics and
numerical algorithm Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods th ...
s to improve an organization's ability to enact rational and meaningful management decisions by arriving at optimal or near optimal solutions to sometimes complex decision problems. Management scientists help businesses to achieve their goals using the scientific methods of operational research. The management scientist's mandate is to use rational, systematic, science-based techniques to inform and improve decisions of all kinds. Of course, the techniques of management science are not restricted to business applications but may be applied to military, medical, public administration, charitable groups, political groups or community groups. Management science is concerned with developing and applying
models A model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a measure. Models c ...
and concepts that may prove useful in helping to illuminate management issues and solve managerial problems, as well as designing and developing new and better models of organizational excellence.What is Management Science?
Lancaster University, 2008. Retrieved 5 June 2008.
The application of these models within the corporate sector became known as management science.
The University of Tennessee, 2006. Retrieved 5 June 2008.


Related fields

Some of the fields that have considerable overlap with Operations Research and Management Science include: * Business analytics * Computer science * Data mining/
Data science Data science is an interdisciplinary field that uses scientific methods, processes, algorithms and systems to extract or extrapolate knowledge and insights from noisy, structured and unstructured data, and apply knowledge from data across a br ...
/
Big data Though used sometimes loosely partly because of a lack of formal definition, the interpretation that seems to best describe Big data is the one associated with large body of information that we could not comprehend when used only in smaller am ...
* Decision analysis *
Decision intelligence Decision intelligence is an engineering discipline that augments data science with theory from social science, decision theory, and managerial science. Its application provides a framework for best practices in organizational decision-making ...
* Engineering * Financial engineering * Forecasting *
Game theory Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has appli ...
* Geography/
Geographic information science Geographic information science or geographical information science (GIScience or GISc) is the scientific discipline that studies geographic information, including how it represents phenomena in the real world, how it represents the way humans unders ...
* Graph theory * Industrial engineering * Inventory Control * Logistics * Mathematical modeling *
Mathematical optimization Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...
* Probability and
statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...
* Project management *
Policy analysis Policy analysis is a technique used in the public administration sub-field of political science to enable civil servants, nonprofit organizations, and others to examine and evaluate the available options to implement the goals of laws and elected ...
* Queuing Theory * Simulation * Social network/ Transportation forecasting models *
Stochastic processes In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used as mathematical models of systems and phenomena that appe ...
*
Supply chain management In commerce, supply chain management (SCM) is the management of the flow of goods and services including all processes that transform raw materials into final products between businesses and locations. This can include the movement and stor ...
*
Systems engineering Systems engineering is an interdisciplinary field of engineering and engineering management that focuses on how to design, integrate, and manage complex systems over their enterprise life cycle, life cycles. At its core, systems engineering util ...


Applications

Applications are abundant such as in airlines, manufacturing companies,
service organization A service club or service organization is a voluntary nonprofit organization where members meet regularly to perform charitable works either by direct hands-on efforts or by raising money for other organizations. A service club is defined firstl ...
s, military branches, and government. The range of problems and issues to which it has contributed insights and solutions is vast. It includes: * Scheduling (of airlines, trains, buses etc.) * Assignment (assigning crew to flights, trains or buses; employees to projects; commitment and dispatch of power generation facilities) * Facility location (deciding most appropriate location for new facilities such as warehouse; factory or fire station) * Hydraulics & Piping Engineering (managing flow of water from reservoirs) * Health Services (information and supply chain management) * Game Theory (identifying, understanding; developing strategies adopted by companies) * Urban Design * Computer Network Engineering (packet routing; timing; analysis) * Telecom & Data Communication Engineering (packet routing; timing; analysis) Management is also concerned with so-called 'soft-operational analysis' which concerns methods for
strategic planning Strategic planning is an organization's process of defining its strategy or direction, and making decisions on allocating its resources to attain strategic goals. It may also extend to control mechanisms for guiding the implementation of the st ...
, strategic decision support,
problem structuring methods Problem structuring methods (PSMs) are a group of techniques used to model or to map the nature or structure of a situation or state of affairs that some people want to change. PSMs are usually used by a group of people in collaboration (rather th ...
. In dealing with these sorts of challenges, mathematical modeling and simulation may not be appropriate or may not suffice. Therefore, during the past 30 years, a number of non-quantified modeling methods have been developed. These include: * stakeholder based approaches including
metagame analysis Metagame analysis involves framing a problem situation as a strategic game in which participants try to realise their objectives by means of the options available to them. The subsequent meta-analysis of this game gives insight in possible strategie ...
and
drama theory {{Use dmy dates, date=July 2021 Drama theory is one of the problem structuring methods in operations research. It is based on game theory and adapts the use of games to complex organisational situations, accounting for emotional responses that ca ...
* morphological analysis and various forms of
influence diagram Influence or influencer may refer to: *Social influence, in social psychology, influence in interpersonal relationships **Minority influence, when the minority affect the behavior or beliefs of the majority *Influencer marketing, through individu ...
s * cognitive mapping * strategic choice * robustness analysis


Societies and journals


Societies

The International Federation of Operational Research Societies (IFORS) is an umbrella organization for operational research societies worldwide, representing approximately 50 national societies including those in the US, UK, France, Germany, Italy, Canada, Australia, New Zealand, Philippines, India, Japan and South Africa. The constituent members of IFORS form regional groups, such as that in Europe, the Association of European Operational Research Societies (EURO). Other important operational research organizations are Simulation Interoperability Standards Organization (SISO) and Interservice/Industry Training, Simulation and Education Conference (I/ITSEC) In 2004 the US-based organization INFORMS began an initiative to market the OR profession better, including a website entitled ''The Science of Better'' which provides an introduction to OR and examples of successful applications of OR to industrial problems. This initiative has been adopted by the Operational Research Society in the UK, including a website entitled ''Learn about OR''.


Journals of INFORMS

The Institute for Operations Research and the Management Sciences (INFORMS) publishes thirteen scholarly journals about operations research, including the top two journals in their class, according to 2005 Journal Citation Reports. They are: * ''Decision Analysis'' * ''Information Systems Research'' * ''INFORMS Journal on Computing'' * ''INFORMS Transactions on Education'' (an open access journal) * ''Interfaces'' * '' Management Science'' * ''
Manufacturing & Service Operations Management ''Manufacturing & Service Operations Management'' is a bi-monthly peer-reviewed academic journal established in 1999 that is published by the Institute for Operations Research and the Management Sciences. It covers analytical research about operat ...
'' * ''
Marketing Science Marketing science is a field that approaches marketing – the understanding of customer needs, and the development of approaches by which they might be fulfilled – predominantly through scientific methods, rather than through tools a ...
'' * ''
Mathematics of Operations Research ''Mathematics of Operations Research'' is a quarterly peer-reviewed scientific journal established in February 1976. It focuses on areas of mathematics relevant to the field of operations research such as continuous optimization, discrete optimiz ...
'' * '' Operations Research'' * ''Organization Science'' * ''Service Science'' * ''
Transportation Science ''Transportation Science'' is a bimonthly peer-reviewed academic journal published by the Institute for Operations Research and the Management Sciences (INFORMS). The studies published in the journal apply operations research techniques to probl ...
''


Other journals

These are listed in alphabetical order of their titles. * ''
4OR ''4OR - A Quarterly Journal of Operations Research'' is a peer-reviewed scientific journal that was established in 2003 and is published by Springer Science+Business Media. It is a joint official journal of the Belgian, French, and Italian Op ...
-A Quarterly Journal of Operations Research'': jointly published the Belgian, French and Italian Operations Research Societies (Springer); * ''
Decision Sciences Decision theory (or the theory of choice; not to be confused with choice theory) is a branch of applied probability theory concerned with the theory of making decisions based on assigning probabilities to various factors and assigning numerical ...
'' published by Wiley-Blackwell on behalf of the Decision Sciences Institute * ''
European Journal of Operational Research The ''European Journal of Operational Research'' (EJOR) is a peer-reviewed academic journal in operations research. It was founded in 1977 by the Association of European Operational Research Societies, and is published by Elsevier, with Roman Sł ...
(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 citations was the second largest amongst Operational Research and Management Science journals; * ''INFOR Journal'': published and sponsored by the Canadian Operational Research Society; * ''Journal of Defense Modeling and Simulation (JDMS): Applications, Methodology, Technology'': a quarterly journal devoted to advancing the science of modeling and simulation as it relates to the military and defense. * '' Journal of the Operational Research Society (JORS)'': an official journal of
The OR Society The Operational Research Society (ORS), also known as The OR Society, is an international learned society in the field of operational research (OR), with more than 3,100 members (2021). It has its headquarters in Birmingham, England. History The ...
; this is the oldest continuously published journal of OR in the world, published by Taylor & Francis; * ''Military Operations Research (MOR)'': published by the Military Operations Research Society; * ''Omega - The International Journal of Management Science''; * ''Operations Research Letters''; * ''Opsearch'': official journal of the Operational Research Society of India; * ''OR Insight'': a quarterly journal of The OR Society, published by Palgrave;The OR Society
;
* ''Pesquisa Operacional'', the official journal of the Brazilian Operations Research Society * ''
Production and Operations Management ''Production and Operations Management'' is a peer-reviewed academic journal covering research on all topics in product and process design, operations, and supply chain management. ''Production and Operations Management'' is published by Wiley-Bla ...
'', the official journal of the Production and Operations Management Society * ''TOP'': the official journal of the
Spanish Statistics and Operations Research Society The Sociedad de Estadística e Investigación Operativa (SEIO, Statistics and Operations Research Society) is the professional non-profit society for the scientific fields of Statistics and Operations Research in Spain. It was founded in 1962 and ...
.


See also

;Operations research topics * Black box analysis * Dynamic programming *
Inventory theory Material theory (or more formally the mathematical theory of inventory and production) is the sub-specialty within operations research and operations management that is concerned with the design of production/ inventory systems to minimize costs: i ...
* Optimal maintenance * Real options valuation * Artificial intelligence ;Operations researchers *
Operations researchers Operation or Operations may refer to: Arts, entertainment and media * ''Operation'' (game), a battery-operated board game that challenges dexterity * Operation (music), a term used in musical set theory * ''Operations'' (magazine), Multi-Man ...
(category) * George Dantzig * Leonid Kantorovich * Tjalling Koopmans *
Russell L. Ackoff Russell Lincoln Ackoff (February 12, 1919 – October 29, 2009) was an American organizational theorist, Management consulting, consultant, and Anheuser-Busch Professor Emeritus of Management Science at the Wharton School, University of Pennsylva ...
* Stafford Beer *
Alfred Blumstein Alfred Blumstein (born 1930) is an American scientist and the J. Erik Jonsson University Professor of Urban Systems and Operations Research at the Heinz College and Department of Engineering and Public Policy at Carnegie Mellon University. He is ...
*
C. West Churchman Charles West Churchman (29 August 1913 – 21 March 2004) was an American philosopher and systems scientist, who was Professor at the School of Business Administration and Professor of Peace and Conflict Studies at the University of California ...
*
William W. Cooper William Wager Cooper (July 23, 1914 – June 20, 2012) was an American operations researcher, known as a father of management science and as "Mr. Linear Programming".. He was the founding president of The Institute of Management Sciences, founding ...
*
Robert Dorfman Robert Dorfman (27 October 1916 – 24 June 2002) was professor of political economy at Harvard University. Dorfman made great contributions to the fields of economics, statistics, group testing and in the process of coding theory. His paper ...
*
Richard M. Karp Richard Manning Karp (born January 3, 1935) is an American computer scientist and computational theorist at the University of California, Berkeley. He is most notable for his research in the theory of algorithms, for which he received a Turing ...
* Ramayya Krishnan *
Frederick W. Lanchester Frederick William Lanchester LLD, Hon FRAeS, FRS (23 October 1868 – 8 March 1946), was an English polymath and engineer who made important contributions to automotive engineering and to aerodynamics, and co-invented the topic of operations ...
*
Thomas L. Magnanti Thomas Lee Magnanti (born 1945) is an American engineer and Institute Professor and former Dean of the School of Engineering at the Massachusetts Institute of Technology. Magnanti served as the founding president of the Singapore University of T ...
*
Alvin E. Roth Alvin Eliot Roth (born December 18, 1951) is an American academic. He is the Craig and Susan McCaw professor of economics at Stanford University and the George Gund (philanthropist), Gund professor of economics and business administration emeritu ...
* Peter Whittle ;Related fields * Behavioral operations research *
Big data Though used sometimes loosely partly because of a lack of formal definition, the interpretation that seems to best describe Big data is the one associated with large body of information that we could not comprehend when used only in smaller am ...
* Business engineering * Business process management * Database normalization * Engineering management *
Geographic information system A geographic information system (GIS) is a type of database containing Geographic data and information, geographic data (that is, descriptions of phenomena for which location is relevant), combined with Geographic information system software, sof ...
s * Industrial engineering * Industrial organization * Managerial economics * Military simulation *
Operational level of war In the field of military theory, the operational level of war (also called operational art, as derived from russian: оперативное искусство, or operational warfare) represents the level of command that connects the details of ...
*
Power system simulation Electrical power system simulation involves power system modeling and network simulation in order to analyze electrical power systems using design/offline or real-time data. Power system simulation software's are a class of computer simulation pro ...
*
Project Production Management Project production management (PPM) is the application of operations managementA Guide to the Project Management Body of Knowledge, Fifth Edition, Project Management Institute Sec 1.5.1.1, p13 http://www.pmi.org/pmbok-guide-standards/foundational ...
*
Reliability engineering Reliability engineering is a sub-discipline of systems engineering that emphasizes the ability of equipment to function without failure. Reliability describes the ability of a system or component to function under stated conditions for a specifie ...
*
Scientific management Scientific management is a theory of management that analyzes and synthesizes workflows. Its main objective is improving economic efficiency, especially labor productivity. It was one of the earliest attempts to apply science to the engineer ...
*
Search-based software engineering Search-based software engineering (SBSE) applies metaheuristic search techniques such as genetic algorithms, simulated annealing and tabu search to software engineering problems. Many activities in software engineering can be stated as optimizatio ...
*
Simulation modeling A simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of models; the model represents the key characteristics or behaviors of the selected system or process, whereas the ...
*
Strategic management In the field of management, strategic management involves the formulation and implementation of the major goals and initiatives taken by an organization's managers on behalf of stakeholders, based on consideration of Resource management, resour ...
*
Supply chain engineering Supply chain engineering is the engineering discipline that concerns the planning, design, and operation of supply chains. Some of its main areas include logistics, production, and pricing. It involves various areas in mathematical modelling such ...
*
System safety The system safety concept calls for a risk management strategy based on identification, analysis of hazards and application of remedial controls using a systems-based approach. This is different from traditional safety strategies which rely on c ...
* Wargaming


References


Further reading


Classic books and articles

* R. E. Bellman, ''Dynamic Programming'', Princeton University Press, Princeton, 1957 * Abraham Charnes, William W. Cooper, ''Management Models and Industrial Applications of Linear Programming'', Volumes I and II, New York, John Wiley & Sons, 1961 * Abraham Charnes, William W. Cooper, A. Henderson, ''An Introduction to Linear Programming'', New York, John Wiley & Sons, 1953 * C. West Churchman, Russell L. Ackoff & E. L. Arnoff, ''Introduction to Operations Research'', New York: J. Wiley and Sons, 1957 * George B. Dantzig, ''Linear Programming and Extensions'', Princeton, Princeton University Press, 1963 * Lester K. Ford, Jr., D. Ray Fulkerson, ''Flows in Networks'', Princeton, Princeton University Press, 1962 * Jay W. Forrester, ''Industrial Dynamics'', Cambridge, MIT Press, 1961 * L. V. Kantorovich, "Mathematical Methods of Organizing and Planning Production" ''Management Science'', 4, 1960, 266–422 * Ralph Keeney, Howard Raiffa, ''Decisions with Multiple Objectives: Preferences and Value Tradeoffs'', New York, John Wiley & Sons, 1976 * H. W. Kuhn, "The Hungarian Method for the Assignment Problem," ''Naval Research Logistics Quarterly'', 1–2, 1955, 83–97 * H. W. Kuhn, A. W. Tucker, "Nonlinear Programming," pp. 481–492 in ''Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability'' * B. O. Koopman, ''Search and Screening: General Principles and Historical Applications'', New York, Pergamon Press, 1980 * Tjalling C. Koopmans, editor, ''Activity Analysis of Production and Allocation'', New York, John Wiley & Sons, 1951 * Charles C. Holt, Franco Modigliani, John F. Muth, Herbert A. Simon, ''Planning Production, Inventories, and Work Force'', Englewood Cliffs, NJ, Prentice-Hall, 1960 * Philip M. Morse, George E. Kimball, ''Methods of Operations Research'', New York, MIT Press and John Wiley & Sons, 1951 * Robert O. Schlaifer, Howard Raiffa, ''Applied Statistical Decision Theory'', Cambridge, Division of Research, Harvard Business School, 1961


Classic textbooks

* Taha, Hamdy A., "Operations Research: An Introduction", Pearson, 10th Edition, 2016 *Frederick S. Hillier & Gerald J. Lieberman, ''Introduction to Operations Research'', McGraw-Hill: Boston MA; 10th Edition, 2014 * Robert J. Thierauf & Richard A. Grosse, "Decision Making Through Operations Research", John Wiley & Sons, INC, 1970 * Harvey M. Wagner, ''Principles of Operations Research'', Englewood Cliffs, Prentice-Hall, 1969 * Wentzel (Ventsel), E. S. ''Introduction to Operations Research'', Moscow: Soviet Radio Publishing House, 1964.


History

* Saul I. Gass, Arjang A. Assad, ''An Annotated Timeline of Operations Research: An Informal History''. New York, Kluwer Academic Publishers, 2005. * Saul I. Gass (Editor), Arjang A. Assad (Editor), ''Profiles in Operations Research: Pioneers and Innovators''. Springer, 2011 * Maurice W. Kirby (Operational Research Society (Great Britain)). Operational Research in War and Peace: The British Experience from the 1930s to 1970, Imperial College Press, 2003. , * J. K. Lenstra, A. H. G. Rinnooy Kan, A. Schrijver (editors) ''History of Mathematical Programming: A Collection of Personal Reminiscences'', North-Holland, 1991 * Charles W. McArthur, ''Operations Analysis in the U.S. Army Eighth Air Force in World War II'', History of Mathematics, Vol. 4, Providence, American Mathematical Society, 1990 * C. H. Waddington, ''O. R. in World War 2: Operational Research Against the U-boat'', London, Elek Science, 1973.


External links


What is Operations Research?

International Federation of Operational Research Societies

The Institute for Operations Research and the Management Sciences (INFORMS)


{{Authority control Industrial engineering Mathematical optimization in business Management science Applied statistics Engineering disciplines Mathematical and quantitative methods (economics) Mathematical economics Decision-making