Editing Operations research (section)

==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 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>