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运筹学 (查看源代码)

2023年1月18日 (三) 20:54的版本

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'''Operations research''' ({{lang-en-GB|'''operational research'''}}), often shortened to the [[initialism]] '''OR''', is a discipline that deals with the development and application of advanced analytical methods to improve decision-making.<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> It is considered to be a subfield of [[mathematical sciences]].<ref>{{cite web|url=http://www.mathontheweb.org/mathweb/mi-mathbyclass.html |title=Mathematics Subject Classification |publisher=American Mathematical Society |date= 23 May 2011 |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>

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Operations research， often shortened to the initialism OR, is a discipline that deals with the development and application of advanced analytical methods to improve decision-making. It is considered to be a subfield of mathematical sciences. The term management science is occasionally used as a synonym.

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运筹学是一门研究如何开发和应用先进的分析方法来改进决策的学科。它的英文名称为Operations research，可缩写成OR，是数学科学的一个分支。管理科学这个术语有时被用作是运筹学的同义词。

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Operations research (), often shortened to the initialism OR, is a discipline that deals with the development and application of advanced analytical methods to improve decision-making. It is considered to be a subfield of mathematical sciences. The term management science is occasionally used as a synonym.

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~~运筹学是一门研究如何开发和应用先进的分析方法来改进决策的学科。它被认为是数学科学的一个分支。管理科学这个术语有时被用作同义词。~~

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 complex decision-making problems. Because of its emphasis on practical applications, operations research has overlap with many other disciplines, notably [[industrial engineering]]. Operations research is often concerned with determining the extreme values of some real-world objective: the [[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}}</ref>

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Employing techniques from other mathematical sciences, such as modeling, statistics, and optimization, operations research arrives at optimal or near-optimal solutions to complex decision-making problems. Because of its emphasis on practical applications, operations research has overlap with many other disciplines, notably industrial engineering. Operations research is often concerned with determining the extreme values of some real-world objective: the maximum (of profit, performance, or yield) or minimum (of loss, risk, or cost). Originating in military efforts before World War II, its techniques have grown to concern problems in a variety of industries.

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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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运筹学运用了其他数学科学的技术，如建模、统计和优化等，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，运筹学与许多其他学科，特别是工业工程学重叠。运筹学通常关注于确定一些现实世界目标的极端值: 最大值(利润、业绩或收益)或最小值(损失、风险或成本)~~。起源于第二次世界大战前的军事努力，其技术已经发展到关注各种行业的问题。~~

==Overview==

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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).

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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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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 models, Markov decision processes, econometric methods, data envelopment analysis, neural networks, expert systems, decision analysis, and the analytic hierarchy process. Nearly all of these techniques involve the construction of mathematical models that attempt to describe the system. Because of the computational and statistical nature of most of these fields, OR also has strong ties to computer science and analytics. 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).

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操作研究(OR)包括开发和使用广泛的解决问题的技术和方法，以追求改进的决策和效率，如模拟，最优化，排队论和其他随机过程模型，马尔可夫决策过程，计量经济学方法，数据包络分析，神经网络，专家系统，决策分析和层级分析法。几乎所有这些技术都涉及到试图描述系统的数学模型的构建。由于这些领域中大多数的计算和统计特性，OR 也与计算机科学和分析学有很强的联系。运筹学研究人员面对一个新问题时，必须根据系统的性质、改进的目标、时间和计算能力的限制，确定这些技术中哪一种最合适，或者针对手头的问题(以及之后针对这种类型的问题)开发一种新技术。

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运筹学寻求优化的决策和效率的提升，涉及的多种研究方法包括模拟，最优化，排队论和其他随机过程模型，包括马尔可夫决策过程，计量经济学方法，数据包络分析，神经网络，专家系统，决策分析和层级分析法。这些方法都涉及到描述系统的数学模型的构建。此外，OR 也与计算机科学和分析学有很强的联系。运筹学研究人员面对一个新问题时，必须根据系统的性质、改进的目标、时间和计算能力的限制去建立模型，改进决策。

The major sub-disciplines 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> are:

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* Transportation

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~~The major sub-disciplines in modern operational research, as identified by the journal Operations Research, are:~~

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运筹学的主要分支学科是:

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* Computing and information technologies

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* Financial engineering

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* Manufacturing, service sciences, and supply chain management

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* Policy modeling and public sector work

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*Revenue management

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* Simulation

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* Stochastic models

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* Transportation

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~~运营研究杂志确定的现代运营研究的主要分支学科是~~:

* 计算和信息技术

* 金融工程

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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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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.

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在两次世界大战之后的几十年里，作战研究工具被更广泛地应用于商业、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从石油化工到航空、金融、物流和政府等行业的领域，转移到可用于分析和优化复杂系统的数学模型的发展上，并已成为一个积极的学术和工业研究领域。

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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。

===Historical origins===

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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

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[[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]]

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[[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]]

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>

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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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[[File:Kammhuber Line Map - Agent Tegal.png|thumb|upright|left|Map of ''[[Kammhuber Line]]'']]

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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 defences]] was noted and the recommendation was given that armour be added in the most heavily damaged areas. This recommendation was not adopted because the fact that the aircraft were able to return with these areas damaged indicated the areas were not vital, and adding armour to non-vital areas where damage is acceptable reduces aircraft performance. Their suggestion to remove some of the crew so that an aircraft loss would result in fewer personnel losses, was also rejected by RAF command. Blackett's team made the logical recommendation that the armour be placed in the areas which were completely untouched by damage in the bombers which returned. They reasoned that the survey was biased, since it only included aircraft that returned to Britain. The areas untouched in returning aircraft were probably vital areas, which, if hit, would result in the loss of the aircraft.<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}}</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>

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* 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

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* critical path analysis or project planning: identifying those processes in a complex project which affect the overall duration of the project

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*critical path analysis or project planning: identifying those processes in a complex project which affect the overall duration of the project

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* Floorplanning: designing the layout of equipment in a factory or components on a computer chip to reduce manufacturing time (therefore reducing cost)

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*Floorplanning: designing the layout of equipment in a factory or components on a computer chip to reduce manufacturing time (therefore reducing cost)

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* Network optimization: for instance, setup of telecommunications or power system networks to maintain quality of service during outages

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*Network optimization: for instance, setup of telecommunications or power system networks to maintain quality of service during outages

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* Resource allocation problems

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*Resource allocation problems

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* Facility location

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*Facility location

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* Assignment Problems:

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*Assignment Problems:

**Assignment problem

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** Generalized assignment problem

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**Generalized assignment problem

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** Quadratic assignment problem

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**Quadratic assignment problem

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** Weapon target assignment problem

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**Weapon target assignment problem

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* Bayesian search theory: looking for a target

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*Bayesian search theory: looking for a target

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* Optimal search

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*Optimal search

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* Routing, such as determining the routes of buses so that as few buses are needed as possible

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*Routing, such as determining the routes of buses so that as few buses are needed as possible

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* Supply chain management: managing the flow of raw materials and products based on uncertain demand for the finished products

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*Supply chain management: managing the flow of raw materials and products based on uncertain demand for the finished products

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* 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"Factory Physics for Managers", E. S. Pound, J. H. Bell, and M. L. Spearman, McGraw-Hill, 2014, p 47<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

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*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"Factory Physics for Managers", E. S. Pound, J. H. Bell, and M. L. Spearman, McGraw-Hill, 2014, p 47<nowiki><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</nowiki>

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* 关键路径分析或项目规划: 识别复杂项目中影响项目整体持续时间的过程

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*关键路径分析或项目规划: 识别复杂项目中影响项目整体持续时间的过程

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* 楼层规划: 在计算机芯片上设计工厂设备或部件的布局，以减少制造时间(从而降低成本)

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*楼层规划: 在计算机芯片上设计工厂设备或部件的布局，以减少制造时间(从而降低成本)

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* 网络优化: 例如,

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*网络优化: 例如,

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* 资源分配问题

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*资源分配问题

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* 设施位置

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*设施位置

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* 分配问题

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*分配问题

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*

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*

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* 广义分配问题

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*广义分配问题

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*

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*

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* 二次分配问题

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*二次分配问题

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*

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*

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* 武器目标分配问题

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*武器目标分配问题

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* 贝叶斯搜索理论: 寻找目标

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*贝叶斯搜索理论: 寻找目标

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* 最佳搜索

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*最佳搜索

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* 路由,

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*路由,

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* 供应链管理: 基于对成品的不确定需求来管理原材料和产品的流动

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*供应链管理: 基于对成品的不确定需求来管理原材料和产品的流动

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* 项目生产活动: 通过运营研究工具来管理基本建设项目中的工作流程，以应对系统的可变性,库存和时间“面向经理人的工厂物理学”，E.S. 庞德，J。贝尔和 M。斯皮尔曼，麦格劳-希尔，2014，第47页 < 参考文献 > “项目交付的新时代-项目作为生产系统”，R。 Shenoy 和 T。 R。 Zabelle，《项目生产管理杂志》，第1卷，2016年11月，第13-24页

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*项目生产活动: 通过运营研究工具来管理基本建设项目中的工作流程，以应对系统的可变性,库存和时间“面向经理人的工厂物理学”，E.S. 庞德，J。贝尔和 M。斯皮尔曼，麦格劳-希尔，2014，第47页 < 参考文献 > “项目交付的新时代-项目作为生产系统”，R。 Shenoy 和 T。 R。 Zabelle，《项目生产管理杂志》，第1卷，2016年11月，第13-24页

<nowiki>https://www.researchgate.net/publication/312602707_New_Era_of_Project_Delivery_-_Project_as_Production_System</nowiki>

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