## George Dantzig Homework Problems Checklist

## Guide to the George B. Dantzig Papers

Daniel Hartwig & Jenny Johnson

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

**Overview **

**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: http://library.stanford.edu/depts/spc/spc.html.

**Repository:**Dept. of Special Collections & University Archives.

Stanford University Libraries.

557 Escondido Mall

Stanford, CA 94305-6064

Email: speccollref@stanford.edu

Phone: (650) 725-1022

URL: http://library.stanford.edu/spc

**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: http://library.stanford.edu/depts/spc/pubserv/permissions.html.

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 Function****1939**

Box 1, Folder 2

**On the Non-Existence of Tests of Students' Hypothesis Involving Power Functions Independent of Sigma****1940**

Box 1, Folder 3

**A Theorem on Linear Inequalities****1948, 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 Model****1951**

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 Problem****1951**

Box 1, Folder 8

**Programming in a Linear Structure****1949**

Box 1, Folder 9

Box 1, Folder 10

**On the Fundamental Lemma of Neyman and Pearson****1591**

Box 1, Folder 11

**The Generalized Simplex Method for Minimizing a Linear Form Under Linear Inequality Constraints****1955**

Box 1, Folder 12

**The Fixed Charge Problem****1954**

Box 1, Folder 13

**A Duality Theorem Based on the Simplex Method****1952**

Box 1, Folder 14

**Alternate Algorithm for the Revised Simplex Method Using Product Form for the Inverse****1953**

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 Algorithm****1954**

Box 1, Folder 18

**Solution for a Large-Scale Traveling Salesman Problem****1954**

Box 1, Folder 19

**Minimizing the Number of Tankers to Meet a Fixed Schedule****1956**

Box 1, Folder 20

**The Product Form for the Inverse in the Simplex Method****1954**

Box 1, Folder 21

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

Box 1, Folder 22

**Linear Programming Under Uncertainty****1955**

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 Problem****1955**

Box 1, Folder 25

**Developments in Linear Programming****1955**

Box 1, Folder 26

**Constructive Proof of the Min-Max Theorem****1956**

Box 1, Folder 27

**Recent Advances in Linear Programming****1956**

Box 1, Folder 28

**On the Max-Flow Min-Cut Theorems of Networks****1955**

Box 1, Folder 28a

**Formulating a Linear Programming Model****1956**

Box 1, Folder 28b

**Computation of Maximal Flows in Networks****1955**

Box 1, Folder 29

**Concepts, Origins and Uses of Linear Programming****1957**

Box 1, Folder 30

**A Primal-Dual Algorithm for Linear Programs****1956**

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 Automation****1957**

Box 1, Folder 33

**Discrete Variable Extremum Problems****1957**

Box 1, Folder 34

**On the Status of Multi-Stage Linear Programs****1957**

Box 1, Folder 35

**Solving Two-Move Games with Perfect Information****1958**

Box 1, Folder 36

**On Integer and Partial Integer Linear Programming Problems****1958**

Box 1, Folder 37

**A Linear Programming Approach to the Chemical Equilibrium Problem****1958**

Box 1, Folder 37a

**Chemical Equilibrium in Complex Mixtures****1958**

Box 1, Folder 38

**Note on Solving Linear Programs in Integers****1959**

Box 1, Folder 39

**Dilworth's Theorem on Partially Ordered Sets****1956**

Box 1, Folder 40

**On a Linear Programming Combinatorial Approach to the Traveling Salesman Problem****1959**

Box 1, Folder 41

**The Allocation of Aircraft to Routes - An Example of Linear Programming Under Uncertain Demand****1956**

Box 1, Folder 42

**Optimum Routing of Gasoline Delivery Trucks****1959**

Box 1, Folder 43

**The Truck Dispatching Problem****1959**

Box 1, Folder 44

**Inductive Proof of the Simplex Method****1960**

Box 1, Folder 45

**On the Shortest Route Through a Network****1960**

Box 1, Folder 46

**On the Significance of Solving Linear Programming with Some Integer Variables****1960**

Box 1, Folder 47

**General Convex Objective Forms****1960**

Box 1, Folder 48

**A Machine-Job Scheduling Model****1960**

Box 1, Folder 49

**Computing Tetraethyl-Lead Requirements in a Linear-Programming Format****1960**

Box 1, Folder 50

**A Mathematical Model of the Respiratory System****1960**

Box 1, Folder 51

**Solving the Chemical Equilibrium Problem Using the Decomposition Principle****1960**

Box 1, Folder 52

**A Mathematical Model of the Chemistry of the External Respiratory System****1961**

Box 1, Folder 53

**On the Solution of the Two-Staged Linear Programs Under Uncertainty****1961**

Box 1, Folder 54

**Decomposition Principle for Linear Programs****1960**

Box 1, Folder 55

**Future Developments of Operations Research****1961**

Box 1, Folder 56

**A Mathematical Model of the Human External Respiratory System****1961**

Box 1, Folder 57

**Quadratic Programming- A Variant of the…Algorithms****1961**

Box 1, Folder 58

**On the Reduction of Certain Multiplicative Chemical Equilibrium Systems to Mathematically Equivalent Additive Systems****1961**

Box 1, Folder 59

**A Proof of a Property of Leontief and Markov Matrices****1962**

Box 1, Folder 60

**Compact Basis Triangularization for the Simplex Method****1962**

Box 1, Folder 61

**Symmetric Dual Nonlinear Programs****1962**

Box 1, Folder 62

**Linear Programming in a Markov Chain****1962**

Box 1, Folder 63

**Molecular-Sized Channels and Flows Against the Gradient****1962**

Box 1, Folder 64

**Positive (Semi-) Definite Matrices and Mathematical Programming****1963**

Box 1, Folder 65

**Maximum Payloads per Unit Time Delivered Through an Air Network****1963**

Box 1, Folder 66

**Linear Programming and Extensions****1963**

Box 1, Folder 67

**A Model for Sodium-Potassium Transport in Red Cells****1963**

Box 1, Folder 68

**Automated Multiphasic Screening and Diagnosis****1964**

Box 1, Folder 69

**New Mathematical Methods in the Life Sciences****1964**

Box 1, Folder 70

**Generalized Upper Bounded Techniques for the Linear Programming- I****1964**

Box 2, Folder 71

**Generalized Upper Bounded Techniques for the Linear Programming- II****1964**

Box 2, Folder 72

Box 2, Folder 73

**Linear Control Processes and Mathematical Programming****1964**

Box 2, Folder 74

**Updating the Product Form of the Inverse for the Revised Simplex Method****1964**

Box 2, Folder 75

**Operations Research in the World of Today and Tomorrow****1965**

Box 2, Folder 76

**Large-Scale System Optimization: A Review****1965**

Box 2, Folder 77

**Optimization in Operations Research****1965**

Box 2, Folder 78

Box 2, Folder 79

**On the Continuity of the Minimum Set of a Continuous Function****1965**

Box 2, Folder 80

**On Steady-State Intercompartamental Flow****1965**

Box 2, Folder 81

**Optimal Assignment of Computer Storage by Chain Decomposition of Partially Ordered Sets****1966**

Box 2, Folder 82

**Linear Programming and its Progeny****1966**

Box 2, Folder 82a

**An Integer Branching Algorithm for Locating Warehouses****1966**

Box 2, Folder 83

**Finding a Cycle in a Graph with Minimum Cost to Time Ratio with Application to a Ship Routing Problem****1966**

Box 2, Folder 84

**All Shortest Routes From a Fixed Origin in a Graph****1966**

Box 2, Folder 85

**All Shortest Routes in a Graph****1966**

Box 2, Folder 86

**On Positive Principal Minors****1966**

Box 2, Folder 87

**Complementary Pivot Theory of Mathematical Programming****1967**

Box 2, Folder 88

**Mathematical Programming Language****1968**

Box 2, Folder 89

**Integral Extreme Points****1968**

Box 2, Folder 90

**Large-Scale Linear Programming****1967**

Box 2, Folder 91

**A Generalization of the Linear Complimentarity Problem****1968**

Box 2, Folder 92

**Sparse Matrix Techniques in Two Mathematical Programming Codes****1969**

Box 2, Folder 93

**Complementary Spanning Trees****1969**

Box 2, Folder 94

**A Hospital Admission Problem****1969**

Box 2, Folder 95

**Existence of A-Avoiding Paths in Abstract Polytopes****1974**

Box 2, Folder 96

**On a Model for Computing Round-Off Error of a Sum****1970**

Box 2, Folder 97

**Natural Gas Transmission System Optimization****1970**

Box 2, Folder 98

**A Control Problem of Bellman****1970**

Box 2, Folder 99

**MPL: Mathematical Programming Language Specification Manual for Committee Review****1970**

Box 2, Folder 100

**Generalized Upper Bounding Techniques****1967**

Box 2, Folder 100a

**Generalized Linear Programming****1971**

Box 2, Folder 101

**Maximum Diameter of Abstract Polytopes****1971**

Box 2, Folder 102

**Existence of X-Paths in Abstract Polytopes****1970**

Box 2, Folder 103

**On the Need for a Systems Optimization Laboratory****1972**

Box 2, Folder 104

**Fourier-Motzkin Elimination and Its Dual****1972**

Box 2, Folder 105

**Health Care in Future Cities****1972**

Box 3, Folder 106

**On the Relation of Operations Research to Mathematics****1972**

Box 3, Folder 107

**The ORSA New Orleans Address on Compact City****1973**

Box 3, Folder 108

**The Price Lecture on Compact City****1972**

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 Method****1973**

Box 3, Folder 111

**A Complementary Algorithm for an Optimal Capital Path with Invariant Proportions****1974**

Box 3, Folder 112

**Drews' Institutionalized Divvy Economy****1973**

Box 3, Folder 113

**On a Convex Programming Problem of Rozanov****1974**

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 Programs****1974**

Box 3, Folder 116

**Determining Optimal Policies for Ecosystems****1974**

Box 3, Folder 117

**On the Reduction of an Integrated Energy and Interindustry Model to a Smaller Linear Program****1974**

Box 3, Folder 118

**Formulating a PILOT Model for Energy in Relation to the National Economy****1974**

Box 3, Folder 119

**On a PILOT Linear Programming Model for Assessing Physical Impact on the Economy of a Changing Energy Picture****1975**

Box 3, Folder 120

**Note on the Objective Function for the PILOT Model****1975**

Box 3, Folder 121

Box 3, Folder 122

**Solution of a Large Scale Airforce Ordnance Planning Problem by Mathematical Programming****1975**

Box 3, Folder 123

**An Algorithm for a Piecewise Linear Model of Trade and Production with Negative Prices and Bankruptcy****1976**

Box 3, Folder 124

**Linear Programming: Its Past and Its Future****1976**

Box 3, Folder 125

**PILOT Model for Assessing Energy-Economic Options****1978**

Box 3, Folder 126

**Determining Prices and Monetary Flows of the PILOT Energy Model****1976**

Box 3, Folder 127

**Energy Models and Large-Scale Systems Optimization****1976**

Box 3, Folder 128

Box 3, Folder 129

**Large-Scale Systems Optimization with Application to Energy****1977**

Box 3, Folder 130

**Discovering Hidden Totally Leontief Substitution Systems****1977**

Box 3, Folder 131

**Stanford PILOT Energy/Economic Model****1977**

Box 3, Folder 131a

**Stanford PILOT Energy/Economic Model****1978**

Box 3, Folder 132

**At the Interface of Modeling and Algorithms Research****1977**

Box 3, Folder 133

**Quantitative Evaluation of Pest Management Options: The Spruce Budworm Case Study****1976**

Box 3, Folder 134

**Are Dual Variables Prices? If Not, How to Make them More So****1978**

Box 3, Folder 135

**A Basic Factorization Method for Block Triangular Linear Programs****1978**

Box 3, Folder 136

**Linear Optimal Control Problems and Generalized Linear Programming****1981**

Box 3, Folder 137

**Computational Experience with a Continuous Network Design Code****1977**

Box 3, Folder 138

**Formulating and Solving the Network Design Problem by Decomposition****1977**

Box 3, Folder 139

**Pricing Underemployed Capacity in a Linear Economic Model****1979**

Box 3, Folder 140

**Framework for a System of Transportation Spatial Form Research Tools****1979**

Box 3, Folder 141

**The Role of Models in Determining Policy for Transition to a More Resilient Technological Society****1979**

Box 3, Folder 142

**Comments on Khachian's Algorithims for Linear Programming****1979**

Box 3, Folder 143

**Expected Number of Steps of the Simplex Method for a Linear Program with a Convexity Constraint****1976**

Box 3, Folder 144

**Large-Scale Linear Programing****1981**

Box 3, Folder 145

**Stanford PILOT Engineering Model****1978**

Box 3, Folder 146

**Concerns About Large-Scale Models****1981**

Box 4, Folder 1

Box 4, Folder 3

Box 4, Folder 4

Box 4, Folder 7

**Reminscences about the origin of LP****9/81**

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 Exhibits****1985**

Box 5, Folder 2

**Graphical Material on George B. Dantzig****1982**

Box 5, Folder 3

Box 5, Folder 4

**Operations Research Program Library Linear Programming System****1981**

Box 5, Folder 5

**An Algorithm for a Piecewise linear model of trade…Bankruptcy. With Eaves-Gale; submitted to: Math Programming****1990**

Box 5, Folder 6

Box 5, Folder 7

Box 5, Folder 8

Box 5, Folder 9

**Math Modelleny St. Louis****Aug 47, 1987**

Box 5, Folder 10

Box 5, Folder 11

**"Impact" - Comp in Math @SU****Jul-86**

Box 5, Folder 12

Box 5, Folder 13

**Expense Reports, G.B. Dantzig****1985**

Box 5, Folder 14

**MIT Math. Programming Symposium****August 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”