The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Dantzig, George B. (1914–2005)

  • Richard W. Cottle
  • B. Curtis Eaves
  • Mukund N. Thapa
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_2839

Abstract

George Dantzig is known as ‘father of linear programming’ and ‘inventor of the simplex method’. This biographical sketch traces the high points of George Dantzig’s professional life and scholarly achievements. The discussion covers his graduate student years, his wartime service at the US Air Force’s Statistical Control Division, his post-war creativity while serving as a mathematical advisor at the US Air Force Comptroller’s Office and as a research mathematician at the RAND Corporation, his distinguished career in academia – at UC Berkeley and later at Stanford University – and finally as an emeritus professor of operations research.

Keywords

Complementarity Computational complexity Convex programming Convexity Dantzig, G. B Decomposition principle Degeneracy Distributed computation Hurwicz, L Integer programming Interior point methods Kantorovich, L.V Koopmans, T.C Lagrangian function Leontief, W. W Linear programming Logarithmic barrier method Mathematical programming Neyman, J Nonlinear programming Operations research Simplex method for solving linear programs Stochastic programming with recourse von Neumann, J Wood, M.K 

JEL Classification

B31 
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Notes

Acknowledgments

Acknowledgments The authors are grateful to David Dantzig, Jessica Dantzig Klass, and many of Dantzig’s friends and colleagues who have contributed to this bio- graphical article. These include A.J. Hoffman, G. Infanger, E. Klotz, J.C. Stone, M.J. Todd, J.A. Tomlin and M.H. Wright. This article has also benefited from other writings on G.B. Dantzig’s life, namely: Albers and Reid (1986), Albers, Alexanderson and Reid (1990), Cottle (2003, 2005, 2006), Cottle and Wright (2006), Dantzig (1982, 1991), Dorfman (1984), Gill et al. (2007), Kersey (1989), Lustig (2001), Gass (1989, 2002, 2005).

Bibliography

  1. Albers, D.J., and C. Reid. 1986. An interview with George B. Dantzig: The father of linear programming. College Mathematics Journal 17: 292–314.CrossRefGoogle Scholar
  2. Albers, D.J., G.L. Alexanderson, and C. Reid. 1990. More mathematical people. New York: Harcourt Brace Jovanovich.Google Scholar
  3. Arrow, K.J., L. Hurwicz, and H. Uzawa. 1958. Studies in linear and non-linear programming. Stanford: Stanford University Press.Google Scholar
  4. Benders, J.K. 1962. Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik 4: 238–252.CrossRefGoogle Scholar
  5. Charnes, A., and W.W. Cooper. 1962. On some works of Kantorovich, Koopmans and others. Management Science 8: 246–263.CrossRefGoogle Scholar
  6. Charnes, A., and C.E. Lemke. 1954. Minimization of non-linear separable convex functionals. Naval Research Logistics Quarterly 1: 301–312.CrossRefGoogle Scholar
  7. Cottle, R.W. 1964. Nonlinear programs with positively bounded Jacobians. Ph.D. thesis. Department of Mathematics. University of California at Berkeley.Google Scholar
  8. Cottle, R.W. 2003. The basic George B. Dantzig. Stanford: Stanford University Press.Google Scholar
  9. Cottle, R.W. 2005. George B. Dantzig: Operations research icon. Operational Research 53: 892–898.CrossRefGoogle Scholar
  10. Cottle, R.W. 2006. George B. Dantzig: A life in mathematical programming. Mathematical Programming 105: 1–8.CrossRefGoogle Scholar
  11. Cottle, R.W., and M.H. Wright. 2006. Remembering George Dantzig. SIAM News 39(3): 2–3.Google Scholar
  12. Dantzig, T. 1930. Number, The language of science. New York: Macmillan. 4th edition, ed. J. Mazur, republished New York: Pi Press, 2005.Google Scholar
  13. de la Vallée Poussin, M.C.J. 1911. Sur la méthode de l’approximation minimum. Annales de la Société Scientifique de Bruxelles 35: 1–16.Google Scholar
  14. Dijkstra, E. 1959. A note on two problems in connection with graphs. Numerische Mathematik 1: 269–271.CrossRefGoogle Scholar
  15. Dongarra, J., and F. Sullivan. 2000. The top 10 algorithms. Computing in Science and Engineering 2(1): 22–23.CrossRefGoogle Scholar
  16. Dorfman, R. 1984. The discovery of linear programming. Annals of the History of Computing 6: 283–295.CrossRefGoogle Scholar
  17. Dorfman, R., P.A. Samuelson, and R.M. Solow. 1958. Linear programming and economic analysis. New York: McGraw-Hill.Google Scholar
  18. Eaves, B.C. 1972. Homotopies for the computation of fixed points. Mathematical Programming 3: 1–22.CrossRefGoogle Scholar
  19. Fiacco, A.V., and G.P. McCormick. 1968. Nonlinear programming: Sequential unconstrained minimization techniques. New York: Wiley.Google Scholar
  20. Flood, M.M. 1956. The traveling-salesman problem. Operational Research 4: 61–75.CrossRefGoogle Scholar
  21. Ford Jr., L.R., and D.R. Fulkerson. 1962. Flows in networks. Princeton: Princeton University Press.Google Scholar
  22. Fourier, J.B.J. 1826. Solution d’une question particulière du calcul des inégalités. Nouveau Bulletin des Sciences par la Société Philomatique de Paris, 99–100. Reprinted in Oeuvres de Fourier, Tome II, ed. G. Darboux. Paris: Gauthier, 1890.Google Scholar
  23. Frisch, R.A.K. 1955. The logarithmic potential method of convex programs. Oslo: University Institute of Economics.Google Scholar
  24. Gale, D., H.W. Kuhn, and A.W. Tucker. 1951. Linear programming and the theory of games. In Activity analysis of production and allocation, ed. T.C. Koopmans. New York: Wiley.Google Scholar
  25. Gass, S.I. 1989. Comments on the history of linear programming. IEEE Annals of the History of Computing 11(2): 147–151.Google Scholar
  26. Gass, S.I. 2002. The first linear-programming shoppe. Operational Research 50: 61–68.CrossRefGoogle Scholar
  27. Gass, S.I. 2005. In Memoriam, George B. Dantzig. 2005. Online. Available at http://www.lionhrtpub.com/orms/orms-8-05/dantzig.html. Accessed 12 Jan 2007.
  28. Gass, S.I., and T.L. Saaty. 1955. The computational algorithm for the parametric objective function. Naval Research Logistics Quarterly 2: 39–45.CrossRefGoogle Scholar
  29. Gill, P.E., Murray, W., Saunders, M.A., Tomlin, J.A. and Wright, M.H. 2007. George B. Dantzig and systems optimization. Online. Available at http://www.stanford.edu/group/SOL/GBDandSOL.pdf. Accessed 2 Feb 2007.
  30. Gomory, R.E. 1958. Essentials of an algorithm for integer solutions to linear programs. Bulletin of the American Mathematical Society 64: 256.CrossRefGoogle Scholar
  31. Hitchcock, F.L. 1941. The distribution of a product from several sources to numerous localities. Journal of Mathematics and Physics 20: 224–230.CrossRefGoogle Scholar
  32. Hoffman, A. 1953. Cycling in the Simplex Algorithm. Report No. 2974. Washington, DC: National Bureau of Standards.Google Scholar
  33. Hopp, W.J., ed. 2004. Ten most influential papers of Management Science’s first fifty years. Management Science 50(12 Supplement), 1764–1769.Google Scholar
  34. Infanger, G. 1991. Monte Carlo (importance) sampling within a Benders decomposition algorithm for stochastic linear programs. Ann. Oper. Res. 39: 41–67.Google Scholar
  35. John, F. 1948. Extremum problems with inequalities as side conditions. In Studies and essays, Courant anniversary volume, ed. K.O. Friedrichs, O.E. Neugebauer, and J.J. Stoker. New York: Wiley-Interscience.Google Scholar
  36. Kantorovich, L.V. 1942. Translocation of masses. Doklady Akademii Nauk SSSR 37: 199–201. Reprinted in Management Science 5 (1958–59), 1–4.Google Scholar
  37. Kantorovich, L.V. 1960. Mathematical methods of organizing and planning production. Management Science 6: 363–422. English translation of original monograph published in 1939.CrossRefGoogle Scholar
  38. Kantorovich, L.V. and Gavurin, M.K. 1949. The application of mathematical methods to freight flow analysis. Problems of Raising the Efficiency of Transport Performance. Akademiia Nauk, USSR. (Kantorovich confirmed the paper was completed and submitted in 1940, but publication delayed by the Second World War.)Google Scholar
  39. Karmarkar, N. 1984. A new polynomial-time algorithm for linear programming. Combinatorica 4: 373–395.CrossRefGoogle Scholar
  40. Karush, W. 1939. Minima of functions of several variables with inequalities as side constraints. MSc dissertation, Department of Mathematics, University of Chicago.Google Scholar
  41. Kersey, C. 1989. Unstoppable. Naperville: Sourcebooks, Inc.Google Scholar
  42. Khachiyan, L.G. 1979. A polynomial algorithm in linear programming in Russian. Doklady Akademii Nauk SSSR 244, 1093–6. English translation: Soviet Mathematics Doklady 20 (1979), 191–4.Google Scholar
  43. Klee, V., and G.J. Minty. 1972. How good is the simplex algorithm? In Inequalities III, ed. O. Shisha. New York: Academic.Google Scholar
  44. Koopmans, T.C. 1947. Optimum utilization of the transportation system. Proceedings of the International Statistical Conferences, 1947, vol. 5. Washington D.C. Also in Econometrica 16 (1948), 66–8.Google Scholar
  45. Koopmans, T.C. 1949. Optimum utilization of the transportation system. Econometrica 17(Supplement): 136–146.CrossRefGoogle Scholar
  46. Koopmans, T.C. (ed.). 1951. Activity analysis of production and allocation. New York: Wiley.Google Scholar
  47. Koopmans, T.C. 1960. A note about Kantorovich’s paper, ‘Mathematical Methods of Organizing and Planning Production’. Management Science 6: 363–365.CrossRefGoogle Scholar
  48. Kuhn, H.W., and A.W. Tucker. 1951. Nonlinear Programming. In Proceedings of the second Berkeley symposium on mathematical statistics and probability, ed. J. Neyman. Berkeley: University of California Press.Google Scholar
  49. Lemke, C.E. 1954. The dual method of solving the linear programming problem. Naval Research Logistics Quarterly 1: 36–47.CrossRefGoogle Scholar
  50. Lemke, C.E. 1965. Bimatrix equilibrium points and mathematical programming. Management Sciences 11: 681–689.CrossRefGoogle Scholar
  51. Leontief, W.W. 1936. Quantitative input and output relations in the economic system of the United States. Review of Economic Statistics 18: 105–125.CrossRefGoogle Scholar
  52. Lustig, I. 2001. e-optimization.com. Interview with G.B. Dantzig. Online. Available at http://e-optimization.com/directory/trailblazers/dantzig. Accessed 29 Dec 2006.
  53. Markowitz, H.M. 1956. The optimization of a quadratic function subject to linear constraints. Naval Research Logistics Quarterly 3: 111–133. RAND Research Memorandum RM-1438, 1955.CrossRefGoogle Scholar
  54. Orchard-Hays, W. 1954. A composite simplex algorithm-II, RAND Research Memorandum RM-1275. Santa Monica: RAND Corporation.Google Scholar
  55. Rockafellar, R.T. 1970. Convex analysis. Princeton: Princeton Press.CrossRefGoogle Scholar
  56. Scarf, H. 1967. The core of an N-person game. Econometrica 35: 50–69.CrossRefGoogle Scholar
  57. Scarf, H. 1973. The computation of economic equilibria. New Haven: Yale University Press.Google Scholar
  58. Schrijver, A. 1986. Theory of linear and integer programming. Chichester: Wiley.Google Scholar
  59. Smale, S. 1976. A convergent process of price adjustment and global Newton methods. Journal of Mathematical Economics 3: 1–14.CrossRefGoogle Scholar
  60. Smale, S. 1983. The problem of the average speed of the simplex method. In Mathematical programming: The state of the art, ed. A. Bachem, M. Grötschel, and B. Korte. Berlin: Springer.Google Scholar
  61. Stigler, G.J. 1945. The cost of subsistence. Journal of Farm Economics 27: 303–314.CrossRefGoogle Scholar
  62. Todd, M.J. 1996. Potential-reduction methods in mathematical programming. Mathematical Programming 76: 3–45.Google Scholar
  63. von Neumann, J. 1947. Discussion of a maximum problem. Unpublished working paper dated 15–16 November. In John von Neumann: Collected works, vol. 6, ed. A.H. Taub. Oxford: Pergamon Press, 1963.Google Scholar
  64. von Neumann, J., and O. Morgenstern. 1944. Theory of games and economic behavior. Princeton: Princeton University Press.Google Scholar

Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Richard W. Cottle
    • 1
  • B. Curtis Eaves
    • 1
  • Mukund N. Thapa
    • 1
  1. 1.