# George Dantzig

#182

Most Influential Person Now

American mathematician

## George Dantzig's AcademicInfluence.com Rankings

George Dantzigmathematics Degrees

Mathematics

#45

World Rank

#138

Historical Rank

#14

USA Rank

Measure Theory

#23

World Rank

#46

Historical Rank

#11

USA Rank

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Mathematics

## George Dantzig's Degrees

- PhD Mathematics University of California, Berkeley
- Masters Mathematics University of California, Berkeley

## Why Is George Dantzig Influential?

(Suggest an Edit or Addition)According to Wikipedia, George Bernard Dantzig was an American mathematical scientist who made contributions to industrial engineering, 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 for his other 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 by Jerzy Neyman.

## George Dantzig's Published Works

### Published Works

- Linear programming and extensions (1965) (4520)
- The Truck Dispatching Problem (1959) (2769)
- Decomposition Principle for Linear Programs (1960) (2312)
- Solution of a Large-Scale Traveling-Salesman Problem (1954) (1838)
- Linear Programming Under Uncertainty (2004) (1357)
- Discrete-Variable Extremum Problems (1957) (914)
- COMPLEMENTARY PIVOT THEORY OF MATHEMATICAL PROGRAMMING (1968) (804)
- Introduction to Combinatorial Mathematics. (1971) (738)
- Chemical Equilibrium in Complex Mixtures (1958) (734)
- THE DECOMPOSITION ALGORITHM FOR LINEAR PROGRAMS (1961) (722)
- Linear Programming 1: Introduction (1997) (507)
- Fourier-Motzkin Elimination and Its Dual (1973) (402)
- Decision Making and Problem Solving (1987) (375)
- Letter to the Editor - A Comment on Edie's "Traffic Delays at Toll Booths" (1954) (366)
- Notes on Linear Programming: Part 1. The Generalized Simplex Method for Minimizing a Linear Form under Linear Inequality Restraints (1954) (324)
- MINIMIZING THE NUMBER OF CARRIERS TO MEET A FIXED SCHEDULE (1954) (293)
- The fixed charge problem (1968) (273)
- Multi-stage stochastic linear programs for portfolio optimization (1993) (266)
- On the continuity of the minimum set of a continuous function (1967) (238)
- On the Shortest Route Through a Network (1960) (216)
- ON THE SIGNIFICANCE OF SOLVING LINEAR PROGRAMMING PROBLEMS WITH SOME INTEGER VARIABLES (1960) (212)
- Programming of Interdependent Activities: II Mathematical Model (1949) (208)
- Symmetric dual nonlinear programs. (1965) (207)
- On the Max Flow Min Cut Theorem of Networks. (1955) (205)
- ON THE SOLUTION OF TWO-STAGE LINEAR PROGRAMS UNDER UNCERTAINTY. NOTES ON LINEAR PROGRAMMING AND EXTENSIONS. PART 55 (1961) (200)
- Parallel processors for planning under uncertainty (1990) (184)
- Generalized Upper Bounding Techniques (1967) (177)
- The Allocation of Aircraft to Routes—An Example of Linear Programming Under Uncertain Demand (1956) (174)
- The decomposition algorithm for linear programming: notes on linear programming and extensions-part 57. (1961) (167)
- A generalization of the linear complementarity problem (1970) (164)
- On a Linear-Programming, Combinatorial Approach to the Traveling-Salesman Problem (1959) (161)
- Reminiscences about the origins of linear programming (1982) (156)
- FINDING A CYCLE IN A GRAPH WITH MINIMUM COST TO TIME RATIO WITH APPLICATION TO A SHIP ROUTING PROBLEM (1966) (139)
- On the Non-Existence of Tests of "Student's" Hypothesis Having Power Functions Independent of $\sigma$ (1940) (137)
- UPPER BOUNDS, SECONDARY CONSTRAINTS, AND BLOCK TRIANGULARITY IN LINEAR PROGRAMMING (1955) (130)
- Formulating and solving the network design problem by decomposition (1979) (127)
- 7* A Primal-Dual Algorithm for Linear Programs (1957) (123)
- The Diet Problem (1990) (119)
- AUTOMATED MULTIPHASIC SCREENING AND DIAGNOSIS. (1964) (114)
- Origins of the simplex method (1990) (114)
- ALL SHORTEST ROUTES IN A GRAPH (1966) (93)
- Large-Scale Stochastic Linear Programs: Importance Sampling and Benders Decomposition (1991) (88)
- 23. A Decomposition Principle for Linear Programs (1963) (88)
- Linear Programming in a Markov Chain (1962) (85)
- Compact city;: A plan for a liveable urban environment (1973) (84)
- Integral Extreme Points (1968) (81)
- Computation of maximal flows in networks (1955) (77)
- RECENT ADVANCES IN LINEAR PROGRAMMING (1956) (76)
- On the Fundamental Lemma of Neyman and Pearson (1951) (76)
- Optimal Solution of a Dynamic Leontief Model with Substitution (1955) (72)
- THE PRODUCT FORM FOR THE INVERSE IN THE SIMPLEX METHOD (1954) (70)
- Mathematics of the decision sciences (1968) (59)
- A Linear Programming Approach to the Chemical Equilibrium Problem (1958) (55)
- Programming of Interdependent Activities: I General Discussion (1949) (55)
- Linear Programming and Its Extensions. (1966) (53)
- Linear Programming (2002) (51)
- A complementarity algorithm for an optimal capital path with invariant proportions (1974) (50)
- A complementarity algorithm for an optimal capital path with invariant proportions (1974) (50)
- Maximum Diameter of Abstract Polytopes (1974) (41)
- Planning under uncertainty using parallel computing (1988) (38)
- A strictly improving linear programming Phase I algorithm (1993) (37)
- Note on solving linear programs in integers (1959) (34)
- On the Status of Multistage Linear Programming Problems (1959) (33)
- Linear Control Processes and Mathematical Programming (1966) (32)
- Lectures in differential equations (1969) (31)
- Converting a Converging Algorithm into a Polynomially Bounded Algorithm (1991) (29)
- Decomposition techniques for multi-area generation and transmission planning under uncertainty: Final report (1989) (27)
- POSITIVE (SEMI-) DEFINITE MATRICES AND MATHEMATICAL PROGRAMMING (1963) (27)
- THE APPLICATION OF DECOMPOSITION TO TRANSPORTATION NETWORK ANALYSIS (1976) (26)
- Inductive Proof of the Simplex Method (1960) (25)
- A Machine-Job Scheduling Model (1960) (25)
- COMPACT BASIS TRIANGULARIZATION FOR THE SIMPLEX METHOD (1962) (25)
- ALL SHORTEST ROUTES FROM A FIXED ORIGIN IN A GRAPH (1966) (25)
- GENERALIZED UPPER BOUNDED TECHNIQUES FOR LINEAR PROGRAMMING - I (1964) (25)
- A PRIMAL--DUAL ALGORITHM (1956) (25)
- On the Reduction of Certain Multiplicative Chemical Equilibrium Systems to Mathematically Equivalent Additive Systems (1962) (24)
- The Problem of Routing Aircraft--A Mathematical Solution. (1954) (23)
- A Build-Up Interior Method for Linear Programming: Affine Scaling Form (1990) (23)
- Stochastic programming : the state of the art : in honor of George B. Dantzig (2011) (23)
- A first order approach to a class of multi-time-period stochastic programming problems (1986) (22)
- The Stanford pilot energy/economic model (1978) (22)
- A Basis Factorization Method for Block Triangular Linear Programs. (1978) (22)
- Constructive proof of the Min-Max theorem (1956) (22)
- Determining Optimal Policies for Ecosystems (1974) (21)
- Solving stochastic linear programs on a Hypercube multicomputer. Technical report (1991) (20)
- Existence of A-avoiding paths in abstract polytopes (1974) (20)
- Making progress during a stall in the simplex algorithm (1989) (20)
- Expected Number of Steps of the Simplex Method for a Linear Program with a Convexity Constraint. (1980) (20)
- A PRODUCTION SMOOTHING PROBLEM (1955) (20)
- A Control Problem of Bellman (1971) (19)
- On a Pilot Linear Programming Model for Assessing Physical Impact on the Economy of a Changing Energy Picture (1975) (19)
- Large-Scale Linear Programming (1981) (19)
- 11. Dilworth’s Theorem on Partially Ordered Sets (1957) (19)
- Approaches to Stochastic Programming with Application to Electric Power Systems (1993) (19)
- A Build-up Interior-point Method for Linear Programming: Aane Scaling Form (1991) (17)
- A Probabilistic Lower Bound for Two-Stage Stochastic Programs (2010) (17)
- QUADRATIC PROGRAMMING. A VARIANT OF THE WOLFE-MARKOWITZ ALGORITHMS (1961) (16)
- Mathematical decomposition techniques for power system expansion planning: Volume 1, Decomposition methods and uses: Final report (1988) (16)
- An algorithm for a piecewise linear model of trade and production with negative prices and bankruptcy (1979) (15)
- On the Reduction of an Integrated Energy and Interindustry Model to a Smaller Linear Program (1976) (15)
- Triangulations (tilings) and certain block triangular matrices (1985) (14)
- Deriving a Utility Function For the U.S. Economy (1988) (14)
- The parallel decomposition of linear programs (1989) (13)
- Intelligent control and optimization under uncertainty with application to hydro power (1997) (13)
- SPARSE MATRIX TECHNIQUES IN TWO MATHEMATICAL PROGRAMMING CODES (1969) (13)
- On a Class of Distributions that Approach the Normal Distribution Function (1939) (12)
- Mathematical programming : essays in honor of George B. Dantzig (1985) (12)
- Comments on Khachian's Algorithm for Linear Programming. (1979) (10)
- The Basic George B. Dantzig (2003) (10)
- Algorithmic advances in stochastic programming (1993) (10)
- A HOSPITAL ADMISSION PROBLEM (1969) (9)
- Brief Survey of Soft Computing Techniques Used for Optimization of TSP (2013) (9)
- A Case Study of Forest Ecosystem Pest Management (1975) (9)
- Thoughts on Linear Programming and Automation (1957) (9)
- Planning under uncertainty (1999) (8)
- A Decomposition and Scaling-Inequality for Line-Sum-Symmetric Nonnegative Matrices (1985) (8)
- Formulating a Pilot Model for Energy in Relation to the National Economy (1975) (8)
- Formulating an objective for an economy (1988) (8)
- Bracketing to speed convergence illustrated on the von Newmann algorithm for finding a feasible solution to a linear program with a convexity contraint (1992) (8)
- OPTIMIZATION IN OPERATIONS RESEARCH: SOME EXAMPLES (1965) (8)
- The Role of Models in Determining Policy for Transition to a more Resilient Technological Society (1979) (8)
- Maximum Payloads Per Unit Time Delivered Through an Air Network (1964) (8)
- Mathematical decomposition techniques for power system expansion planning: Volume 5, Use of parallel computers for multi-area expansion planning: Preliminary results, Final report (1988) (7)
- The ORSA New Orleans Address on Compact City (1973) (7)
- A Strictly Improving Phase 1 Algorithm Using Least-Squares Subproblems (1992) (7)
- CONCEPTS, ORIGINS, AND USE OF LINEAR PROGRAMMING (1957) (7)
- Linear Optimal Control Problems and Generalized Linear Programs (1981) (7)
- COMPLEMENTARY SPANNING TREES (1969) (6)
- Simplex Method for Solving Linear Programs (1987) (6)
- Computing Tetraethyl-Lead Requirements in a Linear-Programming Format (1960) (6)
- Solving Staircase Linear Programs by a Nested Block-Angular Method (1973) (6)
- MPL, Mathematical Programming Language: specification manual for Committee review (1970) (6)
- Deriving a Utility Function For the Economy. (1985) (6)
- THE SIMPLEX METHOD (1956) (6)
- SOLVING TWO-MOVE GAMES WITH PERFECT INFORMATION (1958) (5)
- Fourier-Motzkin Elimination and Its Dual with Application to Integer Programming (1975) (5)
- A Mathematical Model of the Chemistry of the External Respiratory System (1961) (5)
- Integrability of the multiple-period equilibrium model part II (1989) (5)
- Notes on Linear Programming — Part XXXII (1956) (5)
- E.M.L. Beale, FRS; friend and colleague (1987) (4)
- LARGE-SCALE SYSTEM OPTIMIZATION: A REVIEW (1965) (4)
- Time-Staged Linear Programs. (1980) (4)
- Notes on Linear Programming--Part V: A Product-Form Tableau for Revised Simplex Method: Computing Appendix for RM-1268 (1954) (4)
- MATHEMATICS OF THE DECISION SCIENCES, PART 2. LECTURES IN APPLIED MATHEMATICS. VOLUME 12, (1968) (4)
- SOLVING THE CHEMICAL EQUILIBRIUM PROBLEM USING THE DECOMPOSITION PRINCIPLE (1960) (4)
- Discovering Hidden Totally Leontief Substitution Systems (1978) (4)
- On the need for a system optimization laboratory (1972) (4)
- Energy Models and Large-Scale Systems Optimization. (1976) (4)
- Management Science in the World of Today and Tomorrow (1967) (4)
- Updating the Product Form of the Inverse for the Revised Simplex Method (1965) (4)
- Letter to the Editor—Note on Klein's “Direct Use of Extremal Principles in Solving Certain Problems Involving Inequalities” (1956) (3)
- An institutionalized Divvy economy (1975) (3)
- Molecular-Sized Channels and Flows against the Gradient (1962) (3)
- Time-Staged Methods in Linear Programming, Comments and Early History. (1980) (3)
- Pricing underemployed capacity in a linear economic model. Technical report SOL 79-2 (1979) (3)
- Impact of Linear Programming on Computer Development (1985) (3)
- 14. The Classical Transportation Problem (1963) (3)
- GENERALIZED UPPER BOUNDING TECHNIQUES FOR LINEAR PROGRAMMING, 2 (1965) (3)
- ON POSITIVE PRINCIPAL MINORS (1967) (2)
- Using the Pilot Model to Study the Effects of Technological Change (1986) (2)
- 5. The Simplex Method (1963) (2)
- New Mathematical Methods in the Life Sciences (1964) (2)
- NOTE ON B. KLEIN'S 'DIRECT USE OF EXTREMAL PRINCIPLES IN SOLVING CERTAIN PROBLEMS INVOLVING INEQUALITIES' (1957) (2)
- Drews Institutionalized Divvy Economy (1973) (2)
- AT THE INTERFACE OF MODELING AND ALGORITHMS RESEARCH11Research supported by the Energy Research and Development Administration Contracts EY-76-S-03-0326 PA#18, and EY-76-S-03-0326 PA#52; the Office of Naval Research Contract N00014-75-C-0865; the National Science Foundation Grant MCS76-20019; the El (1978) (2)
- Mathematical decomposition techniques for power system expansion planning: Volume 3, An integrated methodology for VAR sources planning: Final report (1988) (2)
- Bracketing to speed convergence illustrated on the von Newmann algorithm for finding a feasible solution to a linear program with a convexity contraint. Technical report (1992) (2)
- 28. The Allocation of Aircraft to Routes under Uncertain Demand (1963) (2)
- Analyzing the effects of technological change: A computable general equilibrium approach (1988) (2)
- The Mathematical Programming Language (MPL) (1971) (2)
- On the relation of operations research to mathematics (1972) (1)
- OPTIMAL ASSIGMENT OF COMPUTER STORAGE BY CHAIN DECOMPOSITION OF PARTIALLY ORDERED SETS (1966) (1)
- OPERATIONS RESEARCH IN THE WORLD OF TODAY AND TOMORROW (1965) (1)
- 1. The Linear Programming Concept (1963) (1)
- Three geographic decomposition approaches in transportation network analysis (1980) (1)
- 9. The Simplex Method Using Multipliers (1963) (1)
- 10. Finiteness of the Simplex Method under Perturbation (1963) (1)
- Linear programming in a Markov chain: notes on linear programming and extensions-part 59. (1962) (1)
- 13. Games And Linear Programs (1963) (1)
- 17. Networks and the Transshipment Problem (1963) (1)
- Formulating a linear programming model (1956) (1)
- On a convex programming problem of Rozanov (1974) (1)
- On a Model for Computing Round-Off Error of a Sum (1970) (1)
- 15. Optimal Assignment and Other Distribution Problems (1963) (1)
- A Generalized Programming Solution to a Convex Programming Problem with a Homogeneous Objective (1973) (1)
- The Stanford PILOT energy/economic model. Technical report (1977) (1)
- Mathematical decomposition techniques for power system expansion planning: Volume 4, Security-constrained optimal power flow with postcontingency corrective rescheduling: Final report (1988) (1)
- On steady-state intercompartmental flows. (1967) (1)
- An equivalent linear-programming problem. (1958) (0)
- 18. Variables with Upper Bounds (1963) (0)
- 2. Origins and Influences (1963) (0)
- PROFESSOR GEORGE BERNARD DANTZIG, LIFE AND LEGEND (2005) (0)
- Parallel processors for planning under uncertainty 3 IA 11 j A 21 A 22 A 31 A 32 A (2005) (0)
- PROGRESS REPORT, JUNE 15, 1970--SEPTEMBER 30, 1971. (1971) (0)
- 8. Pivoting, Vector Spaces, Matrices, and Inverses (1963) (0)
- Systems Optimization Project. Progress report, 1 October 1975--30 June 1976. [Systems Optimization Lab. , Dept. of Operations Research, Stanford Univ] (1976) (0)
- Problems for Solution: 3951, 4810-4815 (1958) (0)
- Large-scale linear programming : proceedings of a IIASA workshop, 2-6 June 1980 (1981) (0)
- 0 ] 1 F ] ILE Coll ) Systems Optimization Laboratory (0)
- Mathematical Methods in Operations Research and Computer Science (1992) (0)
- OlARGE-SCALE SYSTEM OPTIMIZATION : 2 A REVIEW (2014) (0)
- A strictly improving linear programming alorithm based on a series of Phase 1 problems (1992) (0)
- THE JUNE MEETING IN EUGENE The four hundred eight-second meeting of the American Mathe- (2007) (0)
- COMMENTS ON J. VON NEUMANN'S 'THE PROBLEM OF OPTIMAL ASSIGNMENT IN A TWO-PERSON GAME' (1952) (0)
- The Fourth International Conference on Complementarity Problems Dedicated to the Memory of (0)
- Stephen Maurer's Response (1985) (0)
- Solving linear programs under uncertainty, using decomposition, importance sampling and parallel processors. Progress report (1994) (0)
- LECTURE SERIES IN DIFFERENTIAL EQUATIONS, SESSION I. CONTROL THEORY (1965) (0)
- Automated multiphasic screening and diagnosis. 1964. (1994) (0)
- THE NOVEMBER MEETING IN LOS ANGELES The four hundred eighty-seventh meeting of the American Mathe- (2007) (0)
- Numerical applications: updating the product form of the inverse for the revised simplex method (1965) (0)
- 20. The Primal-Dual Method for Transportation Problems (1963) (0)
- COMPLEHENTARY SPANNING TREES BY GEÜRC (2014) (0)
- 24. Convex Programming (1963) (0)
- Comments on the Budworm for Forest Ecology Model (1973) (0)
- MPL: Mathematical Programming Language (1968) (0)
- AD-750 674 FOURIER-MOTZKIN ELIMINATION AND ITS DUAL (2014) (0)
- Selected Rand Books (1963) (0)
- THE CENTRAL MATHEMATICAL PROBLEM (1956) (0)
- 19. Maximal Flows in Networks (1963) (0)
- A Method forOptimizationof NonlinearSystemResponse (1970) (0)
- 22. Programs with Variable Coefficients (1963) (0)
- Notes on Linear Programming: Part VII The Dual Simplex Algorithm (1954) (0)
- 16. The Transshipment Problem (1963) (0)
- Building a linear programming model (1959) (0)
- Bibliography of Soviet and Western European Publications on Large-Scale Linear Programming (1984) (0)
- Special seminar on operations research (1959) (0)
- Systems optimization project. Progress report, 30 September 1972--30 June 1973 (1973) (0)
- Status of Solution of Large-Scale Linear Programming Problems (Notes on Linear Programming: Part 18) (1954) (0)
- Project Status Report: Ecology and Environment Project (1974) (0)
- Deriving a utility function for the US economy. Technical report (1988) (0)
- A Few Remarks on the History of Mst{problem Dedicated to the Memory of Professor Otakar Bor Uvka (1997) (0)
- FUTURE DEVELOPMENT OF OPERATIONS RESEARCH (1961) (0)
- 7. The Geometry of Linear Programs (1963) (0)
- 21. The Weighted Distribution Problem (1963) (0)
- STOCHASTIC MATHEMATICAL PROGRAMS. Project Summary 1966--1972, and Progress Report January 1, 1972--September 30, 1972. (1972) (0)
- New directions in mathematical programmings (1959) (0)
- Energy models and large-scale systems optimization. Technical report (1976) (0)
- Notes on Linear Programming — Part XXXI: A Primal — Dual Algorithm (1956) (0)
- In memory of Tjalling C. Koopmans (1985) (0)
- LINEAR INEQUALITY SYSTEMS ELIMINATION OF VARIABLES ELIMINATION OF EQUATIONS INTEGER PROGRAMS (2014) (0)
- In honor of A. W. Tucker’s contributions to mathematical programming (1974) (0)
- The word " fuzzy " is used in the sense of (2007) (0)
- Interface of modeling and algorithms research. Technical report SOL 77-29 (1977) (0)
- Notes on Linear Programming: Part XLVII Solving Linear Programs in Integers (1958) (0)
- Planning under Uncertainty using Parallel (0)
- 27. Stigler’s Nutrition Model: An Example of Formulation and Solution (1963) (0)
- 11. Variants of the Simplex Algorithm (1963) (0)
- 00 l > ^ OlARGE-SCALE SYSTEM OPTIMIZATION : 2 A REVIEW by (2014) (0)
- 6. Proof of the Simplex Algorithm and the Duality Theorem (1963) (0)
- 4. Linear Equation and Inequality Systems (1963) (0)
- 12. The Price Concept in Linear Programming (1963) (0)
- Upper Bounded Variables in Linear Programming. (1957) (0)
- On Modified Divided Differences II (2010) (0)

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