George Dantzig Homework Problems Checklist

Guide to the George B. Dantzig Papers

Daniel Hartwig & Jenny Johnson

Stanford University Libraries. Dept. of Special Collections & University Archives. March 2012

Copyright © 2015 The Board of Trustees of the Leland Stanford Junior University. All rights reserved.


Call Number: SC0826

Creator: Dantzig, George Bernard, 1914-2005.

Title: George B. Dantzig papers

Dates: 1937-1999

Physical Description: 89.25 Linear feet

Language(s): The materials are in English.

Physical Location: Special Collections and University Archives materials are stored offsite and must be paged 36-48 hours in advance. For more information on paging collections, see the department's website:

Repository: Dept. of Special Collections & University Archives.

Stanford University Libraries.

557 Escondido Mall

Stanford, CA 94305-6064


Phone: (650) 725-1022


Administrative Information

Information about Access

The materials are open for research use. Audio-visual materials are not available in original format, and must be reformatted to a digital use copy.

Ownership & Copyright

All requests to reproduce, publish, quote from, or otherwise use collection materials must be submitted in writing to the Head of Special Collections and University Archives, Stanford University Libraries, Stanford, California 94305-6064. Consent is given on behalf of Special Collections as the owner of the physical items and is not intended to include or imply permission from the copyright owner. Such permission must be obtained from the copyright owner, heir(s) or assigns. See:

Restrictions also apply to digital representations of the original materials. Use of digital files is restricted to research and educational purposes.

Cite As

[identification of item], George B. Dantzig Papers (SC0826). Dept. of Special Collections and University Archives, Stanford University Libraries, Stanford, Calif.

Biographical/Historical note

George Bernard Dantzig (November 8, 1914 – May 13, 2005) was an American mathematical scientist who made important contributions to operations research, computer science, economics, and statistics.

Dantzig is known for his development of the simplex algorithm, an algorithm for solving linear programming problems, and his work with linear programming. In statistics, Dantzig solved two open problems in statistical theory, which he had mistaken for homework after arriving late to a lecture of Jerzy Neyman.

Dantzig was the Professor Emeritus of Transportation Sciences and Professor of Operations Research and of Computer Science at Stanford.

Born in Portland, Oregon, George Bernard Dantzig was named after George Bernard Shaw, the Irish writer. His father, Tobias Dantzig, was a Baltic German mathematician and linguist, and his mother, Anja Dantzig (née Ourisson), was a French linguist. Dantzig's parents met during their study at the Sorbonne University in Paris, where Tobias studied mathematics under Henri Poincaré, after whom Dantzig's brother was named. The Dantzigs immigrated to the United States, where they settled in Portland, Oregon.

Early in the 1920s the Dantzig family moved from Baltimore to Washington. His mother became a linguist at the Library of Congress, and his father became a math tutor at the University of Maryland, College Park, George attended Powell Junior High School and Central High School; one of his friends there was Abraham Seidenberg, who also became a professional mathematician. By the time he reached high school he was already fascinated by geometry, and this interest was further nurtured by his father, challenging him with complicated problems, particularly in projective geometry.

George Dantzig earned bachelor's degrees in mathematics and physics from the University of Maryland in 1936, and his master's degree in mathematics from the University of Michigan in 1938. After a two-year period at the Bureau of Labor Statistics, he enrolled in the doctoral program in mathematics at the University of California, Berkeley, where he studied statistics under Jerzy Neyman.

With the outbreak of World War II, George took a leave of absence from the doctoral program at Berkeley to join the U.S. Air Force Office of Statistical Control. In 1946, he returned to Berkeley to complete the requirements of his program and received his Ph.D. that year. Although he had a faculty offer from Berkeley, he returned to the Air Force as mathematical advisor to the comptroller.

In 1952 Dantzig joined the mathematics division of the RAND Corporation. By 1960 he became a professor in the Department of Industrial Engineering at UC Berkeley, where he founded and directed the Operations Research Center. In 1966 he joined the Stanford faculty as Professor of Operations Research and of Computer Science. A year later, the Program in Operations Research became a full-fledged department. In 1973 he founded the Systems Optimization Laboratory (SOL) there. On a sabbatical leave that year, he headed the Methodology Group at the International Institute for Applied Systems Analysis (IIASA) in Laxenburg, Austria. Later he became the C. A. Criley Professor of Transportation Sciences at Stanford, and kept going, well beyond his mandatory retirement in 1985.

He was a member of the National Academy of Sciences, the National Academy of Engineering, and the American Academy of Arts and Sciences. George was the recipient of many honors, including the first John von Neumann Theory Prize in 1974, the National Medal of Science in 1975, an honorary doctorate from the University of Maryland, College Park in 1976. The Mathematical Programming Society honored Dantzig by creating the George B. Dantzig Prize, bestowed every three years since 1982 on one or two people who have made a significant impact in the field of mathematical programming.

Dantzig died on May 13, 2005, in his home in Stanford, California, of complications from diabetes and cardiovascular disease. He was 90 years old.

Access Terms

Computer science--Research

Computer science--Study and teaching

Mathematicians--United States.

Mathematics --Study and teaching (Higher).

Systems programming (Computer science)

Collection Contents

Box 1, Folder 1

On a Class of Distributions that Approach the Normal Distribution Function1939

Box 1, Folder 2

On the Non-Existence of Tests of Students' Hypothesis Involving Power Functions Independent of Sigma1940

Box 1, Folder 3

A Theorem on Linear Inequalities1948, January 5

Box 1, Folder 4

A Proof of the Equivalence of the Programming Problem and the Game Problem, in T.C. Koopmans (ed.)

Box 1, Folder 5

Programming of Interdependent Activities, II: Mathematical Model1951

Box 1, Folder 6

Maximization of a Linear Function of VariablesSubject to Linear Inequalities

Box 1, Folder 7

Application of the Simplex Method to the Transportation Problem1951

Box 1, Folder 8

Programming in a Linear Structure1949

Box 1, Folder 9

Box 1, Folder 10

On the Fundamental Lemma of Neyman and Pearson1591

Box 1, Folder 11

The Generalized Simplex Method for Minimizing a Linear Form Under Linear Inequality Constraints1955

Box 1, Folder 12

The Fixed Charge Problem1954

Box 1, Folder 13

A Duality Theorem Based on the Simplex Method1952

Box 1, Folder 14

Alternate Algorithm for the Revised Simplex Method Using Product Form for the Inverse1953

Box 1, Folder 15

The Dual Simplex Algorithm (Notes on Linear Programming Part VII)1954

Box 1, Folder 16

Upper Bounds, Secondary Constraints, and Block Triangularity in Linear Programming (Notes on Linear Programming: Part VIII, XI, X) 1954

Box 1, Folder 17

Notes on Linear Programming: Part XI, Composite Simplex-Dual Simplex Algorithm1954

Box 1, Folder 18

Solution for a Large-Scale Traveling Salesman Problem1954

Box 1, Folder 19

Minimizing the Number of Tankers to Meet a Fixed Schedule1956

Box 1, Folder 20

The Product Form for the Inverse in the Simplex Method1954

Box 1, Folder 21

A Comment on Eddie's "Traffic Delays at Toll Booths"1954

Box 1, Folder 22

Linear Programming Under Uncertainty1955

Box 1, Folder 23

Optimal Solution of a Dynamic Leontief Model with Substitution (Notes on Linear Programming: Part XIII)1955

Box 1, Folder 24

A Production Smoothing Problem1955

Box 1, Folder 25

Developments in Linear Programming1955

Box 1, Folder 26

Constructive Proof of the Min-Max Theorem1956

Box 1, Folder 27

Recent Advances in Linear Programming1956

Box 1, Folder 28

On the Max-Flow Min-Cut Theorems of Networks1955

Box 1, Folder 28a

Formulating a Linear Programming Model1956

Box 1, Folder 28b

Computation of Maximal Flows in Networks1955

Box 1, Folder 29

Concepts, Origins and Uses of Linear Programming1957

Box 1, Folder 30

A Primal-Dual Algorithm for Linear Programs1956

Box 1, Folder 31

Note on Klein's "Direct Use of Extremal Principles in Solving Certain Problems Involving Inequalities"1956

Box 1, Folder 32

Thoughts on Linear Programming and Automation1957

Box 1, Folder 33

Discrete Variable Extremum Problems1957

Box 1, Folder 34

On the Status of Multi-Stage Linear Programs1957

Box 1, Folder 35

Solving Two-Move Games with Perfect Information1958

Box 1, Folder 36

On Integer and Partial Integer Linear Programming Problems1958

Box 1, Folder 37

A Linear Programming Approach to the Chemical Equilibrium Problem1958

Box 1, Folder 37a

Chemical Equilibrium in Complex Mixtures1958

Box 1, Folder 38

Note on Solving Linear Programs in Integers1959

Box 1, Folder 39

Dilworth's Theorem on Partially Ordered Sets1956

Box 1, Folder 40

On a Linear Programming Combinatorial Approach to the Traveling Salesman Problem1959

Box 1, Folder 41

The Allocation of Aircraft to Routes - An Example of Linear Programming Under Uncertain Demand1956

Box 1, Folder 42

Optimum Routing of Gasoline Delivery Trucks1959

Box 1, Folder 43

The Truck Dispatching Problem1959

Box 1, Folder 44

Inductive Proof of the Simplex Method1960

Box 1, Folder 45

On the Shortest Route Through a Network1960

Box 1, Folder 46

On the Significance of Solving Linear Programming with Some Integer Variables1960

Box 1, Folder 47

General Convex Objective Forms1960

Box 1, Folder 48

A Machine-Job Scheduling Model1960

Box 1, Folder 49

Computing Tetraethyl-Lead Requirements in a Linear-Programming Format1960

Box 1, Folder 50

A Mathematical Model of the Respiratory System1960

Box 1, Folder 51

Solving the Chemical Equilibrium Problem Using the Decomposition Principle1960

Box 1, Folder 52

A Mathematical Model of the Chemistry of the External Respiratory System1961

Box 1, Folder 53

On the Solution of the Two-Staged Linear Programs Under Uncertainty1961

Box 1, Folder 54

Decomposition Principle for Linear Programs1960

Box 1, Folder 55

Future Developments of Operations Research1961

Box 1, Folder 56

A Mathematical Model of the Human External Respiratory System1961

Box 1, Folder 57

Quadratic Programming- A Variant of the…Algorithms1961

Box 1, Folder 58

On the Reduction of Certain Multiplicative Chemical Equilibrium Systems to Mathematically Equivalent Additive Systems1961

Box 1, Folder 59

A Proof of a Property of Leontief and Markov Matrices1962

Box 1, Folder 60

Compact Basis Triangularization for the Simplex Method1962

Box 1, Folder 61

Symmetric Dual Nonlinear Programs1962

Box 1, Folder 62

Linear Programming in a Markov Chain1962

Box 1, Folder 63

Molecular-Sized Channels and Flows Against the Gradient1962

Box 1, Folder 64

Positive (Semi-) Definite Matrices and Mathematical Programming1963

Box 1, Folder 65

Maximum Payloads per Unit Time Delivered Through an Air Network1963

Box 1, Folder 66

Linear Programming and Extensions1963

Box 1, Folder 67

A Model for Sodium-Potassium Transport in Red Cells1963

Box 1, Folder 68

Automated Multiphasic Screening and Diagnosis1964

Box 1, Folder 69

New Mathematical Methods in the Life Sciences1964

Box 1, Folder 70

Generalized Upper Bounded Techniques for the Linear Programming- I1964

Box 2, Folder 71

Generalized Upper Bounded Techniques for the Linear Programming- II1964

Box 2, Folder 72

Box 2, Folder 73

Linear Control Processes and Mathematical Programming1964

Box 2, Folder 74

Updating the Product Form of the Inverse for the Revised Simplex Method1964

Box 2, Folder 75

Operations Research in the World of Today and Tomorrow1965

Box 2, Folder 76

Large-Scale System Optimization: A Review1965

Box 2, Folder 77

Optimization in Operations Research1965

Box 2, Folder 78

Box 2, Folder 79

On the Continuity of the Minimum Set of a Continuous Function1965

Box 2, Folder 80

On Steady-State Intercompartamental Flow1965

Box 2, Folder 81

Optimal Assignment of Computer Storage by Chain Decomposition of Partially Ordered Sets1966

Box 2, Folder 82

Linear Programming and its Progeny1966

Box 2, Folder 82a

An Integer Branching Algorithm for Locating Warehouses1966

Box 2, Folder 83

Finding a Cycle in a Graph with Minimum Cost to Time Ratio with Application to a Ship Routing Problem1966

Box 2, Folder 84

All Shortest Routes From a Fixed Origin in a Graph1966

Box 2, Folder 85

All Shortest Routes in a Graph1966

Box 2, Folder 86

On Positive Principal Minors1966

Box 2, Folder 87

Complementary Pivot Theory of Mathematical Programming1967

Box 2, Folder 88

Mathematical Programming Language1968

Box 2, Folder 89

Integral Extreme Points1968

Box 2, Folder 90

Large-Scale Linear Programming1967

Box 2, Folder 91

A Generalization of the Linear Complimentarity Problem1968

Box 2, Folder 92

Sparse Matrix Techniques in Two Mathematical Programming Codes1969

Box 2, Folder 93

Complementary Spanning Trees1969

Box 2, Folder 94

A Hospital Admission Problem1969

Box 2, Folder 95

Existence of A-Avoiding Paths in Abstract Polytopes1974

Box 2, Folder 96

On a Model for Computing Round-Off Error of a Sum1970

Box 2, Folder 97

Natural Gas Transmission System Optimization1970

Box 2, Folder 98

A Control Problem of Bellman1970

Box 2, Folder 99

MPL: Mathematical Programming Language Specification Manual for Committee Review1970

Box 2, Folder 100

Generalized Upper Bounding Techniques1967

Box 2, Folder 100a

Generalized Linear Programming1971

Box 2, Folder 101

Maximum Diameter of Abstract Polytopes1971

Box 2, Folder 102

Existence of X-Paths in Abstract Polytopes1970

Box 2, Folder 103

On the Need for a Systems Optimization Laboratory1972

Box 2, Folder 104

Fourier-Motzkin Elimination and Its Dual1972

Box 2, Folder 105

Health Care in Future Cities1972

Box 3, Folder 106

On the Relation of Operations Research to Mathematics1972

Box 3, Folder 107

The ORSA New Orleans Address on Compact City1973

Box 3, Folder 108

The Price Lecture on Compact City1972

Box 3, Folder 109

The User's Guide to MPL/T.1 (Revised)1972

Box 3, Folder 110

Solving Staircase Linear Programs by a Nested Block-Angular Method1973

Box 3, Folder 111

A Complementary Algorithm for an Optimal Capital Path with Invariant Proportions1974

Box 3, Folder 112

Drews' Institutionalized Divvy Economy1973

Box 3, Folder 113

On a Convex Programming Problem of Rozanov1974

Box 3, Folder 114

Optimization, Mathematical Theory of (Linear and Nonlinear Programming)1974

Box 3, Folder 115

Dygam- A Computer System for the Solution of Dynamic Programs1974

Box 3, Folder 116

Determining Optimal Policies for Ecosystems1974

Box 3, Folder 117

On the Reduction of an Integrated Energy and Interindustry Model to a Smaller Linear Program1974

Box 3, Folder 118

Formulating a PILOT Model for Energy in Relation to the National Economy1974

Box 3, Folder 119

On a PILOT Linear Programming Model for Assessing Physical Impact on the Economy of a Changing Energy Picture1975

Box 3, Folder 120

Note on the Objective Function for the PILOT Model1975

Box 3, Folder 121

Box 3, Folder 122

Solution of a Large Scale Airforce Ordnance Planning Problem by Mathematical Programming1975

Box 3, Folder 123

An Algorithm for a Piecewise Linear Model of Trade and Production with Negative Prices and Bankruptcy1976

Box 3, Folder 124

Linear Programming: Its Past and Its Future1976

Box 3, Folder 125

PILOT Model for Assessing Energy-Economic Options1978

Box 3, Folder 126

Determining Prices and Monetary Flows of the PILOT Energy Model1976

Box 3, Folder 127

Energy Models and Large-Scale Systems Optimization1976

Box 3, Folder 128

Box 3, Folder 129

Large-Scale Systems Optimization with Application to Energy1977

Box 3, Folder 130

Discovering Hidden Totally Leontief Substitution Systems1977

Box 3, Folder 131

Stanford PILOT Energy/Economic Model1977

Box 3, Folder 131a

Stanford PILOT Energy/Economic Model1978

Box 3, Folder 132

At the Interface of Modeling and Algorithms Research1977

Box 3, Folder 133

Quantitative Evaluation of Pest Management Options: The Spruce Budworm Case Study1976

Box 3, Folder 134

Are Dual Variables Prices? If Not, How to Make them More So1978

Box 3, Folder 135

A Basic Factorization Method for Block Triangular Linear Programs1978

Box 3, Folder 136

Linear Optimal Control Problems and Generalized Linear Programming1981

Box 3, Folder 137

Computational Experience with a Continuous Network Design Code1977

Box 3, Folder 138

Formulating and Solving the Network Design Problem by Decomposition1977

Box 3, Folder 139

Pricing Underemployed Capacity in a Linear Economic Model1979

Box 3, Folder 140

Framework for a System of Transportation Spatial Form Research Tools1979

Box 3, Folder 141

The Role of Models in Determining Policy for Transition to a More Resilient Technological Society1979

Box 3, Folder 142

Comments on Khachian's Algorithims for Linear Programming1979

Box 3, Folder 143

Expected Number of Steps of the Simplex Method for a Linear Program with a Convexity Constraint1976

Box 3, Folder 144

Large-Scale Linear Programing1981

Box 3, Folder 145

Stanford PILOT Engineering Model1978

Box 3, Folder 146

Concerns About Large-Scale Models1981

Box 4, Folder 1

Box 4, Folder 3

Box 4, Folder 4

Box 4, Folder 7

Reminscences about the origin of LP9/81

Box 4, Folder 13

Box 4, Folder 15

Box 4, Folder 17

Box 4, Folder 19

Box 4, Folder 21

Box 4, Folder 23

The New Palgrave - "Linear Programming" article 164

Box 4, Folder 25

Box 4, Folder 26

Box 4, Folder 27

Box 4, Folder 31

Box 4, Folder 32

Box 4, Folder 34

Box 4, Folder 35

Box 4, Folder 36

Box 4, Folder 37

Box 4, Folder 38

Box 4, Folder 44

Box 4, Folder 46

Box 4, Folder 47

Box 5, Folder 1

Papers about Exhibits1985

Box 5, Folder 2

Graphical Material on George B. Dantzig1982

Box 5, Folder 3

Box 5, Folder 4

Operations Research Program Library Linear Programming System1981

Box 5, Folder 5

An Algorithm for a Piecewise linear model of trade…Bankruptcy. With Eaves-Gale; submitted to: Math Programming1990

Box 5, Folder 6

Box 5, Folder 7

Box 5, Folder 8

Box 5, Folder 9

Math Modelleny St. LouisAug 47, 1987

Box 5, Folder 10

Box 5, Folder 11

"Impact" - Comp in Math @SUJul-86

Box 5, Folder 12

Box 5, Folder 13

Expense Reports, G.B. Dantzig1985

Box 5, Folder 14

MIT Math. Programming SymposiumAugust 5-9, 1985

Accession ARCH-2005-363 Additional material

Tales of Statisticians
George B Dantzig
8 Nov 1914 -13 May 2005

George Dantzig was the son of Russian-born Tobias Dantzig, author of the widely popular book Number: The Language of Science. Though named for George Bernard Shaw, he majored in mathematics at the University of Maryland, where his father then taught (it was cheaper than other schools, and the family was not well off). He began graduate work on a scholarship at the University of Michigan in 1936, and got his MA in 1937, but did not continue, due to his distaste for the abstractness of the mathematics he encountered there. After working as a statistician in Seattle, he wrote in 1939 to Neyman, whose papers had interested him, and an assistantship was arranged for him at Berkeley. This story from that period is a classic:

"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."

[from Albers, More Mathematical People]

The point of the story, which has been quoted frequently in inspirational writings, is that if Dantzig had known the problems were unsolved, he might not have made any serious attempt to solve them, whereas the "positive" assumption that they were not only solvable, but routinely solvable, focused his attention simply on finding the solution. Ignorance can thus be a help to the discoverer. So can youth. A similar point was made by pianist Ruth Laredo, looking back on her acquisition of the fiendishly difficult Ravel literature:

 "I learned the Ravel repertoire mostly when I was so young that the extreme difficulties somehow didn't bother me. Gaspard de la Nuit came into my life at fifteen. I just didn't know how hard it was."

It seems there is a lot to be said for not knowing how hard things are.

Dantzig had all but completed his degree in 1941, but WW2 then interrupted. WW2 had its problems for many of us, but it undeniably gave enormous opportunities for the development of statistics, the practical stepsister of mathematics. Dantzig want to Washington in 1941 as Head of the Combat Analysis Branch of the Air Force's Headquarters Statistical Control.

"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."

This gigantic problem of finding the optimal intersection, the optimal "program," for all these interconnected flowlines, was one of great difficulty. For his contribution to this and other urgent problems of managerial logistics, he was awarded the War Department's Exceptional Civilian Service Medal in 1944.

He left this post in 1946, and returned to Berkeley for a semester to finish his degree. He declined an offered junior position at Berkeley due to the tiny salary. In June he was back in Washington, where he accepted a post as Mathematical Advisor to the Defense Department, to work on mechanizing the planning process. In 1947, based partly on his earlier work with aircraft supply flowlines, he discovered what is called the simplex method of linear programming. Its first large-scale test involved a problem with 9 equations in 77 unknowns, which, with the calculating machinery available at the time, took 120 man-days of labor to solve. Computers, which had been developed but not fully exploited during the war, were the obvious next step. In 1952 Dantzig went to work for the RAND Corporation, on implementing the simplex method on computers. In 1960 he accepted a teaching position at Berkeley, moving in 1966 to Stanford as Professor of Operations Research and Computer Science.

The power of the simplex method (as was also true of Wilcoxon and his nonparametric methods, which had been published two years earlier, in 1945) continued to surprise Dantzig himself. Thanks in large part to his own vigorous following up of his initial success, the simplex method is now said to underlie more computer-time use than anything else. His still classic book on the subject, Linear Programming and Extensions, appeared in 1963. In 1975 came the first of many prizes recognizing the importance of the method. Appropriately enough, given von Neumann's role in pushing for the first computer during WW2, this was the von Neumann Theory Prize in Operational Research. Other recognitions followed. Not including the Nobel (technically, the Bank of Sweden Prize in Economics), which in 1975 went to Koopmans and Kantorovich for an achievement to which Dantzig had also made a decisive contribution: the mathematical theory of the allocation of scarce resources. So upset was Koopmans at Dantzig's omission, that he suggested to Kantorovich that they refuse the prize themselves. Famous once a year is Stockholm, and famous down the years are the lapses of Stockholm.

Dantzig had technically retired in 1973 from Stanford, but continued active until 1977. As late as 2001, he was listed as Chief of Operations Research and Computer Systems at Stanford, as well as Co-Director of the Systems Optimization Lab, and Director of the PILOT Energy-Economic Model Project. His achievements are recorded in detail, along with many reminiscences by himself and others, at the web site maintained by his student Saul Gass.

is Copyright © 2001- by E Bruce Brooks 

1 Feb 2006 / Contact The Project / Exit to Statistics Page

One thought on “George Dantzig Homework Problems Checklist

Leave a Reply

Your email address will not be published. Required fields are marked *