George Bernard Dantzig: The Pioneer of Linear Optimization

John R. Birge University of Chicago Booth School of Business

MBR | Winter 2021 | Volume 01 | Issue 01 161 George Dantzig introduced the world to the power of optimization, creating trillions of dollars of value and saving countless years of life across the globe. In this laudation, John Birge describes the fascinating life and incredible accomplishments of a scholar whose footprints led the way to almost everything the global economy produces.

eorge Bernard Dantzig (1914- program’s focus on abstract math- Dantzig heard nothing from 2005) introduced the world to ematics uninspiring, he left Ann Neyman for several weeks, but linear programming and, more Arbor and returned to Washing- then he was awakened early on a generally, to the power of opti- ton to work at the Bureau of Labor Sunday morning by the sound of Gmization. His work created trillions Statistics (BLS). His new profes- vigorous knocking on his down- of dollars of value and preserved sion prompted him to begin work- stairs door. When he answered, countless years of life across the ing on practical applications of Neyman abruptly informed him globe. By creating the simplex mathematics. As he often remarked that his dissertation was done. The method for solving linear programs later in life, his many mathemati- two problems Dantzig had solved he made vastly complex decisions cal discoveries, while sometimes for homework were actually two amenable to computation. By stated abstractly, were all inspired famous unsolved (and until then, demonstrating the duality between by practical problems facing firms, unsolvable) problems in statistics. activities and prices he paved the organizations, or governments.1 Dantzig’s unshakeable belief that way for new analyses resulting in After a few years at BLS, Dantzig he could solve the problems has greater market efficiency. His work found new inspiration for research become a symbol of the power of has supported growing economies in the work of Jerzy Neyman at the positive thinking. His story contin- and improved healthcare, saving University of California, Berkeley. The ues to inspire others to undertake many from hunger and extending real tale of Dantzig’s world-changing difficult tasks. lives around the world. Dantzig’s career and professional fame began As well as offering a stunning optimism and determination in- with the now-legendary moment example of individual achievement, spired many to increase their own when he arrived late to Neyman’s Dantzig’s solutions of the ‘home- achievements. class. In previous weeks, Neyman work’ problems laid the groundwork Dantzig became interested in had customarily written the week’s for the beginning of linear program- mathematics as a child, although homework problems on the board at ming and countless subsequent his parents, Tobias and Anja, had the beginning of the period. So when applications. While working for the named him after George Bernard Dantzig saw two problems on the U.S. Air Force during and after World Shaw in the hope that he would board, he wrote them down to work War II, Dantzig began to see ways to become a writer. His father, a math- on and hand in before the next class improve its efficiency. He sought to ematics professor at the University session. He found the problems a bit automate the planning or program- of Maryland, gave George “thou- more difficult than usual and was a ming process of delineating detailed sands of geometry problems” that few days late in completing them. He requirements for producing, assem- fascinated him and honed his took his solutions to Neyman’s office bling, training, and locating all of the powers of analysis. After earning to ask the professor if he still wanted military’s personnel and equipment. an undergraduate degree in math- to review the homework. Neyman He developed a model for finding the ematics and physics at Maryland, told him to leave them on his desk, best combination and levels of activ- Dantzig went on to pursue gradu- which was so covered with papers ities and uses of resources which ate studies in mathematics at the that Dantzig feared his hard work became known as linear program- University of Michigan. Finding the would be lost forever. ming. Its solutions were provided by

162 Volume 01 | Issue 01 | Winter 2021 | MBR the pioneering algorithm inspired about $1 trillion each year, in the method is also a remarkable tool, by his dissertation: the simplex US alone. named one of the top ten algorithms method. Fortuitously, his devel- of the twentieth century and an opment of this numerical proce- indispensable part of optimization dure coincided with the advent of Linear programming to this day. Dantzig’s other contribu- computers and contributed to their tions constitute the foundation upon development as well.2 has become a vital tool which the development of many in advancing artificial other decision-making tools over intelligence and machine the past seventy years was built. Linear programs Nonetheless, as Dantzig himself was learning, and it is used known to point out, his most funda- and Dantzig’s many in electrical stimulation mental contribution may have been other contributions to therapy, chemotherapy the very concept of an objective optimization have driven function.5 As he wrote, earlier plan- plans, drug discovery, ners and managers may have shied enormous increases in radiation therapy designs, away from the notion of optimizing productivity throughout the and finding optimal diets. an objective because they thought global economy. it inconceivable to find an optimal solution among possibilities more Beyond traditional industrial numerous than the atoms in the Linear programs and Dantzig’s uses, linear programming has universe. Dantzig dared to conceive many other contributions to opti- become a vital tool in advancing of surmounting that imposing obsta- mization have driven enormous artificial intelligence and machine cle and succeeded, to the substan- increases in productivity through- learning. Such optimization proce- tial benefit of us all. out the global economy. Indus- dures have not just reduced costs tries with expensive capacity or and increased outputs across the John Birge is the Ho- limited production flexibility, like globe, they have also saved count- bart W. Williams Dis- airlines, hotels, rental cars, and less lives. Linear programming is tinguished Service many retailers, have used revenue used in the phylogenetic analy- Professor of Opera- management models, often built sis that determines the origins of tions Management at on linear programming, to achieve organisms (including viruses, such the University of Chi- revenue increases of 5 percent or as SARS-CoV-2, better known as the cago Booth School of more. The electric power industry novel coronavirus). It is also used Business. His work follows that of also uses advanced optimization in electrical stimulation therapy, his doctoral advisor, George Dan- methods to reap cost savings that chemotherapy plans, drug discov- tzig, in exploring ways to make bet- exceed 5 percent of their overall ery, radiation therapy designs, and ter decisions. energy. The logistics field has also finding optimal diets, an application benefited enormously from optimi- which has drawn interest for more zation, reducing shipping costs by than seventy-five years.4 up to 50 percent in many industries Endnotes including retail, chemical, tech, 1. Much of this history appears in Dantzig’s interview and consumer goods. In addition, Linear programming and in D.J. Albers and C. Reid, “An Interview with George B. much of modern finance and asset Dantzig: The Father of Linear Programming,” The College its various extensions Mathematics Journal, 17 (4) (Sep., 1986), pp. 293-314. management is built on Markow- 2. Dantzig’s account of the simplex method’s role in the itz’s efficient portfolio model, continue to play an development of digital computers appears in G.B. Dantzig, which was rooted in Dantzig’s influential role in the “Impact of linear programming on computer development,” work.3 Combining these accom- Technical Report SOL 85-07, Stanford University, economy and in all our 1985, https://apps.dtic.mil/dtic/tr/fulltext/u2/a157659.pdf. plishments with uses in telecom- 3. Markowitz’s discussion of Dantzig’s influence on his munications, manufacturing, and lives. work appears at: http://hmarkowitz.com/about-harry- markowitz/. more, and particularly in complex 4. Dantzig’s discussion of the early history of this problem is process industries like chemical Linear programming and its in: G.B. Dantzig, “The diet problem,” Interfaces 20 (4) (1990), manufacturing, linear optimiza- various extensions continue to play pp. 43-47. 5. Dantzig’s description is in: G.B. Dantzig, “Linear tion probably contributes over 5 an influential role in the economy programming,” Operations Research 50 (1) (2002), pp. percent to the overall output, or and in all our lives. The simplex 42–47.

MBR | Winter 2021 | Volume 01 | Issue 01 163