View source for Operations research

{{Short description|Discipline concerning the application of advanced analytical methods}}
{{Distinguish|Operations management|Operational analysis}}{{For|the academic journal|Operations Research (journal)}}
{{globalize|reason= US perspective completely neglected, George Dantzig gets a passing mention only|date=December 2020}}
{{Use dmy dates|date=June 2020}}
'''Operations research''' ({{langx|en-GB|'''operational research'''}}) (U.S. [[Air Force Specialty Code]]: Operations Analysis), often shortened to the [[initialism]] '''OR''', is a branch of applied mathematics that deals with the development and application of analytical methods to improve management and decision-making.<ref>{{cite web|url=https://www.britannica.com/topic/operations-research |title=Operations research &#124; Definition, History, Examples, & Facts |publisher=Britannica}}</ref><ref>{{cite web|url=https://www.informs.org/Explore/What-is-O.R.-Analytics/What-is-O.R. |title=What is O.R.? |publisher=INFORMS.org |access-date=7 January 2012}}</ref> The term [[management science]] is occasionally used as a synonym.<ref>{{citation|title=Systems analysis for computer-based information systems|series=West series in data processing and information systems|first=James C.|last=Wetherbe|publisher=West Pub. Co.|year=1979|isbn=9780829902280|quotation=A systems analyst who contributes in the area of DSS must be skilled in such areas as management science (synonymous with decision science and operation research), modeling, simulation, and advanced statistics.|url-access=registration|url=https://archive.org/details/systemsanalysisf00wet_ev9}}</ref>

Employing techniques from other mathematical sciences, such as [[mathematical model|modeling]], [[statistics]], and [[mathematical optimization|optimization]], operations research arrives at optimal or near-optimal solutions to [[decision-making]] problems. Because of its emphasis on practical applications, operations research has overlapped with many other disciplines, notably [[industrial engineering]]. Operations research is often concerned with determining the extreme values of some real-world objective: the [[Maxima and minima|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.<ref name="hsor.org">{{cite web |url=http://www.hsor.org/what_is_or.cfm |title=What is OR |publisher=HSOR.org |access-date=13 November 2011 |archive-date=18 November 2010 |archive-url=https://web.archive.org/web/20101118020133/http://www.hsor.org/what_is_or.cfm |url-status=dead }}</ref>
<!--[[File:Operation research study 01.svg|thumb|480px|Model of Operation research study, based on Stafford Beer (1959).<ref>Stafford Beer (1959). ''Cybernetic and Management''. English Universities Press.</ref>]] -->

==Overview==
Operations research (OR) encompasses the development and the use of a wide range of [[problem solving|problem-solving]] techniques and methods applied in the pursuit of improved decision-making and efficiency, such as [[simulation]], [[mathematical optimization]], [[queueing theory]] and other [[stochastic process|stochastic-process]] models, [[Markov Decision Process|Markov decision processes]], [[econometrics|econometric methods]], [[data envelopment analysis]], [[Ordinal Priority Approach|ordinal priority approach]], [[artificial neural network|neural networks]], [[Expert System|expert systems]], [[decision analysis]], and the [[analytic hierarchy process]].<ref>{{cite web|url=http://www.bls.gov/oco/ocos044.htm |title=Operations Research Analysts |publisher=Bls.gov |access-date=27 January 2012}}</ref> 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]]. 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 (but not limited to) in modern operational research, as identified by the journal ''Operations Research''<ref>{{cite web|url=http://www3.informs.org/site/OperationsResearch/index.php?c=10&kat=Forthcoming+Papers |title=OR / Pubs / IOL Home |publisher=INFORMS.org |date=2 January 2009 |access-date=13 November 2011 |url-status=dead |archive-url=https://web.archive.org/web/20090527093022/http://www.informs.org/site/OperationsResearch/index.php?c=10&kat=Forthcoming+Papers |archive-date=27 May 2009 }}</ref> and ''The Journal of the Operational Research Society'' <ref>{{Cite journal |last1=Petropoulos |first1=Fotios |last2=Laporte |first2=Gilbert |last3=Aktas |first3=Emel |last4=Alumur |first4=Sibel A. |last5=Archetti |first5=Claudia |last6=Ayhan |first6=Hayriye |last7=Battarra |first7=Maria |last8=Bennell |first8=Julia A. |last9=Bourjolly |first9=Jean-Marie |last10=Boylan |first10=John E. |last11=Breton |first11=Michèle |last12=Canca |first12=David |last13=Charlin |first13=Laurent |last14=Chen |first14=Bo |last15=Cicek |first15=Cihan Tugrul |date=2023-12-27 |title=Operational Research: methods and applications |url=https://www.tandfonline.com/doi/full/10.1080/01605682.2023.2253852 |journal=Journal of the Operational Research Society |volume=75 |issue=3 |language=en |pages=423–617 |doi=10.1080/01605682.2023.2253852 |issn=0160-5682|arxiv=2303.14217 }}</ref>  are:
* Computing and information technologies
* [[Financial engineering]]
* [[Manufacturing]], [[service science]]s, and [[supply chain management]]
* Policy modeling and public sector work
* [[Revenue management]]
* [[Simulation]]
* [[Stochastics|Stochastic models]]
* [[Transportation theory (mathematics)|Transportation theory]] 
* [[Game theory]] for strategies
* [[Linear programming]] 
* [[Nonlinear programming]] 
* [[Integer programming]] in [[NP-complete problem]] specially for 0-1 integer linear programming for binary
* [[Dynamic programming]] in [[Aerospace engineering]] and [[Economics]] 
* [[Information theory]] used in [[Cryptography]], [[Quantum computing]] 
* [[Quadratic programming]] for solutions of [[Quadratic equation]] and [[Quadratic function]]

==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.<ref name="hsor.org"/>

===Historical origins===
In the 17th century, mathematicians [[Blaise Pascal]] and [[Christiaan Huygens]] solved problems involving sometimes complex decisions ([[problem of points]]) by using [[Game theory|game-theoretic]] ideas and [[expected value]]s; others, such as [[Pierre de Fermat]] and [[Jacob Bernoulli]], solved these types of problems using [[combinatorics|combinatorial reasoning]] instead.<ref>Shafer, G. (2018). ''Pascal's and Huygens's game-theoretic foundations for probability''. [http://probabilityandfinance.com/articles/53.pdf]</ref> [[Charles Babbage]]'s research into the cost of transportation and sorting of mail led to England's [[Uniform Penny Post|universal "Penny Post"]] in 1840, and to studies into the dynamical behaviour of railway vehicles in defence of the [[Great Western Railway|GWR]]'s broad gauge.<ref>M.S. Sodhi, "What about the 'O' in O.R.?" OR/MS Today, December, 2007, p. 12, http://www.lionhrtpub.com/orms/orms-12-07/frqed.html {{Webarchive|url=https://web.archive.org/web/20090714004205/http://www.lionhrtpub.com/orms/orms-12-07/frqed.html |date=14 July 2009 }}</ref> Beginning in the 20th century, study of inventory management could be considered{{by whom|date=November 2019}} the origin of modern operations research with [[economic order quantity]] developed by [[Ford W. Harris]] in 1913. Operational research may{{original research inline|date=November 2019}} 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.<ref>P. W. Bridgman, The Logic of Modern Physics, The MacMillan Company, New York, 1927.</ref>

Modern operational research originated at the [[Telecommunications Research Establishment|Bawdsey Research Station]] in the UK in 1937 as the result of an initiative of the station's superintendent, [[Albert Percival Rowe|A. P. Rowe]] and [[Robert Watson-Watt]].<ref name="Beginning">{{cite journal |last1=Zuckerman |first1=Solly |title=In the Beginning -- And Later |journal=OR |date=1964 |volume=15 |issue=4 |pages=287–292 |doi=10.2307/3007115 |jstor=3007115 |issn=1473-2858}}</ref> 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]]" (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.<ref>{{cite encyclopedia|url= https://www.britannica.com/EBchecked/topic/682073/operations-research/68171/History#ref22348 |title= operations research (industrial engineering) :: History – Britannica Online Encyclopedia |encyclopedia= Britannica.com |access-date= 13 November 2011}}</ref>

Scientists in the United Kingdom (including [[Patrick Maynard Stuart Blackett|Patrick Blackett]] (later Lord Blackett OM PRS), [[Cecil Gordon (scientist)|Cecil Gordon]], [[Solly Zuckerman, Baron Zuckerman|Solly Zuckerman]], (later Baron Zuckerman OM, KCB, FRS), [[Conrad Hal Waddington|C. H. Waddington]], [[Owen Wansbrough-Jones]], [[Frank Yates]], [[Jacob Bronowski]] 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.{{dubious||what about "[[Bawdsey Research Station|Telecommunications Research Establishment]] in 1937" above?|date=March 2019}} 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".<ref name=C67-3-4-48-para-1>"Operational Research in the British Army 1939–1945", October 1947, Report C67/3/4/48, UK National Archives file WO291/1301<br />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.</ref> Other names for it included operational analysis (UK Ministry of Defence from 1962)<ref name="PROCATWO291">[http://www.nationalarchives.gov.uk/catalogue/displaycataloguedetails.asp?CATID=109&CATLN=2&Highlight=&FullDetails=True UK National Archives Catalogue for WO291] lists a War Office organisation called [[Army Operational Research Group]] (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 Analysis Establishment|Defence Operational Research Establishment]] (DOAE) which was formed in 1965, and it absorbed the Army Operational Research Establishment based at West Byfleet."</ref> and quantitative management.<ref>{{Cite web |url=http://brochure.unisa.ac.za/myunisa/data/subjects/Quantitative%20Management.pdf |title=Archived copy |access-date=7 October 2009 |archive-url=https://web.archive.org/web/20110812213540/http://brochure.unisa.ac.za/myunisa/data/subjects/Quantitative%20Management.pdf |archive-date=12 August 2011 |url-status=dead }}</ref>

During the [[World War II|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]].<ref>Kirby, [https://books.google.com/books?id=DWITTpkFPEAC&lpg=PA141&pg=PA117 p. 117] {{webarchive |url=https://web.archive.org/web/20130827004623/https://books.google.com/books?id=DWITTpkFPEAC&lpg=PA141&pg=PA117 |date=27 August 2013 }}</ref>

[[Patrick Blackett]] worked for several different organizations during the war. Early in the war while working for the [[Royal Aircraft Establishment]] (RAE) he set up a team known as the "Circus" which helped to reduce the number of [[anti-aircraft artillery]] 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.<ref>Kirby, [https://books.google.com/books?id=DWITTpkFPEAC&lpg=PA141&pg=PA94 pp. 91–94] {{webarchive |url=https://web.archive.org/web/20130827041022/https://books.google.com/books?id=DWITTpkFPEAC&lpg=PA141&pg=PA94 |date=27 August 2013 }}</ref>

[[File:Liberator B Mk.I in RAF service 23 03 05.jpg|thumb|A [[Consolidated B-24 Liberator|Liberator]] in standard RAF green/dark earth/black night bomber finish as originally used by Coastal Command]]
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 [[British Admiralty|Admiralty]].<ref>Kirby, [https://books.google.com/books?id=DWITTpkFPEAC&lpg=PA141&pg=PA109 p. 96,109] {{webarchive |url=https://web.archive.org/web/20131002032938/https://books.google.com/books?id=DWITTpkFPEAC&lpg=PA141&pg=PA109 |date=2 October 2013 }}</ref> Blackett's team at Coastal Command's Operational Research Section (CC-ORS) included [[Evan James Williams|E. J. Williams]],<ref>{{cite journal|work=Nature|volume=250|date=2 August 1974|title=Patrick Blackett...an appreciation|last=Bullard|first=Edward}}</ref> two future [[Nobel Prize]] winners and many other people who went on to be pre-eminent in their fields.<ref>Kirby, [https://books.google.com/books?id=DWITTpkFPEAC&lpg=PA141&pg=PA96 p. 96] {{webarchive |url=https://web.archive.org/web/20140327234509/https://books.google.com/books?id=DWITTpkFPEAC&lpg=PA141&pg=PA96 |date=27 March 2014 }}</ref><ref name= dyson >[[Freeman Dyson]], ''MIT Technology Review'' (1 November 2006) "[https://www.technologyreview.com/s/406789/a-failure-of-intelligence/ A Failure of Intelligence: Part I]"</ref> 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-boat]]s 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.<ref>{{cite web|url=http://www.familyheritage.ca/Articles/victory1943.html |title="Numbers are Essential": Victory in the North Atlantic Reconsidered, March–May 1943 |publisher=Familyheritage.ca |date=24 May 1943 |access-date=13 November 2011}}</ref>

<!-- [[WP:NFCC]] violation: [[File:Vickers Warwick B ASR Mk1 - BV285.jpg|thumb|A [[Vickers Warwick|Warwick]] in the revised RAF Coastal Command green/dark grey/white finish]] -->
{{anchor|RAF Coastal Command's Operational Research Section}}
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.<ref>Kirby, [https://books.google.com/books?id=DWITTpkFPEAC&lpg=PA141&pg=PA101 p. 101]</ref> 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]]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".<ref>(Kirby, [https://books.google.com/books?id=DWITTpkFPEAC&lpg=PA141&pg=PA103 pp. 102,103])</ref>

[[File:Kammhuber Line Map - Agent Tegal.png|thumb|upright|left|Map of ''[[Kammhuber Line]]'']]
{{anchor|RAF Bomber Command's Operational Research Section}}
Bomber Command's Operational Research Section (BC-ORS), analyzed a report of a survey carried out by [[RAF Bomber Command]].{{Citation needed|date=February 2007}} For the survey, Bomber Command inspected all bombers returning from bombing raids over Germany over a particular period. All damage inflicted by German [[Anti-aircraft warfare|air defenses]] was noted and the recommendation was given that armor be added in the most heavily damaged areas. This [[Survivorship bias#Military|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 armor 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 armor be placed in the areas which were completely untouched by damage in the bombers who 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.<ref>{{cite book | title=Dirty Little Secrets of the Twentieth Century | publisher=[[Harper Paperbacks]] | author=James F. Dunnigan | year=1999 | pages=215–217}}</ref> This story has been disputed,<ref>{{Cite web|url=http://lesswrong.com/lw/bbv/examine_your_assumptions/|title = Examine your assumptions – LessWrong| date=30 March 2012 }}</ref> with a similar damage assessment study completed in the US by the [[Statistical Research Group]] at [[Columbia University]],<ref>{{Cite journal|doi = 10.1080/01621459.1980.10477469|title = The Statistical Research Group, 1942–1945|journal = Journal of the American Statistical Association|volume = 75|issue = 370|pages = 320–330|year = 1980|last1 = Wallis|first1 = W. Allen}}</ref> the result of work done by [[Abraham Wald]].<ref>{{Cite journal|jstor = 2288257|title = Abraham Wald's Work on Aircraft Survivability|journal = Journal of the American Statistical Association|volume = 79|issue = 386|pages = 259|last1 = Mangel|first1 = Marc|last2 = Samaniego|first2 = Francisco J|doi = 10.2307/2288257|year = 1984}}</ref>

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.<ref>{{cite web |url=http://www.raf.mod.uk/bombercommand/thousands.html |title=RAF History – Bomber Command 60th Anniversary |publisher=Raf.mod.uk |access-date=13 November 2011 |archive-url=https://web.archive.org/web/20111105053432/http://www.raf.mod.uk/bombercommand/thousands.html |archive-date=5 November 2011 |url-status=dead }}</ref>

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 [[Mine (naval)|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.<ref name="Proceedings">{{cite magazine|last=Milkman|first= Raymond H. |title=Operations Research in World War II |publisher=[[United States Naval Institute]]|magazine=[[Proceedings (magazine)|Proceedings]] |date=May 1968|volume=94/5/783|url=https://www.usni.org/magazines/proceedings/1968/may/operations-research-world-war-ii}}</ref>

Operational research doubled the on-target bomb rate of [[B-29]]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 conventional dull camouflage paint finish, and a smooth paint finish increased airspeed by reducing skin friction.<ref name="Proceedings"/>

On land, the operational research sections of the Army Operational Research Group (AORG) of the [[Ministry of Supply]] (MoS) were landed in [[Operation Overlord|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 organized in [[Dundee]]. In his opening address, Watson-Watt 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."<ref name="Beginning"/>
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. The development of the [[simplex algorithm]] for [[linear programming]] was in 1947.<ref name="pitt.edu">{{cite book|title=Principles and Applications of Operations Research|contribution=Section 1.2: A Historical Perspective|url=http://www.pitt.edu/~jrclass/or/or-intro.html#history}}</ref>

In the 1950s, the term Operations Research was used to describe heterogeneous mathematical methods such as [[game theory]], dynamic programming, linear programming, warehousing, [[spare parts theory]], [[Queueing theory|queue theory]], simulation and production control, which were used primarily in civilian industry. Scientific societies and journals on the subject of operations research were founded in the 1950s, such as the [[Institute for Operations Research and the Management Sciences|Operation Research Society of America]] (ORSA) in 1952 and the Institute for Management Science (TIMS) in 1953.<ref>Richard Vahrenkamp: Mathematical Management – Operations Research in the United States and Western Europe, 1945 – 1990, in: Management Revue – Socio-Economic Studies, vol. 34 (2023), issue 1, pp. 69–91</ref> Philip Morse, the head of the Weapons Systems Evaluation Group of the Pentagon, became the first president of ORSA and attracted the companies of the [[Military–industrial complex|military-industrial complex]] to ORSA, which soon had more than 500 members. In the 1960s, ORSA reached 8000 members.{{Citation needed|date=July 2023}} Consulting companies also founded OR groups. In 1953, Abraham Charnes and William Cooper published the first textbook on Linear Programming.{{Citation needed|date=July 2023}}

In the 1950s and 1960s, chairs of operations research were established in the U.S. and United Kingdom (from 1964 in Lancaster) in the management faculties of universities. Further influences from the U.S. on the development of operations research in Western Europe can be traced here. The authoritative{{Citation needed|date=July 2023}} OR textbooks from the U.S. were published in Germany in German language and in France in French (but not in Italian{{Citation needed|date=July 2023}}), such as the book by George Dantzig "Linear Programming"(1963) and the book by [[C. West Churchman]] et al. "Introduction to Operations Research"(1957). The latter was also published in Spanish in 1973, opening at the same time Latin American readers to Operations Research. [[NATO]] gave important impulses for the spread of Operations Research in Western Europe; NATO headquarters (SHAPE) organised four conferences on OR in the 1950s{{Mdash}}the one in 1956 with 120 participants{{Mdash}}bringing OR to mainland Europe. Within NATO, OR was also known as "Scientific Advisory" (SA) and was grouped together in the Advisory Group of Aeronautical Research and Development (AGARD). SHAPE and AGARD organized an OR conference in April 1957 in Paris. When [[Withdrawal from NATO#France|France withdrew from the NATO military command structure]], the transfer of NATO headquarters from France to Belgium led to the institutionalization of OR in Belgium, where Jacques Drèze founded CORE, the Center for Operations Research and Econometrics at the [[Catholic University of Leuven (1834–1968)|Catholic University of Leuven]] in 1966.{{Citation needed|date=July 2023}}

With 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."<ref name="pitt.edu"/> 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 includes 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 counterterrorist 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.<ref>{{cite journal |first=Richard |last=Vahrenkamp |title= Nominal Science without Data: The Cold War Content of Game Theory and Operations Research |journal= Real World Economics Review |volume= 88 |date=2019 |pages=19–50 |url=http://www.paecon.net/PAEReview/issue88/Vahrenkamp88.pdf}}.</ref>

==Problems addressed==
* [[Critical path analysis]] or [[project planning]]: identifying those processes in a multiple-dependency project which affect the overall duration of the project
* [[Floorplanning]]: designing the layout of equipment in a factory or components on a [[computer chip]] to reduce [[manufacturing]] time (therefore reducing cost)
* [[Telecommunications network|Network optimization]]: for instance, setup of telecommunications or power system networks to maintain quality of service during outages
* [[Resource allocation]] problems
* [[Optimal facility location|Facility location]]
* Assignment Problems:
** [[Assignment problem]]
** [[Generalized assignment problem]]
** [[Quadratic assignment problem]]
** [[Weapon target assignment problem]]
* [[Bayesian search theory]]: looking for a target
* [[Search theory|Optimal search]]
* [[Routing]], such as determining the routes of buses so that as few buses are needed as possible
* [[Supply chain management]]: 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<ref>"Factory Physics for Managers", E. S. Pound, J. H. Bell, and M. L. Spearman, McGraw-Hill, 2014, p 47</ref><ref>"New Era of Project Delivery – Project as Production System", R. G. Shenoy and T. R. Zabelle, Journal of Project Production Management, Vol 1, pp Nov 2016, pp. 13–24

https://www.researchgate.net/publication/312602707_New_Era_of_Project_Delivery_-_Project_as_Production_System 
</ref>
* 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: [[less-than-truckload shipping|LTL shipping]], [[intermodal freight transport]], [[travelling salesman problem]], [[driver scheduling problem]])
* [[Scheduling (computing)|Scheduling]]:
** [[Nurse scheduling problem|Personnel staffing]]
** Manufacturing steps
** [[Project management|Project tasks]]
** Network data traffic: these are known as [[queueing model]]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]]
* [[Cutting stock problem]]: Cutting small items out of bigger ones.
* Finding the optimal parameter (weights) setting of an algorithm that generates the realisation of a [[figured bass]] in [[Baroque]] compositions (classical music) by using weighted local cost and transition cost rules

Operational research is also used extensively in government where [[evidence-based policy]] is used.

==Management science==
{{Main|Management science}}
The field of management science (MS) is known as using operations research models in business.<ref name="UTK">[http://bus.utk.edu/soms/information/whatis_msci.html What is Management Science?] {{Webarchive|url=https://web.archive.org/web/20081207155115/http://bus.utk.edu/soms/information/whatis_msci.html|date=7 December 2008}} The University of Tennessee, 2006. Retrieved 5 June 2008.</ref> [[Stafford Beer]] characterized this in 1967.<ref>[[Stafford Beer]] (1967) ''Management Science: The Business Use of Operations Research''</ref> Like operational research itself, management science is an interdisciplinary branch of applied mathematics devoted to optimal decision planning, with strong links with economics, business, engineering, and other [[science]]s. It uses various [[science|scientific]] [[research]]-based principles, [[strategy|strategies]], and [[analytical method]]s including [[mathematical model]]ing, statistics and [[numerical algorithm]]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 [[scientific modeling|models]] and [[concept]]s 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.<ref name="LS">[http://www.lums.lancs.ac.uk/departments/ManSci/DeptProfile/WhatisManSci/ What is Management Science?] {{webarchive|url=https://web.archive.org/web/20080914101120/http://www.lums.lancs.ac.uk/departments/ManSci/DeptProfile/WhatisManSci/ |date=14 September 2008 }} Lancaster University, 2008. Retrieved 5 June 2008.</ref>

===Related fields===
Some of the fields that have considerable overlap with Operations Research and Management Science include:<ref>{{Cite journal |last1=Merigó |first1=José M |last2=Yang |first2=Jian-Bo |date=2017|title=A bibliometric analysis of operations research and management science |url=https://www.research.manchester.ac.uk/portal/en/publications/a-bibliometric-analysis-of-operations-research-and-management-science(97b111d2-d178-4f37-a26e-08076d778b4a).html|journal=Omega - International Journal of Management Science | volume=73 | pages=37–48 |doi=10.1016/j.omega.2016.12.004 |issn=0305-0483}}</ref>
{{cols|colwidth=13em}}
* [[Artificial Intelligence]]
* [[Business analytics]]
* [[Computer science]]
* [[Data mining]]/[[Data science]]/[[Big data]]
* [[Decision analysis]]
* [[Decision intelligence]]
* [[Engineering]]
* [[Financial engineering]]
* [[Forecasting]]
* [[Game theory]]
* [[Geography]]/[[Geographic information science]]
* [[Graph theory]]
* [[Industrial engineering]]
* [[Inventory control]]
* [[Logistics]]
* [[Mathematical modeling]]
* [[Mathematical optimization]]
* [[Probability]] and [[statistics]]
* [[Project management]]
* [[Policy analysis]]
* [[Queueing theory]]
* [[Simulation]]
* [[Social network]]/[[Transportation forecasting]] models
* [[Stochastic processes]]
* [[Supply chain management]]
* [[Systems engineering]]
{{colend}}

===Applications===
Applications are abundant such as in airlines, manufacturing companies, [[service organization]]s, military branches, and government. The range of problems and issues to which it has contributed insights and solutions is vast. It includes:<ref name="LS"/>
* 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 warehouses; factories 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)
<ref>{{Cite web |url=http://nak-architecture.com/index.php/en/services/blog/55-urban-operations-research-uor |title=Blog |access-date=28 June 2017 |archive-url=https://web.archive.org/web/20170929183803/http://nak-architecture.com/index.php/en/services/blog/55-urban-operations-research-uor |archive-date=29 September 2017 |url-status=dead }}</ref>

Management is also concerned with so-called soft-operational analysis which concerns methods for [[strategic planning]], strategic [[decision support]], [[problem structuring methods]]. 
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{{vague|date=November 2017}}, a number of non-quantified modeling methods have been developed. These include:{{Citation needed|date=June 2016}}
* stakeholder based approaches including [[metagame analysis]] and [[drama theory]]
* [[Morphological analysis (problem-solving)|morphological analysis]] and various forms of [[influence diagram]]s
* cognitive mapping
* strategic choice 
* robustness analysis

==Societies and journals==
===Societies===
The [[International Federation of Operational Research Societies]] (IFORS)<ref>{{cite web|url=http://www.ifors.org/ |title=IFORS |publisher=IFORS |access-date=13 November 2011}}</ref> is an [[umbrella organization]] for operational research societies worldwide, representing approximately 50 national societies including those in the US,<ref>{{cite web|last=Leszczynski |first=Mary |url=http://www.informs.org/ |title=Informs |publisher=Informs |date=8 November 2011 |access-date=13 November 2011}}</ref> [[Operational Research Society|UK]],<ref>{{cite web |url=http://www.orsoc.org.uk |title=The OR Society |publisher=Orsoc.org.uk |access-date=13 November 2011 |url-status=dead |archive-url=http://webarchive.loc.gov/all/20060424161729/http://www.orsoc.org.uk/ |archive-date=24 April 2006}}</ref> France,<ref>{{cite web|url=http://www.roadef.org/content/index.htm |title=Société française de Recherche Opérationnelle et d'Aide à la Décision |publisher=ROADEF |access-date=13 November 2011}}</ref> Germany, [[Italian Operations Research Society|Italy]],<ref>{{cite web|author=airo.org |url=http://www.airo.org |title=AIRO |publisher=airo.org |access-date=31 March 2018}}</ref> Canada,<ref>{{cite web|author=cors.ca |url=http://www.cors.ca |title=CORS |publisher=Cors.ca |access-date=13 November 2011}}</ref> Australia,<ref>{{cite web|url=http://www.asor.org.au |title=ASOR |publisher=ASOR |date=1 January 1972 |access-date=13 November 2011}}</ref> New Zealand,<ref>{{cite web|url=http://www.orsnz.org.nz/ |title=ORSNZ |publisher=ORSNZ |access-date=13 November 2011}}</ref> Philippines,<ref>{{cite web|url=http://www.orsp.org.ph/ |title=ORSP |publisher=ORSP |access-date=13 November 2011}}</ref> India,<ref>{{cite web|url=http://www.orsi.in/ |title=ORSI |publisher=Orsi.in |access-date=13 November 2011}}</ref> Japan and South Africa.<ref>{{cite web|url=http://www.orssa.org.za/ |title=ORSSA |publisher=ORSSA |date=23 September 2011 |access-date=13 November 2011}}</ref> For the institutionalization of Operations Research, the foundation of IFORS in 1960 was of decisive importance, which stimulated the foundation of national OR societies in Austria, Switzerland and Germany. IFORS held important international conferences every three years since 1957.<ref>{{citation|author=[[Richard Vahrenkamp]]|date=2023|doi=10.5771/0935-9915-2023-1-69|issue=1|pages=69–91|periodical=Management Revue – Socio-Economic Studies|title=Mathematical Management – Operations Research in the United States and Western Europe, 1945 – 1990|volume=34|s2cid=258937881 }}<!-- auto-translated by Module:CS1 translator --></ref> The constituent members of IFORS form regional groups, such as that in Europe, the [[Association of European Operational Research Societies]] (EURO).<ref>{{cite web|url=http://www.euro-online.org/ |title=EURO (EURO) |publisher=Euro-online.org |access-date=13 November 2011}}</ref> Other important operational research organizations are [[Simulation Interoperability Standards Organization]] (SISO)<ref>{{cite web|url=http://www.sisostds.org/ |title=SISO |publisher=Sisostds.org |access-date=13 November 2011}}</ref> and [[Interservice/Industry Training, Simulation and Education Conference]] (I/ITSEC)<ref>{{cite web|url=http://www.iitsec.org/ |title=I/Itsec |publisher=I/Itsec |access-date=13 November 2011}}</ref>

In 2004, the US-based organization INFORMS began an initiative to market the OR profession better, including a website entitled ''The Science of Better''<ref>{{cite web|url=http://www.scienceofbetter.org/ |title=The Science of Better |publisher=The Science of Better |access-date=13 November 2011}}</ref> 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''.<ref>{{cite web |url=http://www.learnaboutor.co.uk/ |title=Learn about OR |publisher=Learn about OR |access-date=13 November 2011 |archive-url=https://web.archive.org/web/20111115172529/http://www.learnaboutor.co.uk/ |archive-date=15 November 2011 |url-status=dead }}</ref>

===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]].<ref>{{cite web |url=http://www.informs.org/index.php?c=31&kat=-+INFORMS+Journals |title=INFORMS Journals |publisher=Informs.org |access-date=13 November 2011 |archive-url=https://web.archive.org/web/20100309051916/http://www3.informs.org/index.php?c=31&kat=-+INFORMS+Journals |archive-date=9 March 2010 |url-status=dead }}</ref> They are:
* ''Decision Analysis''<ref>{{cite web |url=http://pubsonline.informs.org/journal/deca |title=Decision Analysis |publisher=Informs.org |access-date=19 March 2015}}</ref>
* ''Information Systems Research''<ref>{{cite web |url=http://pubsonline.informs.org/journal/isre |title=Information Systems Research |publisher=Informs.org |access-date=19 March 2015}}</ref>
* ''INFORMS Journal on Computing''<ref>{{cite web |url=http://pubsonline.informs.org/journal/ijoc |title=INFORMS Journal on Computing |publisher=Informs.org |access-date=19 March 2015}}</ref>
* ''INFORMS Transactions on Education''<ref>{{cite web |url=http://pubsonline.informs.org/journal/ited |title=INFORMS Transactions on Education |publisher=Informs.org |access-date=19 March 2015}}</ref> (an open access journal)
* ''Interfaces''<ref>{{cite web |url=http://pubsonline.informs.org/journal/inte |title=Interfaces |publisher=Informs.org |access-date=19 March 2015}}</ref>
* ''[[Management Science (journal)|Management Science]]''
* ''[[Manufacturing & Service Operations Management]]''
* ''[[Marketing Science (journal)|Marketing Science]]''
* ''[[Mathematics of Operations Research]]''
* ''[[Operations Research (journal)|Operations Research]]''
* ''Organization Science''<ref>{{cite web |url=http://pubsonline.informs.org/journal/orsc |title=Organization Science |publisher=Informs.org |access-date=19 March 2015}}</ref>
* ''Service Science''<ref>{{cite web |url=http://pubsonline.informs.org/journal/serv |title=Service Science |publisher=Informs.org |access-date=19 March 2015}}</ref>
* ''[[Transportation Science]]''

===Other journals===
These are listed in alphabetical order of their titles.
* ''[[4OR]]-A Quarterly Journal of Operations Research'': jointly published the Belgian, French and Italian Operations Research Societies (Springer);
* ''[[Decision Sciences]]'' published by [[Wiley-Blackwell]] on behalf of the [[Decision Sciences Institute]]
* ''[[European Journal of Operational Research]] (EJOR)'': Founded in 1975 and is presently{{when|date=March 2019}} 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.<ref>{{cite web |author=The Society for Modeling & Simulation International |url=http://www.scs.org/pubs/jdms/jdms.html |title=JDMS |publisher=Scs.org |access-date=13 November 2011 |author-link=The Society for Modeling & Simulation International |archive-url=https://web.archive.org/web/20090823062356/http://www.scs.org/pubs/jdms/jdms.html |archive-date=23 August 2009 |url-status=dead }}</ref>
* ''[[Journal of the Operational Research Society]] (JORS)'': an official journal of [[The OR Society]]; 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;<ref name="The OR Society">[http://www.orsoc.org.uk The OR Society] {{webarchive|url=http://webarchive.loc.gov/all/20060424161729/http://www.orsoc.org.uk/ |date=24 April 2006 }};</ref>
* ''Pesquisa Operacional'', the official journal of the Brazilian Operations Research Society
* ''[[Production and Operations Management]]'', the official journal of the Production and Operations Management Society
* ''TOP'': the official journal of the [[Spanish Statistics and Operations Research Society]].<ref>{{cite web|url=https://www.springer.com/east/home/business/operations+research?SGWID=5-40521-70-173677307-detailsPage=journal%7Cdescription |title=TOP |publisher=Springer.com |access-date=13 November 2011}}</ref>

==See also==
{{Col-begin}}
{{Col-break}}
;Operations research topics
* [[Black box|Black box analysis]]
* [[Dynamic programming]]
* [[Inventory theory]]
* [[Optimal maintenance]]
* [[Real options valuation]]
* [[Artificial intelligence]]
{{Col-break}}
;Operations researchers
* [[:Category:Operations researchers|Operations researchers]] (category)
* [[George Dantzig]]
* [[Leonid Kantorovich]]
* [[Tjalling Koopmans]]
* [[Russell L. Ackoff]]
* [[Stafford Beer]]
* [[Alfred Blumstein]]
* [[C. West Churchman]]
{{Col-break}}
* [[William W. Cooper]]
* [[Robert Dorfman]]
* [[Richard M. Karp]]
* [[Ramayya Krishnan]]
* [[Frederick W. Lanchester]]
* [[Thomas L. Magnanti]]
* [[Alvin E. Roth]]
* [[Peter Whittle (mathematician)|Peter Whittle]]
{{Col-break}}
;Related fields
* [[Behavioral operations research]]
* [[Big data]]
* [[Business engineering]]
* [[Business process management]]
* [[Database normalization]]
* [[Engineering management]]
* [[Geographic information system]]s
* [[Industrial engineering]]
* [[Industrial organization]]
* [[Managerial economics]]
{{Col-break}}
* [[Military simulation]]
* [[Operational level of war]]
* [[Power system simulation]]
* [[Project production management]]
* [[Reliability engineering]]
* [[Scientific management]]
* [[Search-based software engineering]]
* [[Simulation modeling]]
* [[Strategic management]]
* [[Supply chain engineering]]
* [[System safety]]
* [[Wargaming]]
{{col-end}}

==References==
{{Reflist}}

==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.&nbsp;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
* [[Elena Ventsel|Wentzel (Ventsel), E. S.]]: ''Introduction to Operations Research'', Moscow: Soviet Radio Publishing House, 1964.
* [https://algorithmsbook.com/decisionmaking/ Mykel J. Kochenderfer, Tim A. Wheeler, and Kyle H. Wray: ''Algorithms for Decision Making'', MIT Press, 2022]

===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. {{isbn|1-86094-366-7}}, {{isbn|978-1-86094-366-9}}
* 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.
* Richard Vahrenkamp: ''Mathematical Management – Operations Research in the United States and Western Europe, 1945 – 1990'', in: Management Revue – Socio-Economic Studies, vol. 34 (2023), issue 1, pp.&nbsp;69–91.

==External links==
{{Commons category|Operations research}}
{{Wikiquote}}
* [https://www.informs.org/Build-Your-Career/Consider-an-Analytics-OR-Career What is Operations Research?]
* [http://www.ifors.org/ International Federation of Operational Research Societies]
* [http://www.informs.org/ The Institute for Operations Research and the Management Sciences (INFORMS)]
* [https://web.archive.org/web/20080509183835/http://stats.bls.gov/oco/ocos044.htm Occupational Outlook Handbook, U.S. Department of Labor Bureau of Labor Statistics]
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{{Operations research topics}}
{{Systems}}
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[[Category:Operations research| ]]
[[Category:Industrial engineering]]
[[Category:Mathematical optimization in business]]
[[Category:Applied statistics]]
[[Category:Engineering disciplines]]
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[[Category:Decision-making]]
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