乔治·伯纳德·丹齐格George Bernard Dantzig

乔治·伯纳德·丹齐格的父母是Tobias Dantzig和Anja Ourisson。Tobias出生于俄罗斯，但去了法国，在巴黎学习数学，师从儒勒·昂利·庞加莱。此时Tobias遇到了Anja，她当时也在索邦大学学习数学。他们结婚后移民到美国，定居在俄勒冈州。Tobias认为他浓重的俄罗斯口音会使他除了当劳工之外无法找到其他工作，起初他的工作包括伐木工、筑路工和油漆工。丹齐格就出生在这个非常贫穷的家庭中。

Tobias和Anja为他们的孩子选择名字，希望这些名字能影响他们未来的职业。丹齐格被命名为“丹齐格 丹齐格”，以丹齐格 丹齐格 Shaw命名，因为他的父母希望他们的第一个孩子成为作家。同样，丹齐格的弟弟以儒勒·昂利·庞加莱命名为Henry，他确实成为了一名数学家。Tobias有幸获得在印第安纳大学攻读数学博士学位的机会，而Anja获得了法语硕士学位，成为华盛顿特区国会图书馆的语言学家。

这个家庭现在住在华盛顿特区，在那里丹齐格就读于鲍威尔初级中学，起初他的数学进步相当差。在父亲的鼓励下，并决心在数学和科学上取得好成绩，他很快开始在数学上获得最高分。这种情况在中央高中继续，在那里他对几何学产生了浓厚兴趣。此时，他得到了三个人的大力支持：高中一位杰出的数学老师、一位后来成为乔治·伯克利数学教授的学校朋友，以及他的父亲。丹齐格后来写道，他的父亲：-

……在我还在高中时，给了我数千个几何问题。……解决它们所需的心智锻炼是我父亲给我的伟大礼物。在我高中时代——我的大脑正在成长的时候——解决数千个问题，比任何其他事情都更能发展我的分析能力。

Tobias在20世纪20年代末正致力于他最著名的著作Number: the language of science，丹齐格帮助了他。他后来写道：-

十几岁时，我准备了书中出现的一些图。

这本书于1930年出版，在20世纪70年代重印时，一位评论者写道：-

自近半个世纪前首次问世以来，这本书已经经历了多次印刷，并理所当然地保持了其受欢迎程度。

高中毕业后，丹齐格决定在马里兰大学学习数学，此时他的父亲已是该校数学系的教员。尽管家庭地位有所改善，丹齐格的父母仍然相当贫穷，无力资助他们的儿子上一所更有声望的大学。他于1936年在马里兰大学获得数学和物理学学士学位，并于当年夏天与Anne Shmuner结婚。这对新婚夫妇搬到了安娜堡，丹齐格作为Horace Rackham学者在密歇根大学开始了研究生学习。1937年，丹齐格在T H Hildebrandt、R L Wilder和G Y Rainer的指导下获得了数学硕士学位。

由于对抽象数学不满，他唯一喜欢的课程是统计学，丹齐格决定放弃研究生学业。他搬到华盛顿，从1937年到1939年在美国劳工统计局担任初级统计员，参与了一个名为“城市消费者购买研究”的项目。在阅读了耶日·奈曼的统计学论文后，丹齐格于1939年写信给他，询问是否有可能在伯克利获得助教职位，以便他能在耶日·奈曼的指导下完成博士学业。耶日·奈曼花了一些时间才安排好助教职位，但他设法做到了，丹齐格第二次开始攻读研究生。我们引用丹齐格自己关于这段时间的一个经常被重复的故事[3]（另见[2]）：-

在伯克利的第一年，有一天我迟到了耶日·奈曼的一节课。黑板上有两道题，我以为是为家庭作业布置的。我把它们抄了下来。几天后，我向耶日·奈曼道歉，说做作业花了这么长时间——这些题似乎比平时难做一点。我问他是否还想要这份作业。他让我把它扔到他桌上。我不情愿地照做了，因为他的桌子上堆满了那么多纸张，我担心我的作业会永远丢失在那里。

大约六周后，一个星期天早上八点左右，安妮和我被有人猛敲前门吵醒。是耶日·奈曼。他手里拿着论文冲进来，非常兴奋：“我刚为你的一篇论文写了引言。读一下，这样我就可以马上寄出去发表。”有一分钟我完全不知道他在说什么。长话短说，黑板上我以为是作业而解出的那两个问题，实际上是统计学中两个著名的未解决问题。那是我第一次隐约意识到它们有什么特别之处。

1941年美国参加第二次世界大战时，丹齐格第二次暂停了他的研究生学业，尽管此时他已经完成了课程并写好了博士学位论文。他去了华盛顿，作为文职人员加入了空军。从1941年到1946年，他担任美国空军总部统计控制战斗分析处处长。1944年，他被授予战争部杰出文职服务奖章。他这样写到他在那里的时光：-

我的办公室收集关于出动架次、投下炸弹、损失飞机等的数据……我还帮助空军参谋部的其他部门准备称为“计划”的方案。……一切都计划得极为详细：所有螺母和螺栓、飞机的采购、一切物品的详细制造。有数十万种不同的物资，也许有五万种专业人才。我的办公室收集关于空战的数据，例如出动架次、投下炸弹吨数、损耗率。我也成了一名熟练的专家，擅长用人工技术做规划。

1946年，在中断五年之后，丹齐格回到伯克利一个学期，从加利福尼亚大学获得数学博士学位。伯克利向他提供了一个学术职位，但他拒绝了这一提议：-

伯克利向我提出了一个提议，但我不喜欢，因为它太小了。或者更准确地说，我妻子不喜欢。那是一千四百美元年薪的丰厚薪水。她看不出我们带着孩子弗洛伦斯·南丁格尔·大卫怎么能靠这个生活。

到1946年6月，他已在华盛顿考虑若干不同的可能职位。五角大楼的同事请他承担规划过程机械化的工作。这似乎与他的兴趣完全契合，因此那年他被任命为国防部数学顾问来承担这项任务。

1947年，丹齐格做出了他最著名的数学贡献，即优化的单纯形法。它源于他与美国空军的工作，在那里他成为用台式计算机求解规划方法的专家。事实上，这被称为“programming”，一个军事术语，当时指的是训练、后勤供应或人员部署的计划或日程。丹齐格通过引入“线性结构中的programming”使规划过程机械化，其中“programming”具有上述军事含义。“线性规划”这一术语是由特亚林·科普曼斯在丹齐格1948年访问兰德公司讨论他的想法时提出的。发现他的算法后，丹齐格早期将其应用于以最低成本获得充足饮食的问题。他在其著作Linear programming and extensions（1963年）中描述了这一点：-

单纯形算法最早的应用之一是确定成本最低的充足饮食。1947年秋，国家标准局数学表格项目的Jack Laderman作为对新提出的单纯形法的检验，承担了该领域的首次大规模计算。这是一个包含77个未知数的9个方程的系统。使用手动台式计算机，大约需要120人日才能获得一个解。……所解决的具体问题正是丹齐格 Stigler（后来成为诺贝尔奖得主）早先研究过的一个问题，他提出了一种基于用其他食物替代某些食物以提供每美元更多营养的解决方案。然后他检查了所选食物可能的510种组合方式中的“一小把”。他并未声称该解是最便宜的，但给出了他相信每年成本无法再降低超过几美元的理由。事实上，结果表明Stigler的解（以1945年美元表示）仅比真正的最小值每年39.69美元高出24美分。

在[11]中，丹齐格写道（另见[9]、[10]和[12]）：-

线性规划被视为一项革命性发展，使人类能够陈述总体目标，并通过单纯形法为一大类极其复杂的实际决策问题找到最优政策决策。在现实世界中，由于许多特殊利益集团及其多重目标，规划往往是临时性的。

但他也谦逊地写道：-

单纯形法的巨大威力始终令我惊讶。

1980年，拉兹洛·洛瓦兹描述了线性规划方法的重要性，他写道：-

如果统计一下世界上哪个数学问题消耗的计算机时间最多，那么……答案很可能是线性规划。

同样在1980年，Eugene Lawler写道：-

[线性规划]被用于分配资源、规划生产、安排工人、规划投资组合以及制定营销（和军事）策略。线性规划在当今工业世界中的多功能性和经济影响确实令人惊叹。

Balinski [4]写道：-

数学规划有幸得到了至少两位极具创造力的天才的参与：丹齐格和列昂尼德·坎托罗维奇。

他接着说道，列昂尼德·坎托罗维奇因其贡献获得了诺贝尔奖，并对丹齐格未能获奖表示“愤慨”。特亚林·科普曼斯也分享了这一诺贝尔奖。

丹齐格于1952年成为兰德公司的研究数学家，在此期间领导了在计算机上实现线性规划的工作。Orchard-Hays在[14]中写道：-

线性规划实用计算方法的系统性开发始于1952年，在圣莫尼卡的兰德公司进行，由丹齐格 B 丹齐格指导。作者在那里 intensive 地从事这一项目直到1956年末，那时在第一代计算机上已取得了巨大进展。

然而，由于感到兰德公司无法为他提供新思想的来源，他于1960年接受了伯克利的教授职位，并被任命为运筹学中心主任。在那里期间，他撰写了Linear programming and extensions（1963年）。一位评论者写道：-

这是一本令人印象深刻的书，工作非常完整，科学水平高，读起来令人愉快。

1966年，他被任命为斯坦福大学运筹学与计算机科学教授，此后一直在那里工作直至职业生涯结束。

多年来，他在与优化和运筹学相关的广泛主题上的工作具有重大意义。然而，丹齐格在1991年写道：-

……有趣的是，最初引发我研究的问题至今仍未解决——即随时间动态规划或调度的问题，特别是在不确定性下的动态规划。如果这样的问题能够成功解决，它最终可能通过更好的规划为世界的福祉和稳定做出贡献。

丹齐格获得过许多荣誉，包括1975年的冯·诺伊曼理论奖运筹学；1976年由美国总统颁发的国家科学奖章；1977年的国家科学院应用数学与数值分析奖；1985年以色列理工学院的哈维科学与技术奖；1986年英国运筹学会的银奖；1989年弗吉尼亚州颁发的阿道夫·库尔斯美国独创性奖表彰证书；以及1994年数学规划学会的特别表彰奖。

科学奖章的引文指出，授予该奖章是为了：-

发明线性规划并发现导致大规模科学和技术应用的方法，应用于物流、调度和网络优化中的重要问题，以及利用计算机有效运用数学理论。

哈维奖的引文如下：-

表彰他通过数学规划的开创性工作以及单纯形法的开发，对工程和科学做出的杰出贡献。他的工作使许多先前棘手的问题得以求解，并使线性规划成为现代应用数学中最常用的技术之一。

斯坦福大学对他的工作总结如下：-

作为美国国家工程院院士、National Academy of Science、American Academy of Arts and Sciences以及国家科学奖章获得者和八个荣誉学位的获得者，丹齐格教授的开创性工作为系统工程领域的许多方面奠定了基础，并广泛应用于计算机、机械和电气工程中的网络设计和组件设计。

George Dantzig's parents were Tobias Dantzig and Anja Ourisson. Tobias was born in Russia, but went to France where he studied mathematics in Paris being taught there by Poincaré. At this time Tobias met Anja who was at the Sorbonne at this time also studying mathematics. They married and emigrated to the United States, settling in Oregon. Tobias believed that his strong Russian accent would prevent him from obtaining jobs other than as a labourer, and at first his jobs included that of lumberjack, road builder and painter. It was into this very poor family that George was born.

Tobias and Anja chose names for their children hoping that these would influence their future careers. George was named "George Bernard" after George Bernard Shaw since his parents hoped their first child would become a writer. Similarly George's younger brother was named Henry after Henri Poincaré, and he did indeed become a mathematician. Tobias was fortunate to gain the chance of reading for a Ph.D. in mathematics at Indiana University, while Anja obtained a Master's degree in French becoming a linguist at the Library of Congress in Washington D.C.

The family were now living in Washington D.C., and there George attended Powell Junior High School where his progress in mathematics was, at first, rather poor. Encouraged by his father, and determined to do well in mathematics and science, he soon began to obtain top marks in mathematics. This continued at Central High School where he became fascinated by geometry. By this time he was getting strong support from three people: an outstanding mathematics teacher at the High School, a school friend who would go on to become a professor of mathematics at Berkeley, and his father. George later wrote that his father:-

... gave me thousands of geometry problems while I was still in high school. ... the mental exercise required to solve them was the great gift from my father. The solving of thousands of problems during my high school days - at the time when my brain was growing - did more than anything else to develop my analytic power.

Tobias was working on his most famous work Number: the language of science in the late 1920s and George helped him. He later wrote:-

As a teenager, I prepared some of the figures that appeared in the book.

The book was published in 1930 and when it was reprinted in the 1970s a reviewer wrote:-

Since its first appearance nearly half a century ago the book has gone through a number of printings and has deservedly maintained its popularity.

After graduating from High School, Dantzig decided to study mathematics at the University of Maryland, where by this time his father was on the Mathematics Faculty. Despite the improved status of his family, Dantzig's parents were still quite poor and not in a position to finance their son through a more prestigious university. He received his A.B. in Mathematics and Physics from the University of Maryland in 1936 and in the summer of that year he married Anne Shmuner. The newly married couple moved to Ann Arbour where Dantzig began graduate studies at the University of Michigan as a Horace Rackham Scholar. In 1937 Dantzig was awarded an M.A. in mathematics, having studied under T H Hildebrandt, R L Wilder and G Y Rainer.

Unhappy with abstract mathematics, the only courses he enjoyed being on statistics, Dantzig decided to give up his graduate studies. He moved to Washington where he worked as a Junior Statistician on a project "Urban study of consumer purchase" at the U.S. Bureau of Labor Statistics from 1937 to 1939. Having read statistics papers by Neyman, Dantzig wrote to him in 1939 asking if there was any possibility he could obtain a teaching assistantship at Berkeley so that he could complete his doctoral studies under Neyman's supervision. It took Neyman a little while to arrange the teaching assistantship but he managed to do so and Dantzig began for a second time to undertake graduate studies. We quote an often repeated story from this time in Dantzig's own words [3] (see also [2]):-

During my first year at Berkeley I arrived late one day to one of Neyman's classes. On the blackboard were two problems which I assumed had been assigned for homework. I copied them down. A few days later I apologized to Neyman for taking so long to do the homework - the problems seemed to be a little harder to do than usual. I asked him if he still wanted the work. He told me to throw it on his desk. I did so reluctantly because his desk was covered with such a heap of papers that I feared my homework would be lost there forever.

About six weeks later, one Sunday morning about eight o'clock, Anne and I were awakened by someone banging on our front door. It was Neyman. He rushed in with papers in hand, all excited: "I've just written an introduction to one of your papers. Read it so I can send it out right away for publication." For a minute I had no idea what he was talking about. To make a long story short, the problems on the blackboard which I had solved thinking they were homework were in fact two famous unsolved problems in statistics. That was the first inkling I had that there was anything special about them.

When the United States entered World War II in 1941 Dantzig put his graduate studies on hold for a second time, although by this time he had already completed the coursework and written his Ph.D. thesis. He went to Washington and joined the Air Force as a civilian. From 1941 to 1946 he was Head of the Combat Analysis Branch, U.S.A.F. Headquarters Statistical Control. In 1944 he was awarded the War Department Exceptional Civilian Service Medal. He wrote of his time there:-

My office collected data about sorties flown, bombs dropped, aircraft lost... I also helped other divisions of the Air Staff prepare plans called "programs". ... everything was planned in greatest detail: all the nuts and bolts, the procurement of airplanes, the detailed manufacture of everything. There were hundreds of thousands of different kinds of material goods and perhaps fifty thousand specialties of people. My office collected data about the air combat such as the number of sorties flown, the tons of bombs dropped, attrition rates. I also became a skilled expert on doing planning by hand techniques.

In 1946, after a break of five years, Dantzig returned to Berkeley for one semester, receiving his doctorate in mathematics from the University of California. He was offered an academic post by Berkeley but had turned down the offer:-

Berkeley made me an offer, but I didn't like it because it was too small. Or, to be more exact, my wife did not like it. It was a grand salary of fourteen hundred dollars a year. She did not see how we could live on that with our child David.

By June 1946 he was in Washington considering a number of different possible jobs. His colleagues at the Pentagon asked him to take on the job of mechanizing the planning process. This appeared to fit in exactly with his interests so that year he was appointed Mathematical Advisor at the Defense Department to undertake the task.

In 1947 Dantzig made the contribution to mathematics for which he is most famous, the simplex method of optimisation. It grew out of his work with the U.S. Air Force where he become an expert on planning methods solved with desk calculators. In fact this was known as "programming", a military term that, at that time, referred to plans or schedules for training, logistical supply or deployment of men. Dantzig mechanised the planning process by introducing "programming in a linear structure", where "programming" has the military meaning explained above. The term "linear programming" was proposed by T J Koopmans during a visit Dantzig made to the RAND corporation in 1948 to discuss his ideas. Having discovered his algorithm, Dantzig made an early application to the problem of eating adequately at minimum cost. He describes this in his book Linear programming and extensions (1963):-

One of the first applications of the simplex algorithm was to the determination of an adequate diet that was of least cost. In the fall of 1947, Jack Laderman of the Mathematical Tables Project of the National Bureau of Standards undertook, as a test of the newly proposed simplex method, the first large-scale computation in this field. It was a system with nine equations in seventy-seven unknowns. Using hand-operated desk calculators, approximately 120 man-days were required to obtain a solution. ... The particular problem solved was one which had been studied earlier by George Stigler (who later became a Nobel Laureate) who proposed a solution based on the substitution of certain foods by others which gave more nutrition per dollar. He then examined a "handful" of the possible 510 ways to combine the selected foods. He did not claim the solution to be the cheapest but gave his reasons for believing that the cost per annum could not be reduced by more than a few dollars. Indeed, it turned out that Stigler's solution (expressed in 1945 dollars) was only 24 cents higher than the true minimum per year $39.69.

In [11] Dantzig wrote (see also [9], [10] and [12]):-

Linear programming is viewed as a revolutionary development giving man the ability to state general objectives and to find, by means of the simplex method, optimal policy decisions for a broad class of practical decision problems of great complexity. In the real world, planning tends to be ad hoc because of the many special-interest groups with their multiple objectives.

But he also modestly wrote:-

The tremendous power of the simplex method is a constant surprise to me.

The importance of linear programming methods was described, in 1980, by Laszlo Lovasz who wrote:-

If one would take statistics about which mathematical problem is using up most of the computer time in the world, then ... the answer would probably be linear programming.

Also in 1980 Eugene Lawler wrote:-

[Linear programming] is used to allocate resources, plan production, schedule workers, plan investment portfolios and formulate marketing (and military) strategies. The versatility and economic impact of linear programming in today's industrial world is truly awesome.

Balinski [4] writes:-

Mathematical programming has been blessed by the involvement of at least two exceptionally creative geniuses: George Dantzig and Leonid Kantorovich.

He then goes on to say that Kantorovich received the Nobel Prize for his contribution and expresses "outrage" that Dantzig did not. Koopmans also had a share of this Nobel prize.

Dantzig became a research mathematician with the RAND Corporation in 1952 and during this period led the work on implementing linear programming on computers. Orchard-Hays writes in [14]:-

The systematic development of practical computing methods for linear programming began in 1952 at the Rand Corporation in Santa Monica, under the direction of George B Dantzig. The author worked intensively on this project there until late 1956, by which time great progress had been made on first-generation computers.

However, feeling that the RAND Corporation was not providing him with a source of fresh ideas, he took up an appointment as professor at Berkeley in 1960 and he was appointed Chairman of the Operations Research Center. While there he wrote Linear programming and extensions (1963). A reviewer wrote:-

An impressive book, the work is very complete, its scientific level high, and its reading pleasant.

In 1966 he was appointed Professor of Operations Research and Computer Science at Stanford University where he remained for the rest of his career.

His work in a wide range of topics related to optimisation and operations research over the years has been of major importance. However, writing in 1991, Dantzig noted that:-

... it is interesting to note that the original problem that started my research is still outstanding - namely the problem of planning or scheduling dynamically over time, particularly planning dynamically under uncertainty. If such a problem could be successfully solved it could eventually through better planning contribute to the well-being and stability of the world.

Dantzig has received many honours including the Von Neumann Theory Prize in Operational Research in 1975; The National Medal of Science presented by the president of the United States in 1976; the National Academy of Sciences Award in Applied Mathematics and Numerical Analysis in 1977; the Harvey Prize in Science and Technology from Technion, Israel, in 1985; the Silver Medal from the Operational Research Society of Britain in 1986; the Adolph Coors American Ingenuity Award Certificate of Recognition from the State of Virginia in 1989; and the Special Recognition Award from the Mathematical Programming Society in 1994.

The citation for the Medal of Science states that it was awarded:-

For inventing linear programming and discovering methods that led to wide-scale scientific and technical applications to important problems in logistics, scheduling, and network optimization, and to the use of computers in making efficient use of the mathematical theory.

The citation for The Harvey Prize reads:-

In recognition of his outstanding contribution to engineering and the sciences through his pioneering work in mathematical programming and his development of the simplex method. His work permits the solution of many previously intractable problems and has made linear programming into one of the most frequently used techniques of modern applied mathematics.

His work is summarised by Stanford University as follows:-

A member of the National Academy of Engineering, the National Academy of Science, the American Academy of Arts and Sciences and recipient of the National Medal of Science, plus eight honorary degrees, Professor Dantzig's seminal work has laid the foundation for much of the field of systems engineering and is widely used in network design and component design in computer, mechanical, and electrical engineering.