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运筹学 (查看源代码)

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~~此词条暂由彩云小译翻译，翻译字数共4567，未经人工整理和审校，带来阅读不便，请见谅。~~

{{short description|Discipline concerning the application of advanced analytical methods}}

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运筹学运用了其他数学科学分支的方法，如建模、统计和优化等，这些方法为复杂的决策问题找到了最优或接近最优的解决方案。由于其强调实际应用，运筹学与许多学科，特别是工业工程学高度相关。运筹学通常关注于确定一些现实世界目标的极值: 最大值(利润、业绩或收益)或最小值(损失、风险或成本)。运筹学起源于第二次世界大战前的军事博弈，它至今已经影响了不少行业。

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==Overview==

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==Overview 总览==

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]], [[queueing theory]] and other [[Stochastic process|stochastic-process]] models, [[Markov Decision Process|Markov decision processes]], [[Econometrics|econometric methods]], [[data envelopment analysis]], [[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) ， which contributes to make better decisions.

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* 运输

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==History==

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==History of OR'S Development 运筹学的发展史==

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 complex systems, and has become an area of active academic and industrial research.<ref name="hsor.org"/>

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在两次世界大战之后的几十年里，运筹学更多地用于解决商业、工业和社会问题。从那时起，运筹学已经扩展到一个广泛应用于石油化工、航空、金融、物流和政府等行业的学科，用于建立数学模型去分析、优化决策与系统，并已成为一个活跃的学术和工业研究领域。

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===Historical origins===

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===Historical origins 历史起源===

In the 17th century, mathematicians [[Blaise Pascal]] and [[Christiaan Huygens]] solved problems involving complex decisions ([[problem of points]]) by using [[Game theory|game-theoretic]] ideas and [[Expected value|expected values]]; 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>

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In the 17th century, mathematicians Blaise Pascal and Christiaan Huygens solved problems involving complex decisions (problem of points) by using game-theoretic ideas and expected values; others, such as Pierre de Fermat and Jacob Bernoulli, solved these types of problems using combinatorial reasoning instead.Shafer, G. (2018). Pascal's and Huygens's game-theoretic foundations for probability. Charles Babbage'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.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 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 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.P. W. Bridgman, The Logic of Modern Physics, The MacMillan Company, New York, 1927.

在17世纪，数学家布莱斯 · 帕斯卡(Blaise Pascal)和克里斯蒂安·惠更斯通过博弈论思想和期望值解决了复杂决策(点的问题) ，而其他人，如皮埃尔·德·费马和雅各布 · 伯努利(Jacob Bernoulli)则用组合推理解决了这类问题。谢弗，G (2018)。帕斯卡和惠更斯关于概率的博弈论基础。查尔斯 · 巴贝奇对邮件运输和分类成本的研究导致了1840年英国通用的“便士邮政”，以及为了保护 GWR 的宽轨距而研究铁路车辆的动力学行为。Sodhi“手术室里的 O 怎么办?”OR/MS 今天，2007年12月，第12页， http://www.lionhrtpub.com/orms/orms-12-07/frqed.html 从20世纪开始，库存管理研究可以被认为是现代运筹学的起源，经济订单量是福特 · W · 哈里斯在1913年发展起来的。作战研究可能起源于第一次世界大战期间军事计划者的努力(护航理论和兰彻斯特法则)。珀西 · 布里奇曼在20世纪20年代将运筹学应用到物理学问题上，后来试图将这些应用扩展到社会科学领域。布里奇曼，《现代物理学的逻辑》，麦克米伦，纽约，1927年。

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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>

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Modern operational research originated at the Bawdsey Research Station 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" (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.

现代运筹学起源于1937年英国的鲍德西研究站，这是该站负责人 A.P.Rowe 和劳勃·沃森-瓦特发起的一项倡议的结果。罗伊将这一想法视为一种分析和改善英国预警雷达系统(代号为“连锁住宅”(Chain Home，CH))运作的手段。最初，罗分析了雷达设备及其通信网络的运行情况，后来扩展到包括操作人员的行为。这暴露了 CH 网络的局限性，并允许采取补救行动。

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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.

Scientists in the United Kingdom (including Patrick Blackett (later Lord Blackett OM PRS), Cecil Gordon, Solly Zuckerman, (later Baron Zuckerman OM, KCB, FRS), 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.

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在第二次世界大战期间，英国有将近1000名男女从事作战研究。大约200名作战研究科学家为英国陆军工作

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[[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>

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[[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>

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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.Kirby, pp. 91–94

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帕特里克 · 布莱克特在战争期间为几个不同的组织工作。战争初期，在为皇家飞机制造公司(RAE)工作时，他成立了一个名为“马戏团”的团队，帮助将击落敌机所需的高射炮弹数量从不列颠战役开始时的平均超过2万发减少到1941年的4000发。

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帕特里克 · 布莱克特在战争期间为几个不同的组织工作。战争初期，在为皇家飞机制造公司(RAE)工作时，他成立了一个名为“马戏团”的团队，帮助将击落敌机所需的高射炮弹数量从不列颠战役开始时的平均超过2万发减少到1941年的4000发。Kirby 警官。91–94

[[File:B 24 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|链接=Special:FilePath/B_24_in_raf_service_23_03_05.jpg]]

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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.Kirby, p. 96,109 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.Kirby, p. 96 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.

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1941年，布莱克特从英国皇家空军转入海军，此前他曾在英国皇家空军海防司令部工作，1941年转入英国皇家空军，1942年初转入英国海军部。布莱克特在海岸司令部作战研究部(CC-ORS)的团队包括两位未来的诺贝尔奖获得者和许多其他人，他们在自己的领域中继续取得卓越成就。科比，第96页，弗里曼戴森，麻省理工学院技术评论(2006年11月1日)“智力的失败: 第一部分”他们进行了一些关键的分析，以帮助战争的努力。英国引入护航系统是为了减少航运损失，但是尽管使用军舰陪同商船的原则得到普遍接受，但是护航船队是小型还是大型还不清楚。车队以最慢的成员的速度行驶，因此小型车队可以行驶得更快。还有人认为，小型护航舰队将更难被德国 U 型潜艇发现。另一方面，大型护航舰队可以部署更多的战舰对付攻击者。布莱克特的工作人员表示，护航船队遭受的损失在很大程度上取决于护航船只的数量，而不是护航船队的规模。他们的结论是，少数大型车队比许多小型车队更容易防御。

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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.

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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>

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Other work by the CC-ORS indicated that on average if the trigger depth of aerial-delivered depth charges 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".(Kirby, pp. 102,103)

CC-ORS 的其他工作表明，如果空投深水炸弹的触发深度平均从100英尺改为25英尺，炸死率将上升。原因在于，如果 U 型潜艇在飞机到达目标上空前不久就看到了飞机，那么在100英尺的高度，炸药不会造成任何损害(因为 U 型潜艇没有时间下降到100英尺的高度) ，如果它看到飞机离目标很远，它就有时间在水下改变航向，因此它进入20英尺炸药杀伤区的可能性很小。当目标的位置更加清楚时，攻击那些靠近水面的潜艇要比试图在更深的地方摧毁它们更有效率，因为它们的位置只能靠猜测。在设置从100英尺改为25英尺之前，1% 的潜艇沉没，14% 的潜艇受损。改变之后，7% 的潜艇被击沉，11% 的潜艇被损坏; 如果潜艇在水面上被抓住，但在被攻击之前有时间潜入水中，数字上升到11% 的潜艇被击沉，15% 的潜艇被损坏。布莱克特指出，“通过如此微小而简单的战术改变，就能获得如此巨大的行动收益的情况很少。”。(Kirby，pp.102,103)

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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>

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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.

当德国将其防空系统组织到 Kammhuber 防线时，英国人意识到，如果英国皇家空军的轰炸机以轰炸机群的形式飞行，他们就可以压倒由地面控制员指挥的夜间战斗机。当时的问题是计算碰撞造成的统计损失和夜间战斗机造成的统计损失，以计算轰炸机应飞多近，以尽量减少英国皇家空军的损失。

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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 journal|author=Milkman, Raymond H. |title=Operation Research in World War II |publisher=[[United States Naval Institute]] Proceedings |date=May 1968}}</ref>

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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.

产出与投入的“汇率”比率是运筹学的一个特征。通过比较盟军飞机投入的飞行时数和某一地区发现 U 型潜艇的次数，可以将飞机重新分配到生产力更高的巡逻区。比较汇率确定的“有效性比率”在规划中有用。每艘沉船埋设60枚地雷的比例在几次战役中都很常见: 德国在英国港口埋设地雷，英国在德国航线埋设地雷，美国在日本航线埋设地雷。

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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 traditional dull camouflage paint finish, and a smooth paint finish increased airspeed by reducing skin friction.<ref name="Proceedings"/>

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Operational research doubled the on-target bomb rate of B-29s 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.

作战研究通过将训练时间从4% 提高到10% ，使从 Marianas Islands 轰炸日本的 b-29轰炸机的命中率翻了一番; 揭示了三艘美国潜艇的狼群是最有效的数量，使所有成员都能够接触到在各自巡逻站发现的目标; 揭示了光泽的珐琅涂料比传统的暗淡的伪装涂料涂层更有效地伪装夜间战斗机，光滑的涂料涂层通过减少皮肤摩擦来提高空速。

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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.

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On land, the operational research sections of the Army Operational Research Group (AORG) of the Ministry of Supply (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.

在陆地上，供应部(MoS)的陆军作战研究小组(AORG)的作战研究部门于1944年在诺曼底登陆，他们跟随英国军队在整个欧洲推进。他们分析了火炮、空中轰炸和反坦克射击的有效性。

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In 1967 [[Stafford Beer]] characterized the field of management science as "the business use of operations research".<ref>[[Stafford Beer]] (1967) ''Management Science: The Business Use of Operations Research''</ref> 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 [[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 complex decision problems. Management scientists help businesses to achieve their goals using the scientific methods of operational research.

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In 1967 Stafford Beer characterized the field of management science as "the business use of operations research".Stafford Beer (1967) Management Science: 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 modeling, statistics and numerical algorithms to improve an organization's ability to enact rational and meaningful management decisions by arriving at optimal or near optimal solutions to complex decision problems. Management scientists help businesses to achieve their goals using the scientific methods of operational research.

= = 管理科学 = = 1967年，斯塔福德 · 比尔(Stafford Beer)将管理科学描述为“运筹学的商业应用”。Stafford Beer (1967)管理科学: 运筹学的商业应用就像运筹学本身一样，管理科学(MS)是应用数学的一个跨学科分支，致力于最优决策规划，与经济学、商业、工程学和其他科学有着密切的联系。它使用各种科学研究为基础的原则，战略和分析方法，包括数学建模，统计和数值算法，以提高组织的能力，制定合理和有意义的管理决策，通过达到最佳或接近最佳的解决方案，复杂的决策问题。管理科学家利用运筹学的科学方法帮助企业实现目标。

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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.

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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.

管理科学家的使命是使用理性的、系统的、以科学为基础的技术来告知和改进各种决策。当然，管理科学的技术并不局限于商业应用，而是可以应用于军事、医疗、公共管理、慈善团体、政治团体或社区团体。

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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>

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Management science is concerned with developing and applying models 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.

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管理科学涉及开发和应用可能有助于阐明管理问题和解决管理问题的模型和概念，以及设计和开发新的和更好的组织卓越模型。什么是管理科学？兰卡斯特大学，2008年。2008年6月5日检索。

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管理科学涉及开发和应用可能有助于阐明管理问题和解决管理问题的模型和概念，以及设计和开发新的和更好的组织卓越模型。

The application of these models within the corporate sector became known as management science.<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>

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~~The application of these models within the corporate sector became known as management science.What is Management Science? The University of Tennessee, 2006. Retrieved 5 June 2008.~~

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~~这些模型在企业部门的应用被称为管理科学。什么是管理科学？田纳西大学，2006年。2008年6月5日检索。~~

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这些模型在企业部门的应用被称为管理科学。

===Related fields===

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<ref>{{Cite web |url=http://nak-architecture.com/index.php/en/services/blog/55-urban-operations-research-uor |title=Archived copy |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>

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Applications are abundant such as in airlines, manufacturing companies, service organizations, military branches, and government. The range of problems and issues to which it has contributed insights and solutions is vast. It includes:

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* Scheduling (of airlines, trains, buses etc.)

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* Assignment (assigning crew to flights, trains or buses; employees to projects; commitment and dispatch of power generation facilities)

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* Facility location (deciding most appropriate location for new facilities such as warehouse; factory or fire station)

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* Hydraulics & Piping Engineering (managing flow of water from reservoirs)

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* Health Services (information and supply chain management)

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* Game Theory (identifying, understanding; developing strategies adopted by companies)

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* Urban Design

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* Computer Network Engineering (packet routing; timing; analysis)

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* Telecom & Data Communication Engineering (packet routing; timing; analysis)

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* robustness analysis

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~~Management is also concerned with so-called 'soft-operational analysis' which concerns methods for strategic planning, strategic decision support, problem structuring methods.~~

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*

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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:

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* ~~stakeholder based approaches including metagame analysis and drama theory~~

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* morphological analysis and various forms of influence diagrams

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* cognitive mapping

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* strategic choice

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* robustness analysis

管理还涉及所谓的“软运营分析”，涉及战略规划方法、战略决策支持、问题结构化方法。在应对这类挑战时，数学建模与模拟可能不合适，也可能不够。因此，在过去的30年中，一些非量化的建模方法得到了发展。这些包括:

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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> 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>

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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)

国际运筹学会联合会(IFORS)是全球运筹学会的伞状组织，代表了大约50个国家的学会，包括美国、英国、法国、德国、意大利、加拿大、澳大利亚、新西兰、菲律宾、印度、日本和南非的学会。IFORS 的组成成员组成区域组织，例如在欧洲，欧洲运筹学会协会(欧洲运筹学会)。其他重要的运营研究组织包括模拟互操作性标准组织(SISO)和跨服务/行业培训、模拟和教育会议(I/ITSEC)

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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>

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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.

2004年，总部位于美国的 INFORMS 组织开始了一项旨在更好地推销 OR 专业的倡议，其中包括一个名为“更好的科学”的网站，该网站提供了 OR 的介绍以及 OR 在工业问题上的成功应用实例。这一倡议已被英国运筹学会采纳，包括一个名为“了解或”的网站。

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* ''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>

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~~These are listed in alphabetical order of their titles.~~

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* 4OR-A Quarterly Journal of Operations Research: jointly published the Belgian, French and Italian Operations Research Societies (Springer);

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* Decision Sciences published by Wiley-Blackwell on behalf of the Decision Sciences Institute

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* European Journal of Operational Research (EJOR): Founded in 1975 and is presently by far the largest operational research journal in the world, with its around 9,000 pages of published papers per year. In 2004, its total number of citations was the second largest amongst Operational Research and Management Science journals;

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* INFOR Journal: published and sponsored by the Canadian Operational Research Society;

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* International Journal of Operations Research and Information Systems (IJORIS): an official publication of the Information Resources Management Association, published quarterly by IGI Global;

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* 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.

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* 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;

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* Military Operations Research (MOR): published by the Military Operations Research Society;

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* Omega - The International Journal of Management Science;

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* Operations Research Letters;

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* Opsearch: official journal of the Operational Research Society of India;

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* OR Insight: a quarterly journal of The OR Society, published by Palgrave;The OR Society ;

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* Pesquisa Operacional, the official journal of the Brazilian Operations Research Society

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* Production and Operations Management, the official journal of the Production and Operations Management Society

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* TOP: the official journal of the Spanish Statistics and Operations Research Society.

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~~= = = 其他杂志 = = = 这些杂志在字母顺序中列出了它们的名称。~~

* 4OR ——《运筹学季刊》 : 联合出版比利时、法国和意大利运筹学会(Springer) ;

* 决策科学由 Wiley-Blackwell 代表决策科学研究所出版

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