Abstract
George Dantzig is known as the ‘father of linear programming’ and the ‘inventor of the simplex method: Employed at the Pentagon (the US government’s defence establishment) in 1947 and motivated to ‘mechanize’ programming in large time-staged planning problems, George Dantzig gave a general statement of what is now known as a linear program, and invented an algorithm, the simplex method, for solving such optimization problems. By the force of Dantzig’s theory, algorithms, practice, and professional interaction, linear programming flourished. Linear programming has had an impact on economics, engineering, statistics, finance, transportation, manufacturing, management, and mathematics and computer science, among other fields. The list of industrial activities whose practice is affected by linear programming is very long.
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Selected works
1947. Prospectus for the AAF electronic computer. Unpublished manuscript.
1948a. A theorem on linear inequalities. Unpublished manuscript, 5 January.
1948b. Programming in a linear structure. Washington, DC: Comptroller, USAR February. Abstract in Econometrica 17(1949), 73–4.
1951. Application of the simplex method to a transportation problem. In Activity Analysis of Production and Allocation, ed. T.C. Koopmans. New York: John Wiley & Sons.
1951. (With A. Wald.) On the fundamental lemma of Neyman and Pearson. Annals of Mathematical Statistics 22, 87–93.
1954. (With D.R. Fulkerson.) Minimizing the number of tankers to meet a fixed schedule. Naval Research Logistics Quarterly 1, 217–22.
1954. (With D.R. Fulkerson and S.M. Johnson.) Solution of a large scale traveling-salesman problem. Journal of Operations Research Society of America 2, 393–410.
1954. (With W Orchard-Hays.) The product form for the inverse in the simplex method. Mathematical Tables and Other Aids to Computation 8, 64–7.
1955a. Upper bounds, secondary constraints, and block triangularity in linear programming. Econometrica 23, 174–83.
1955b. Linear programming under uncertainty. Management Science 1, 197–206.
1955. (With A.R. Fergusson.) The problem of routing aircraft. Aeronautical Engineering Review 14(4), 51–5. RAND Research Memorandum RM 1369, 1954.
1955. (With D.R. Fulkerson.) Computation of maximal flows in networks. Naval Research Logistics Quarterly 2, 277–83.
1955. (With A. Orden, A. and P. Wolfe.) The generalized simplex method for minimizing a linear form under linear inequality restraints. Pacific Journal of Mathematics 5(2), 183–195. RAND Research Memorandum RM–1264, 1954.
1956. Recent advances in linear programming. Management Science 2, 131–44.
1956. (With L.R. Ford, Jr. and D.R. Fulkerson.) A primal-dual algorithm for linear programs. In Linear Inequalities and Related Systems, Annals of Mathematics Study No. 38, ed. H.W Kuhn and A.W Tucker. Princeton, NJ: Princeton University Press.
1957. Discrete variable extremum problems. Operations Research 5, 226–77.
1960a. On the shortest route through a network. Management Science 6, 187–90. RAND memorandum P-1345, 1959.
1960b. On the significance of solving linear programming problems with some integer variables. Econometrica 28, 30–44.
1960. (With P. Wolfe.) Decomposition principle for linear programs. Operations Research 8, 101–11.
1961. (With A. Madansky.) On the solution of two-stage linear programs under uncertainty. In Proceedings, Fourth Berkeley Symposium on Mathematical Statistics and Probability, I, ed. J. Neyman. Berkeley University of California Press. RAND memorandum P–2039, 1960.
1961. (With P. Wolfe.) The decomposition algorithm for linear programming. Econometrica 29, 767–78.
1963. Linear Programming and Extensions. Princeton, NJ: Princeton University Press.
1968. Large-scale linear planning. In Mathematics of the Decision Sciences, vol. 1, ed. G.B. Dantzig and A.F. Veinott, Jr. Providence, RI: American Mathematical Society.
1968. (With R.W Cottle.) Complementary pivot theory of mathematical programming. Linear Algebra and its Applications 1, 103–25.
1973. (With others.) On the need for a System Optimization Laboratory. In Mathematical Programming, ed. T.C. Hu and S.M. Robinson. New York: Academic Press.
1982. Reminiscences about the origins of linear programming. Operations Research Letters 1(2), 43–48.
1990. (With P.W Glynn.) Parallel processors for planning under uncertainty. Annals of Operations Research 22, 1–21.
1991. Linear programming. In History of Mathematical Programming: A Collection of Personal Reminiscences, ed. J.K. Lenstra, A.H.G. Rinnooy Kan and A. Schrijver. Amsterdam: North-Holland.
1992. (With G. Infanger.) Large-scale stochastic linear programs: importance sampling and Benders decomposition. In Computational and Applied Mathematics I - Algorithms and Theory, Proceedings of the 13th IMACS World Congress, ed. C. Brezinski and U. Kulisch. Amsterdam: North-Holland.
1997. (With M.N. Thapa.) Linear Programming, 1. Introduction. New York: Springer.
2003. (With M.N. Thapa.) Linear Programming 2: Theory and Extensions. New York: Springer.
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Cotile, R.W., Eaves, B.C., Thapa, M.N. (2008). Dantzig, George B. (1914–2005). In: Durlauf, S.N., Blume, L.E. (eds) The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1007/978-1-349-58802-2_355
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