运筹学

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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.[1] It is considered to be a subfield of mathematical sciences.[2] The term management science is occasionally used as a synonym.[3]

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.

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。

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.[4]


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。

Overview 总览

Operational research (OR) encompasses the development and applies a wide range of problem-solving techniques to pursuit optimized decision-making process and efficient result , 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.[5] All of these techniques involve the construction of mathematical models that relate 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, which contributes to make better decisions.


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,[6] are:

运筹学的主要分支学科是:

  • 计算和信息技术
  • 金融工程
  • 制造业、服务科学和供应链管理
  • 政策建模和公共部门工作
  • 收入管理
  • 模拟
  • 随机模型
  • 运输

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.[4]


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 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-theoretic ideas and expected values; others, such as Pierre de Fermat and Jacob Bernoulli, solved these types of problems using combinatorial reasoning instead.[7] 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.[8] Beginning in the 20th century, study of inventory management could be considered模板:By whom the origin of modern operations research with economic order quantity developed by Ford W. Harris in 1913. 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) ,而其他数学家,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。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。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,对经济活动的量化管理是福特 · W · 哈里斯在1913年发展起来的。

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.[9] 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.[10]


现代运筹学起源于1937年英国的鲍德西研究站,这离不开该站负责人 A.P.Rowe 和劳勃·沃森-瓦特发起的一项倡议。罗伊将这一学科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,后来扩展到分析操作人员的行为。这暴露了 CH 网络的局限性,并允许采取补救行动。


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.

英国的科学家(包括帕特里克 · 布莱克特(后来的布莱克特勋爵 OM PRS)、塞西尔 · 戈登(Cecil Gordon)、索利 · 祖克曼(后来的扎克曼男爵 OM、 KCB、 FRS)、 C · H · 沃丁顿(C. H. Waddington)、欧文 · 万斯布罗-琼斯(Owen Wansbrough-Jones)、弗兰克 · 耶茨(Frank Yates)、雅各布 · 布罗诺夫斯基(Jacob Bronowski)和弗里曼 · 戴森(Freeman Dyson)) ,以及美国的科学家(乔治 · 丹齐格(George Dantzig))都在寻找物流运输过程与事物运作规程的更优解。

Second World War 第二次世界大战

The modern field of operational research arose during World War II. In the World War II era, operational research was defined as "a scientific method of providing executive departments with a quantitative basis for decisions regarding the operations under their control".[11] Other names for it included operational analysis (UK Ministry of Defence from 1962)[12] and quantitative management.[13]

现代运筹学兴起于第二次世界大战期间。在第二次世界大战时期,运筹学被定义为“为执行部门在其控制下的作战决策提供量化基础的一种科学的方法。它又被称为战略分析或量化管理。

During the Second World War, nearly 1,000 men and women in Britain were engaged in operational research. About 200 operational research scientists worked for the British Army.[14]

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。

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.[15]

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。

文件:B 24 in raf service 23 03 05.jpg
A 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, Then, early in 1942, to the Admiralty.[16] 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.[17][18] They undertook a number of crucial analyses that aided to win the war. 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.[19]

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,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其他在自己的领域中继续取得卓越成就的人。他们进行了一些关键的分析,以协助战争胜利。英国引入护航系统是为了减少航运损失。尽管使用军舰陪同商船的原则得到普遍接受,但护航船队是小型还是大型还不清楚。实际上,船队虽然以最慢的速度行驶,但船小好调头,因此可以得出小型船队可以行驶得更快的结论。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程度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,小型船队比大型船队更有利于迂回作战。

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.[20] As a result of these findings Coastal Command changed their aircraft to using white undersurfaces.

在分析英国皇家空军海防司令部捕猎和摧毁潜艇的方法时,其中一名分析师询问这些飞机是什么颜色的。由于他们中的大多数飞机属于轰炸机司令部,他们被涂成黑色,用作夜间行动。根据 CC-ORS 的建议,进行了一次测试,以确定这是否是在北大西洋灰色天空中白天作业时对飞机进行伪装的最佳颜色。试验表明,涂成白色的飞机平均要比涂成黑色的飞机的距离近20%才会被发现。这一变化表明,同样数量的目击事件将导致30% 以上的潜艇被攻击和击沉。由于这些发现,海岸指挥部改变了他们的飞机使用白色的下表面。

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".[21]


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,炸药没有炸毁潜艇。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,因为在更深的地方只能靠猜测。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。”


Bomber Command's Operational Research Section (BC-ORS), analyzed a report of a survey carried out by RAF Bomber Command. For the survey, Bomber Command inspected all bombers returning from bombing raids over Germany over a particular period. All damage inflicted by German air defences was noted and the recommendation was given that armour be added in the most heavily damaged areas. This recommendation was not adopted because the fact that the aircraft were able to return with these areas damaged indicated the areas were not vital, and adding armour to non-vital areas where damage is acceptable reduces aircraft performance. Their suggestion to remove some of the crew so that an aircraft loss would result in fewer personnel losses, was also rejected by RAF command. Blackett's team made the logical recommendation that the armour be placed in the areas which were completely untouched by damage in the bombers which returned. They reasoned that the survey was biased, since it only included aircraft that returned to Britain. The areas untouched in returning aircraft were probably vital areas, which, if hit, would result in the loss of the aircraft. This story has been disputed, with a similar damage assessment study completed in the US by the Statistical Research Group at Columbia University, the result of work done by Abraham Wald.

轰炸机司令部作战研究部(BC-ORS)分析了一份由皇家空军轰炸机司令部进行的调查报告。为了调查,轰炸机司令部检查了所有在德国的作战时期执行过任务的轰炸机。在调查过程中,关注到了德国防空系统存在的问题,并建议在轰炸机受损最严重的地方增加装甲。这项建议没有获得通过,因为飞机能够在这些地区受损后返回,这表明这些地区并不重要,在损坏可以接受的非重要地区增加装甲会降低飞机的性能。他们建议撤掉一些机组人员,以减少飞机损失造成的人员损失,但这一建议也遭到了英国皇家空军司令部的拒绝。布莱克特的团队提出了合乎逻辑的建议,把装甲部队放在那些完全没有被返回的轰炸机损坏的地方。他们的理由是,这项调查是有偏见的,因为它只包括返回英国的飞机。返航飞机没有触及的区域可能是至关重要的区域,如果被击中,将导致飞机损失。哥伦比亚大学统计研究小组在美国完成了一项类似的损失评估研究,这项研究是亚伯拉罕•沃尔德(Abraham Wald)的工作成果。

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.[22]


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。当时的计算重点是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。

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.[23]


产出与投入的比率是运筹学的一个重要指标。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。比较投入产出比在规划中起着重要作用。此外,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。

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.[23]


经过运筹学分析后,将训练时间从4% 提高到10% ,使 Marianas Islands 轰炸日本的 b-29轰炸机的命中率翻了一番; 同时揭示了三艘美国潜艇是最利于执行战术的数量,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表面摩擦来提高空速。

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。

After World War II 二战之后

In 1947 under the auspices of the British Association, a symposium was organised in Dundee. In his opening address Watson-Watts offered a definition of the aims of OR:

"to examine quantitatively whether the user organization is getting from the operation of its equipment the best attainable contribution to its overall objective."[9]

With expanded techniques and growing awareness of the field at the close of the war, operational research was no longer limited to only operational, but was extended to encompass equipment procurement, training, logistics and infrastructure. Operations Research also grew in many areas other than the military once scientists learned to apply its principles to the civilian sector. With the development of the simplex algorithm for linear programming in 1947[24] and the development of computers over the next three decades, Operations Research can now solve problems with hundreds of thousands of variables and constraints. Moreover, the large volumes of data required for such problems can be stored and manipulated very efficiently."[24] Much of operations research (modernly known as 'analytics') relies upon stochastic variables and a therefore access to truly random numbers. Fortunately the cybernetics field also required the same level of randomness. The development of increasingly better random number generators has been a boon to both disciplines. Modern applications of operations research include city planning, football strategies, emergency planning, optimizing all facets of industry and economy, and undoubtedly with the likelihood of the inclusion of terrorist attack planning and definitely counter-terrorist attack planning. More recently, the research approach of operations research, which dates back to the 1950s, has been criticized for being collections of mathematical models but lacking an empirical basis of data collection for applications. How to collect data is not presented in the textbooks. Because of the lack of data, there are also no computer applications in the textbooks.[25]


http://www.paecon.net/PAEReview/issue88/Vahrenkamp88.pdf).

1947年,在英国协会的赞助下,在邓迪组织了一个研讨会。沃森-瓦茨在开幕词中对 OR 的目标给出了一个定义: “定量地检查用户组织是否从其设备的运行中获得了对其总体目标的最佳可达贡献。”战争结束后,随着技术的发展和人们对战场认识的提高,作战研究不再局限于作战,而是扩展到包括装备采购、训练、后勤和基础设施。科学家学会将其原理应用于民用部门,运筹学在军事以外的许多领域也得到了发展。随着1947年单纯形法线性规划的发展和未来30年计算机的发展,运筹学现在可以解决数十万个变量和约束条件下的问题。此外,这些问题所需的大量数据可以非常有效地存储和处理。”许多运筹学研究(现代称为“分析学”)依赖于随机变量,因此可以获得真正的随机数。此外,控制论领域也需要同样水平的随机性。越来越好的随机数发生器的发展对这两个学科都是有益的。作战研究的现代应用包括城市规划、足球战略、应急规划、优化工业和经济的各个方面,毫无疑问还包括恐怖袭击规划和明确的反恐袭击规划。最近,可以追溯到1950年代的运筹学研究方法被批评为是数学模型的集合,但缺乏应用数据收集的经验基础。教科书中没有提到如何收集数据。由于缺乏数据,教材中也没有计算机应用。理查德 · 瓦伦坎普: 《没有数据的名义科学: 博弈论和运筹学的冷战内容》 ,《现实世界经济评论》卷。88,2019,pp.19-50( http://www.paecon.net/paereview/issue88/vahrenkamp88.pdf ).

Problems addressed 运筹学的相关研究问题

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: LTL shipping, intermodal freight transport, travelling salesman problem, driver scheduling problem)
  • Scheduling:
    • Personnel staffing
    • Manufacturing steps
    • Project tasks
    • Network data traffic: these are known as queueing models 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.

Https://www.researchgate.net/publication/312602707_new_era_of_project_delivery_-_project_as_production_system </ref >

  • 有效的信息传递和客户响应策略
  • 自动化: 在人类驱动的操作过程中自动化或集成机器人系统
  • 全球化: 全球化操作过程,以便利用更廉价的材料、劳动力、土地或其他生产力投入
  • 运输: 管理货运和交付系统(例如: LTL 运输、多式联运货运、旅行推销员问题、司机调度问题)
  • 计划:
  • 人员配置
  • 制造步骤
  • 项目任务
  • 网络数据流量: 这些被称为排队模型或排队系统。
  • 体育赛事及其电视报道
  • 炼油厂原材料的混合
  • 在定价科学学科范围内,在许多零售和 B2B 环境中确定最优价格
  • 削减库存问题: 从大件商品中削减小件商品。

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

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

运筹学也广泛应用于政府采用循证政策的地方。

Management science 管理科学

In 1967 Stafford Beer characterized the field of management science as "the business use of operations research".[28] 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.

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”。像运筹学一样,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。

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、科学导向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,它可以应用于军事、医疗、公共管理、慈善团体、政治团体或社区团体。

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.[29]


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。

Related fields 相关领域

Some of the fields that have considerable overlap with Operations Research and Management Science include:[30]

Some of the fields that have considerable overlap with Operations Research and Management Science include:

  • 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
  • Queuing Theory
  • Simulation
  • Social network/Transportation forecasting models
  • Stochastic processes
  • Supply chain management
  • Systems engineering


  • 商业分析
  • 计算机科学
  • 数据挖掘/数据科学/大数据
  • 决策分析
  • 决策智能
  • 金融工程
  • 预测
  • 博弈论
  • 地理/地理信息科学
  • 图论
  • 工业工程
  • 库存控制
  • 物流
  • 数学建模
  • 最优化
  • 概率和统计
  • 项目管理
  • 政策分析
  • 排队论
  • 模拟
  • 社会网络/运输预测模型
  • 随机过程
  • 供应链管理
  • 系统工程

Applications 应用

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:[29]

  • Scheduling (of airlines, trains, buses etc.)
  • Assignment (assigning crew to flights, trains or buses; employees to projects; commitment and dispatch of power generation facilities)
  • Facility location (deciding most appropriate location for new facilities such as warehouse; factory or fire station)
  • Hydraulics & Piping Engineering (managing flow of water from reservoirs)
  • Health Services (information and supply chain management)
  • Game Theory (identifying, understanding; developing strategies adopted by companies)
  • Urban Design
  • Computer Network Engineering (packet routing; timing; analysis)
  • Telecom & Data Communication Engineering (packet routing; timing; analysis)

[31]


应用程序是丰富的,如在航空公司,制造公司,服务组织,军事分支机构和政府。它提出的见解和解决办法涉及的问题和问题范围很广。它包括: (航空公司、火车、公共汽车等的)日程安排

  • 设施位置(决定新设施如仓库、工厂或消防站的最合适位置)
  • 水力和管道工程(管理水库的水流)
  • 卫生服务(信息和供应链管理)
  • 博弈论(识别、理解; 发展公司采用的策略)
  • 城市设计
  • 计算机网络工程(包路由; 计时; 分析)
  • 电信和数据通信工程(包路由; 计时; 分析)

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模板:Vague, a number of non-quantified modeling methods have been developed. These include:[citation needed]

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:

  • 基于利益相关者的方法,包括元游戏分析和戏剧理论
  • 形态分析和各种形式的影响图
  • 认知映射
  • 战略选择
  • 稳健性分析

Societies and journals 社会组织与学术期刊

Societies

The International Federation of Operational Research Societies (IFORS)[32] is an umbrella organization for operational research societies worldwide, representing approximately 50 national societies including those in the US,[33] UK,[34] France,[35] Germany, Italy,[36] Canada,[37] Australia,[38] New Zealand,[39] Philippines,[40] India,[41] Japan and South Africa.[42] The constituent members of IFORS form regional groups, such as that in Europe, the Association of European Operational Research Societies (EURO).[43] Other important operational research organizations are Simulation Interoperability Standards Organization (SISO)[44] and Interservice/Industry Training, Simulation and Education Conference (I/ITSEC)[45]


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)

In 2004 the US-based organization INFORMS began an initiative to market the OR profession better, including a website entitled The Science of Better[46] 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.


2004年,总部位于美国的 INFORMS 组织开始了一项旨在更好地推广 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.

Journals of INFORMS 运筹学与管理科学的相关期刊

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.[47] They are:

The Institute for Operations Research and the Management Sciences (INFORMS) publishes thirteen scholarly journals about operations research, according to 2005 Journal Citation Reports. They are:

  • Decision Analysis
  • Information Systems Research
  • INFORMS Journal on Computing
  • INFORMS Transactions on Education (an open access journal)
  • Interfaces
  • Management Science
  • Manufacturing & Service Operations Management
  • Marketing Science
  • Mathematics of Operations Research
  • Operations Research
  • Organization Science
  • Service Science
  • Transportation Science

根据2005年的期刊引证报告,运筹学和管理科学研究所(INFORMS)出版了13种关于运筹学的学术期刊,它们是:

  • 决策分析
  • 信息系统研究
  • 信息系统计算杂志
  • 信息系统教育杂志(开放获取期刊)
  • 界面
  • 管理科学
  • 制造与服务运营管理
  • 营销科学
  • 运营研究数学
  • 运营研究
  • 组织科学
  • 服务科学
  • 运输科学

Other journals 其它期刊

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模板:When 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;
  • International Journal of Operations Research and Information Systems (IJORIS): an official publication of the Information Resources Management Association, published quarterly by IGI Global;[55]
  • 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.[56]
  • 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;[57]
  • 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.[58]
  • 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
  • 《欧洲运筹学期刊》(EJOR) : 创建于1975年,目前是世界上最大的运筹学期刊,每年发表论文约9000页。国际作战研究和信息系统杂志(IJORIS) : 信息资源管理协会的官方出版物,由 IGI 全球公司每季度出版; 国防建模与模拟杂志(JDMS) : 应用、方法、技术: 致力于推进与军事和国防有关的建模与模拟科学的季刊。作战研究协会杂志(JORS) : 作战研究协会的官方杂志,这是世界上最古老的连续出版的作战研究杂志,由泰勒弗朗西斯集团出版
  • Omega-国际管理科学杂志;
  • 运筹学研究快报;
  • Opsearch: 印度运筹学会的官方杂志;
  • OR Insight: 由 Palgrave 出版的 OR 学会季刊;
  • Pesquisa Operacional,巴西运筹学会的官方杂志;
  • ProductionandOperationManagement,生产和运筹管理学会的官方杂志;
  • TOP: 西班牙统计和运筹学会的官方杂志。

See also 更多信息

模板:Col-begin 模板:Col-break

Operations research topics 运筹学的研究领域

模板:Col-break

Operations researchers 运筹学的研究者们

模板:Col-break

模板:Col-break

Related fields 相关领域

模板:Col-break

模板:Col-end


运筹学的研究领域

  • 黑盒分析
  • 动态规划
  • 库存理论
  • 最优维护

运筹学的研究者们

  • 乔治 · 丹齐格
  • 列昂尼德·坎托罗维奇
  • 特亚林·科普曼斯
  • 拉塞尔 · L · 阿科夫
  • 斯塔福德啤酒
  • 阿尔弗雷德 · 布鲁姆斯坦
  • C · 西丘奇曼
  • 威廉 · W · 库珀
  • 罗伯特 · 多夫曼
  • 理查德 · M · 卡普
  • 拉马亚 · 克里希南
  • 弗雷德里克·威廉·兰彻斯特
  • 托马斯.L.马尼安提
  • 阿尔文 · E · 罗斯
  • 相关领域
  • 行为操作研究
  • 大数据
  • 商业工程
  • 商业过程管理
  • 数据库规范化
  • 工程管理
  • 地理信息系统
  • 工业工程
  • 管理经济
  • 兵棋推演
  • 战争的操作水平
  • 电力系统仿真
  • 项目生产管理
  • 可靠度
  • 科学管理
  • 基于搜索的软件工程
  • 仿真建模
  • 战略管理
  • 供应链工程
  • 系统安全
  • 战争游戏

References 参考文献

  1. "What is O.R.?". INFORMS.org. Retrieved 7 January 2012.
  2. "Mathematics Subject Classification". American Mathematical Society. 23 May 2011. Retrieved 7 January 2012.
  3. Wetherbe, James C. (1979), Systems analysis for computer-based information systems, West series in data processing and information systems, West Pub. Co., ISBN 9780829902280, 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.
  4. 4.0 4.1 "What is OR". HSOR.org. Retrieved 13 November 2011.
  5. "Operations Research Analysts". Bls.gov. Retrieved 27 January 2012.
  6. "OR / Pubs / IOL Home". INFORMS.org. 2 January 2009. Archived from the original on 27 May 2009. Retrieved 13 November 2011.
  7. Shafer, G. (2018). Pascal's and Huygens's game-theoretic foundations for probability. [1]
  8. 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 -{zh-cn:互联网档案馆; zh-tw:網際網路檔案館; zh-hk:互聯網檔案館;}-存檔,存档日期14 July 2009.
  9. 9.0 9.1 Zuckerman, Solly (1964). "In the Beginning -- And Later". OR. 15 (4): 287–292. doi:10.2307/3007115. ISSN 1473-2858. JSTOR 3007115.
  10. "operations research (industrial engineering) :: History – Britannica Online Encyclopedia". Britannica.com. Retrieved 13 November 2011.
  11. "Operational Research in the British Army 1939–1945", October 1947, Report C67/3/4/48, UK National Archives file WO291/1301
    Quoted on the dust-jacket of: Morse, Philip M, and Kimball, George E, Methods of Operation Research, 1st edition revised, MIT Press & J Wiley, 5th printing, 1954.
  12. 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 Research Establishment (DOAE) which was formed in 1965, and it the Army Operational Research Establishment based at West Byfleet."
  13. "Archived copy" (PDF). Archived from the original (PDF) on 12 August 2011. Retrieved 7 October 2009.{{cite web}}: CS1 maint: archived copy as title (link)
  14. Kirby, p. 117 -{zh-cn:互联网档案馆; zh-tw:網際網路檔案館; zh-hk:互聯網檔案館;}-存檔,存档日期27 August 2013.
  15. Kirby, pp. 91–94 -{zh-cn:互联网档案馆; zh-tw:網際網路檔案館; zh-hk:互聯網檔案館;}-存檔,存档日期27 August 2013.
  16. Kirby, p. 96,109 -{zh-cn:互联网档案馆; zh-tw:網際網路檔案館; zh-hk:互聯網檔案館;}-存檔,存档日期2 October 2013.
  17. Kirby, p. 96 -{zh-cn:互联网档案馆; zh-tw:網際網路檔案館; zh-hk:互聯網檔案館;}-存檔,存档日期27 March 2014.
  18. Freeman Dyson, MIT Technology Review (1 November 2006) "A Failure of Intelligence: Part I"
  19. ""Numbers are Essential": Victory in the North Atlantic Reconsidered, March–May 1943". Familyheritage.ca. 24 May 1943. Retrieved 13 November 2011.
  20. Kirby, p. 101
  21. (Kirby, pp. 102,103)
  22. "RAF History – Bomber Command 60th Anniversary". Raf.mod.uk. Archived from the original on 5 November 2011. Retrieved 13 November 2011.
  23. 23.0 23.1 Milkman, Raymond H. (May 1968). "Operation Research in World War II". United States Naval Institute Proceedings. {{cite journal}}: Cite journal requires |journal= (help)
  24. 24.0 24.1 "1.2 A HISTORICAL PERSPECTIVE". PRINCIPLES AND APPLICATIONS OF OPERATIONS RESEARCH. http://www.pitt.edu/~jrclass/or/or-intro.html#history. 
  25. Richard Vahrenkamp: Nominal Science without Data: The Cold War Content of Game Theory and Operations Research, in: Real World Economics Review, vol. 88, 2019, pp. 19–50, (http://www.paecon.net/PAEReview/issue88/Vahrenkamp88.pdf).
  26. "Factory Physics for Managers", E. S. Pound, J. H. Bell, and M. L. Spearman, McGraw-Hill, 2014, p 47
  27. "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
    • critical path analysis or project planning: identifying those processes in a complex 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)
    • Network optimization: for instance, setup of telecommunications or power system networks to maintain quality of service during outages
    • Resource allocation problems
    • Facility location
    • Assignment Problems:
      • Assignment problem
      • Generalized assignment problem
      • Quadratic assignment problem
      • Weapon target assignment problem
    • Bayesian search theory: looking for a target
    • 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"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
    • 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
    • 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)
    • 网络优化: 例如,
    • 资源分配问题
    • 设施位置
    • 分配问题
    • 广义分配问题
    • 二次分配问题
    • 武器目标分配问题
    • 贝叶斯搜索理论: 寻找目标
    • 最佳搜索
    • 路由,
    • 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
    • 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
    https://www.researchgate.net/publication/312602707_New_Era_of_Project_Delivery_-_Project_as_Production_System
  28. Stafford Beer (1967) Management Science: The Business Use of Operations Research
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Further reading 更多资料

Classic books and articles 经典文献

  • R. E. Bellman, Dynamic Programming, Princeton University Press, Princeton, 1957
  • Abraham Charnes, William W. Cooper, Management Models and Industrial Applications of Linear Programming, Volumes I and II, New York, John Wiley & Sons, 1961
  • Abraham Charnes, William W. Cooper, A. Henderson, An Introduction to Linear Programming, New York, John Wiley & Sons, 1953
  • C. West Churchman, Russell L. Ackoff & E. L. Arnoff, Introduction to Operations Research, New York: J. Wiley and Sons, 1957
  • George B. Dantzig, Linear Programming and Extensions, Princeton, Princeton University Press, 1963
  • Lester K. Ford, Jr., D. Ray Fulkerson, Flows in Networks, Princeton, Princeton University Press, 1962
  • Jay W. Forrester, Industrial Dynamics, Cambridge, MIT Press, 1961
  • L. V. Kantorovich, "Mathematical Methods of Organizing and Planning Production" Management Science, 4, 1960, 266–422
  • Ralph Keeney, Howard Raiffa, Decisions with Multiple Objectives: Preferences and Value Tradeoffs, New York, John Wiley & Sons, 1976
  • H. W. Kuhn, "The Hungarian Method for the Assignment Problem," Naval Research Logistics Quarterly, 1–2, 1955, 83–97
  • H. W. Kuhn, A. W. Tucker, "Nonlinear Programming," pp. 481–492 in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability
  • B. O. Koopman, Search and Screening: General Principles and Historical Applications, New York, Pergamon Press, 1980
  • Tjalling C. Koopmans, editor, Activity Analysis of Production and Allocation, New York, John Wiley & Sons, 1951
  • Charles C. Holt, Franco Modigliani, John F. Muth, Herbert A. Simon, Planning Production, Inventories, and Work Force, Englewood Cliffs, NJ, Prentice-Hall, 1960
  • Philip M. Morse, George E. Kimball, Methods of Operations Research, New York, MIT Press and John Wiley & Sons, 1951
  • Robert O. Schlaifer, Howard Raiffa, Applied Statistical Decision Theory, Cambridge, Division of Research, Harvard Business School, 1961
  • R. E. Bellman, Dynamic Programming, Princeton University Press, Princeton, 1957
  • Abraham Charnes, William W. Cooper, Management Models and Industrial Applications of Linear Programming, Volumes I and II, New York, John Wiley & Sons, 1961
  • Abraham Charnes, William W. Cooper, A. Henderson, An Introduction to Linear Programming, New York, John Wiley & Sons, 1953
  • C. West Churchman, Russell L. Ackoff & E. L. Arnoff, Introduction to Operations Research, New York: J. Wiley and Sons, 1957
  • George B. Dantzig, Linear Programming and Extensions, Princeton, Princeton University Press, 1963
  • Lester K. Ford, Jr., D. Ray Fulkerson, Flows in Networks, Princeton, Princeton University Press, 1962
  • Jay W. Forrester, Industrial Dynamics, Cambridge, MIT Press, 1961
  • L. V. Kantorovich, "Mathematical Methods of Organizing and Planning Production" Management Science, 4, 1960, 266–422
  • Ralph Keeney, Howard Raiffa, Decisions with Multiple Objectives: Preferences and Value Tradeoffs, New York, John Wiley & Sons, 1976
  • H. W. Kuhn, "The Hungarian Method for the Assignment Problem," Naval Research Logistics Quarterly, 1–2, 1955, 83–97
  • H. W. Kuhn, A. W. Tucker, "Nonlinear Programming," pp. 481–492 in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability
  • B. O. Koopman, Search and Screening: General Principles and Historical Applications, New York, Pergamon Press, 1980
  • Tjalling C. Koopmans, editor, Activity Analysis of Production and Allocation, New York, John Wiley & Sons, 1951
  • Charles C. Holt, Franco Modigliani, John F. Muth, Herbert A. Simon, Planning Production, Inventories, and Work Force, Englewood Cliffs, NJ, Prentice-Hall, 1960
  • Philip M. Morse, George E. Kimball, Methods of Operations Research, New York, MIT Press and John Wiley & Sons, 1951
  • Robert O. Schlaifer, Howard Raiffa, Applied Statistical Decision Theory, Cambridge, Division of Research, Harvard Business School, 1961
  • R.E. 贝尔曼,动态编程,普林斯顿大学出版社,普林斯顿,1957
  • 亚伯拉罕 · 查恩斯,威廉 · W · 库珀,线性规划管理模型和工业应用,第一卷和第二卷,纽约,约翰威立,1961
  • 亚伯拉罕 · 查恩斯,威廉 · W · 库珀,A · 亨德森,线性规划导论,纽约,约翰威立,1953
  • c. 西丘奇曼,拉塞尔 · L · 阿科夫和 E · L · 阿尔诺夫,运筹学导论,纽约: j · 威利父子,1957
  • 乔治 · B · 丹齐格,线性规划和延伸,普林斯顿,普林斯顿大学出版社,1963
  • 莱斯特 · K · 福特,小。雷富尔克森,《网络中的流动》 ,普林斯顿大学,普林斯顿大学出版社,1962
  • 杰伊 · W · 福雷斯特,工业动力学,剑桥大学,麻省理工学院出版社,1961
  • L · V · 坎特罗维奇,《组织和计划生产的数学方法》 ,管理科学,4,1960,266-422
  • 拉尔夫 · 基尼,霍华德 · 雷法,《多目标决策: 偏好和价值权衡》 ,纽约,约翰威立,1976
  • H · W · 库恩,“分配问题的匈牙利方法”海军研究后勤季刊,1-2,1955,83-97
  • H.W. Kuhn,A.W. Tucker,“非线性规划”,pp。伯克利第二届数学统计与概率研讨会会议录481-492
  • B.O. 库普曼,《搜索与筛选: 一般原理与历史应用》 ,纽约,佩加蒙出版社,1980
  • Tjaling C. 库普曼,编辑,《生产与分配的活动分析》 ,纽约,约翰威立,1951
  • 查尔斯 C. 霍尔特,弗兰科·莫迪利安尼,约翰 F. 穆特,1951年,赫伯特·西蒙,计划生产,库存和劳动力,恩格尔伍德克利夫斯,新泽西,普伦蒂斯-霍尔,1960
  • 菲利普 · 莫尔斯,乔治 · E · 金博尔,运筹学方法,纽约,麻省理工学院出版社和约翰威立,1951
  • 罗伯特 · O · 施莱弗,霍华德 · 雷法,应用统计决策理论,剑桥,研究部,哈佛商学院,1961

Classic textbooks 经典教科书

  • Taha, Hamdy A., "Operations Research: An Introduction", Pearson, 10th Edition, 2016
  • Frederick S. Hillier & Gerald J. Lieberman, Introduction to Operations Research, McGraw-Hill: Boston MA; 10th Edition, 2014
  • Robert J. Thierauf & Richard A. Grosse, "Decision Making Through Operations Research", John Wiley & Sons, INC, 1970
  • Harvey M. Wagner, Principles of Operations Research, Englewood Cliffs, Prentice-Hall, 1969
  • Wentzel (Ventsel), E. S. Introduction to Operations Research, Moscow: Soviet Radio Publishing House, 1964.
  • Taha, Hamdy A., "Operations Research: An Introduction", Pearson, 10th Edition, 2016
  • Frederick S. Hillier & Gerald J. Lieberman, Introduction to Operations Research, McGraw-Hill: Boston MA; 10th Edition, 2014
  • Robert J. Thierauf & Richard A. Grosse, "Decision Making Through Operations Research", John Wiley & Sons, INC, 1970
  • Harvey M. Wagner, Principles of Operations Research, Englewood Cliffs, Prentice-Hall, 1969
  • Wentzel (Ventsel), E. S. Introduction to Operations Research, Moscow: Soviet Radio Publishing House, 1964.
  • Taha,Hamdy A. “运营研究: 介绍”,Pearson,第10版,2016
  • Frederick S. Hillier & Gerald J. Lieberman,“运营研究介绍”,McGraw-Hill: Boston MA;第10版,2014
  • 罗伯特 · J · 蒂耶劳夫和理查德 · 格罗斯,《通过运筹学研究做决定》 ,国家公司,约翰威立,1970
  • 哈维 · M · 瓦格纳,《运筹学原理》 ,恩格尔伍德克利夫斯,普伦蒂斯-霍尔出版社,1969
  • 温策尔(文特尔出版社) ,《运筹学导论》 ,莫斯科: 苏联广播出版社,1964年。

History 运筹学学科史相关