George B. Dantzig: Operations Research Icon

References

• Albers D. George Dantzig 1914–2005. Focus: Newsletter of the Math. Assoc. America (2005) 25(6, August/September):8–10[This article is excerpted from Albers et al. 1990.]Google Scholar
• Albers D. J., Reid C. An interview with George B. Dantzig: The father of linear programming. College Math. J. (1986) 17:292–314Crossref, Google Scholar
• Albers D. J., Alexanderson G. J., Reid C.More Mathematical People: Contemporary Conversations (1990) (Harcourt Brace Jovanovich, Boston, MA) . [Based on Albers and Reid 1986.]Google Scholar
• Cottle R. W.The Basic George B. Dantzig (2003) (Stanford University Press, Stanford, CA) Google Scholar
• Cottle R. W. George B. Dantzig: A legendary life in mathematical programming. Math. Programming (2005) . ForthcomingGoogle Scholar
• Dantzig G. B. On the non-existence of tests of “Student’s” hypothesis having power functions independent of sigma. Ann. Math. Statist. (1940) 11:186–192Crossref, Google Scholar
• Dantzig G. B.I Complete Form of the Neyman-Pearson Lemma; II On the Non-Existence of Tests of “Student’s” Hypothesis Having Power Functions Independent of Sigma (1946) . Doctoral dissertation, Department of Mathematics, University of California, Berkeley, CA. [QA276.D3 at Math-Stat Library, University of California, Berkeley.]Google Scholar
• Dantzig G. B. Programming in a linear structure. Econometrica (1949) 17:73–74Crossref, Google Scholar
• Dantzig G. B. Upper bounds, secondary constraints, and block triangularity in linear programming. Econometrica (1955a) 23:174–183Crossref, Google Scholar
• Dantzig G. B. Optimal solution of a dynamic Leontief model with substitution. Econometrica (1955b) 23:295–302Crossref, Google Scholar
• Dantzig G. B. Linear programming under uncertainty. Management Sci. (1955c) 1:197–206Link, Google Scholar
• Dantzig G. B. Constructive proof of the min-max theorem. Pacific J. Math. (1956) 6:25–33Crossref, Google Scholar
• Dantzig G. B. Discrete variable extremum problems. Oper. Res. (1957) 5:266–277Link, Google Scholar
• Dantzig G. B. Note on solving linear programs in integers. Naval Res. Logist. Quart. (1959) 6:75–76Crossref, Google Scholar
• Dantzig G. B. On the shortest route through a network. Management Sci. (1960a) 6:187–190Link, Google Scholar
• Dantzig G. B. Inductive proof of the simplex method. IBM J. Res. Development (1960b) 4:505–506Crossref, Google Scholar
• Dantzig G. B. On the significance of solving linear programs with some integer variables. Econometrica (1960c) 28:30–44Crossref, Google Scholar
• Dantzig G. B.Linear Programming and Extensions (1963) (Princeton University Press, Princeton, NJ) Crossref, Google Scholar
• Dantzig G. B. Reminiscences about the origins of linear programming. Oper. Res. Lett. (1982) 1:43–48Crossref, Google Scholar
• Dantzig G. B., Bachem A., Grötschel M., Korte B. Reminiscences about the origins of linear programming. Mathematical Programming: The State of the Art (1983) (Springer-Verlag, Berlin, Germany) Crossref, Google Scholar
• Dantzig G. B., Cottle R. W., Kelmanson M. L., Korte B. Reminiscences about the origins of linear programming. Mathematical Programming (1984) (North-Holland, Amsterdam, The Netherlands) . [Proc. Internat. Congress Math. Programming Rio de Janeiro, Brazil, 6–8 April, 1981]Crossref, Google Scholar
• Dantzig G. B., Lenstra J. K., et al. Linear programming. History of Mathematics (1991) (CWI and North-Holland, Amsterdam, The Netherlands) Google Scholar
• Dantzig G. B. (2002) . Personal communicationGoogle Scholar
• Dantzig G. B., Fulkerson D. R. Minimizing the number of tankers to meet a fixed schedule. Naval Res. Logist. Quart. (1954) 1:217–222Crossref, Google Scholar
• Dantzig G. B., Fulkerson D. R., Kuhn H. W., Tucker A. W. On the max-flow min-cut theorem of networks. Linear Inequalities and Related Systems (1956) (Princeton University Press, Princeton, NJ) Google Scholar
• Dantzig G. B., Hoffman A., Kuhn H. W., Tucker A. W. Dilworth’s theorem on partially ordered sets. Linear Inequalities and Related Systems (1956) (Princeton University Press, Princeton, NJ) Google Scholar
• Dantzig G. B., Infanger G., Brezinski C., Kulisch U. Large-scale stochastic linear programs: Importance sampling and Benders decomposition. Computation and Applied Mathematics—Algorithms and Theory (1992a) (North-Holland, Amsterdam, The Netherlands) . [Proc. 13th IMACS World Congress on Comput. Appl. Math., Dublin, Ireland, July, 1991]Google Scholar
• Dantzig G. B., Infanger G., Frauendorfer K., Glavitsch H., Bacher R. Approaches to stochastic programming with applications to electric power systems. Optimization in Planning and Operation of Electric Power Systems (1992b) (Springer-Verlag (Physica-Verlag), Heidelberg, Germany) . Lecture Notes of the SVOR/ASRO Tutorial, Thun, SwitzerlandGoogle Scholar
• Dantzig G. B., Infanger G. Multi-stage stochastic linear programs for portfolio selection. Ann. Oper. Res. (1993) 45:59–76Crossref, Google Scholar
• Dantzig G. B., Johnson S. A production smoothing problem. Proc. Second Sympos. Linear Programming (1955) (National Bureau of Standards and Comptroller, U.S.A.F. Headquarters, Washington, DC) Google Scholar
• Dantzig G. B., Madansky A., Neyman J. On the solution of two-staged linear programs under uncertainty. Proc. Fourth Berkeley Sympos. Math. Statist. Probab. Volume I, Theory of Statist. (1961) (University of California Press, Berkeley, CA) Google Scholar
• Dantzig G. B., Orchard-Hays W. The product form of the inverse in the simplex method. Math. Tables and Other Aids to Comput. (1954) 8:64–67Crossref, Google Scholar
• Dantzig G. B., Orden A. A duality theorem based on the simplex method. Symposium on Linear Inequalities and Programming (1952) . Report 10, Project SCOOP. Planning Research Division, Director of Management Analysis Service, Comptroller, U.S.A.F Headquarters, Washington, DCGoogle Scholar
• Dantzig G. B., Thapa M. N.Linear Programming 1: Introduction (1997) (Springer, New York) Google Scholar
• Dantzig G. B., Thapa M. N.Linear Programming 2: Theory and Extensions (2003) (Springer, New York) Google Scholar
• Dantzig G. B., Wald A. On the fundamental lemma of Neyman and Pearson. Ann. Math. Statist. (1951) 22:87–93Crossref, Google Scholar
• Dantzig G. B., Wolfe P. Decomposition principle for linear programs. Oper. Res. (1960) 8:101–111Link, Google Scholar
• Dantzig G. B., Wolfe P. The decomposition algorithm for linear programming. Econometrica (1961) 29:767–778Crossref, Google Scholar
• Dantzig G. B., Ford L. R., Fulkerson D. R., Kuhn H. W., Tucker A. W. A primal-dual algorithm for linear programs. Linear Inequalities and Related Systems (1956) (Princeton University Press, Princeton, NJ) Google Scholar
• Dantzig G. B., Fulkerson D. R., Johnson S. Solution of a large-scale traveling-salesman problem. J. Oper. Res. Soc. America (1954) 2:393–410Link, Google Scholar
• Dantzig G. B., Johnson S., White W. A linear programming approach to the chemical equilibrium problem. Management Sci. (1958) 5:38–43Link, Google Scholar
• Dantzig G. B., McAllister P. H., Stone J. C. Formulating an objective for an economy. Math. Programming, Series B (1988) 42:11–32Crossref, Google Scholar
• Dantzig G. B., Orden A., Wolfe P. The generalized simplex method for minimizing a linear form under linear inequality constraints. Pacific J. Math. (1955) 5:183–195Crossref, Google Scholar
• Dantzig G. B., et al., Hu T. C., Robinson S. M. On the need for a system (sic) optimization laboratory. Mathematical Programming (1973) (Academic Press, New York) . [See also, G. B. Dantzig. 1974. On the need for a systems optimization laboratory. R. W. Cottle, J. Krarup, eds. Optimisation Methods. The English Universities Press, London, UK.]Crossref, Google Scholar
• Dupacova J., Morton D. P. (2005) . George Dantzig (1914–2005) www. stoprog.org/GBD/GBDantzig.htmlGoogle Scholar
• Ferguson A., Dantzig G. B. The allocation of aircraft to routes—An example of linear programming under uncertain demand. Management Sci. (1956) 3:45–73Link, Google Scholar
• Fulkerson D. R., Dantzig G. B. Computations of maximal flows in networks. Naval Res. Logist. Quart. (1955) 2:277–283Crossref, Google Scholar
• Hitchcock F. L. The distribution of a product from several sources to numerous localities. J. Math. and Physics (1941) 20:224–230Crossref, Google Scholar
• Kantorovich L. V.Mathematical Methods in the Organization and Planning of Production (1939) (Publication House of the Leningrad State University, Leningrad, U.S.S.R.) 68[In Russian.] English translation (1960) in Management Sci. 6 366–422Google Scholar
• Koopmans T. C. Optimum utilization of the transportation system. Proc. Statist. Conferences (1947) 5(Washington, DC)Google Scholar
• Koopmans T. C.Activity Analysis of Production and Allocation (1951) (John Wiley and Sons, New York) . [The Introduction and contents of this book are available at http://cowles.econ.yale.edu/P/cm/m13.htm.]Google Scholar
• Leontief W.The Structure of the American Economy (1951) (Oxford University Press, New York) Google Scholar
• O’Connor J. J., Robertson E. F. (2005) . George B. Dantzig, www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Dantzig_George.htmlGoogle Scholar
• Reid C.Neyman—From Life (1982) (Springer-Verlag, New York) Crossref, Google Scholar
• White W., Johnson S., Dantzig G. B. Chemical equilibrium in complex mixtures. J. Chemical Physics (1958) 28:751–755Crossref, Google Scholar