The First Linear-Programming Shoppe

References

  • Bargmann V., Montgomery D., von Neumann J.Solution of Linear Systems of High Order (1946) (Institute of Advanced Studies, Princeton, NJ) Google Scholar
  • Bodington C. E., Baker T. E. A history of mathematical programming in the petroleum industry. Interfaces (1990) 20:117–127LinkGoogle Scholar
  • Brown G. W. Notes on the solution of linear systems involving inequalities. (1949) (The RAND Corporation, Santa Monica, CA) . Report P-78BGoogle Scholar
  • Brown G. W., Koopmans T. C. Iterative solution of games by fictitious play. Activity Analysis of Production and Allocation (1951) (John Wiley and Sons, New York) 374–376Google Scholar
  • Chancellor J., Sheldon J. W., Tatum G. L. The solution of simultaneous linear equations using the IBM cardprogrammed electronic calculator. Proc. Indust. Comput. Sem. (1950) (IBM, New York) 57–61Google Scholar
  • Charnes A., Cooper W. W., Mellon B. Blending aviation gasolines. Symp. Linear Inequalities Programming (1951) (Headquarters, U.S. Air Force, Washington, D.C.) Google Scholar
  • Crout P. D. A short method for evaluating determinants and solving systems of linear equations with real or complex coefficients, Marchant methods. (1941) (MM-182, Marchant Calculating Machine Co., Oakland, CA) Google Scholar
  • Dantzig G. B. Programming of inter-dependent activities II, mathematical model. (1949) . Also published in T. C. Koopmans, ed. Activity Analysis of Production and Allocation. John Wiley and Sons, New York, 1951, 19–32.Google Scholar
  • Dantzig G. B., Koopmans T. C. Maximization of a linear function of variables subject to linear inequalities. Activity Analysis of Production and Allocation (1951a) (John Wiley and Sons, New York) 339–347Google Scholar
  • Dantzig G. B., Koopmans T. C. Application of the simplex method to a game theory problem. Activity Analysis of Production and Allocation (1951b) (John Wiley and Sons, New York) 348–358Google Scholar
  • Dantzig G. B., Koopmans T. C. Application of the simplex method to a transportation problem. Activity Analysis of Production and Allocation (1951c) (John Wiley and Sons, New York) 359–373Google Scholar
  • Dantzig G. B. Concepts, origins, and use of linear programming. Report P-980. (1957) (The RAND Corporation, Santa Monica, CA) Google Scholar
  • Dantzig G. B.Linear Programming and Extensions (1963) (Princeton University Press, Princeton, NJ) CrossrefGoogle Scholar
  • Dantzig G. B. Impact of linear programming on computer development. OR/MS TODAY (1988) 15(Aug):12–17Google Scholar
  • Dantzig G. B., Orchard-Hays W. Alternate algorithm for the revised simplex method: Using a product form of the inverse. (1953) (The RAND Corporation, Santa Monica, CA) . RM-1268Google Scholar
  • Directorate of Management AnalysisProceedings of the Symposium on Linear Inequalities and Programming (1952) (Headquarters, U.S. Air Force, Washington, D.C.) Google Scholar
  • Directorate of Management AnalysisProc. Second Sympos. Linear Programming (1955) (Headquarters, U.S. Air Force, Washington, D.C.) Google Scholar
  • Eames C., Eames R., Fleck G.A Computer Perspective (1973) (Harvard University Press, Cambridge, MA) Google Scholar
  • Eisemann K. Linear programming. (1954) (IBM, New York) . Internal Report, Applied Science DivisionGoogle Scholar
  • Fox L. Practical methods for the solution of linear equations and the inversion of matrices. J. Royal Statist. Soc., Series B (1950) 12:120–136Google Scholar
  • Fox L., Huskey H. D., Wilkinson J. H. Notes on the solution of algebraic linear simultaneous equations. Quart. J. Mech. Appl. Math. (1948) 1:149–173CrossrefGoogle Scholar
  • Gainen L. Linear programming in bid evaluation. Proc. Second Sympos. Linear Programming (1955) 1(DC/S Comptroller, USAF, Washington, D.C.) 19–38Google Scholar
  • Gass S. I., Alt F. L. Recent advances in linear programming. Advances in Computers (1961) 2(Academic Press, New York) 259–377Google Scholar
  • Gass S. I.Linear Programming (1964) 2nd edition(McGraw-Hill, New York) Google Scholar
  • Gass S. I. Model world: In the beginning there was linear programming. Interfaces (1990) 20:128–132LinkGoogle Scholar
  • Gass S. I. Project Mercury's man-in-space real-time computer system: You have a go, at least seven orbits. IEEE Ann. History Comput. (1999) 21:37–48CrossrefGoogle Scholar
  • Gass S. I., Saaty T. L. The computational algorithm for the parametric objective function. Naval Res. Logist. Quart. (1955) 2:39–45CrossrefGoogle Scholar
  • Gass S. I., Zafra P. M. R. Modified fictitious play for solving matrix games and linear-programming problems. Comput. Oper Res. (1995) 22:893–903CrossrefGoogle Scholar
  • Gass S. I., Zafra P. M. R., Qiu Z. Modified fictitious play. Naval Res. Logist. Quart. (1996) 43:955–970CrossrefGoogle Scholar
  • Gill P. E., Murray W., Wright M. H.Practical Optimization (1981) (Academic Press, New York) Google Scholar
  • Gill P. E., Murray W., Wright M. H.Numerical Linear Algebra and Optimization (1991) (Addison Wesley, Reading, MA) Google Scholar
  • Goldstine H. M.The Computer from Pascal to von Neumann (1972) (Princeton University Press, Princeton, NJ) Google Scholar
  • Gruenberger F. The history of the JOHHNIAC. (1968) (The RAND Corporation, Santa Monica, CA) . Report RM-5654-PRGoogle Scholar
  • Hillier F. S., Lieberman G. J.Introduction to Operations Research (2001) 7th ed.(McGraw-Hill, New York) Google Scholar
  • Hoffman A. J., Jacobs W. W. Smooth patterns of production. Management Sci. (1954) 1:86–91LinkGoogle Scholar
  • Hotelling H. Some new methods in matrix calculations. Ann. Math. Statist. (1943) 14:1–34CrossrefGoogle Scholar
  • IEEE The top ten algorithms of the century. Supplement to. Comput. Sci. Engrg. (1943) 1:6Google Scholar
  • Jacobs W. W. Military applications of linear programming. Proceedings of the Second Symposium in Linear Programming (1955) (Headquarters, USAF, Washington, D.C.) 1–27Google Scholar
  • Koopmans T. C.Activity Analysis of Production and Allocation (1951) (John Wiley and Sons, New York) Google Scholar
  • Liggett I. G. Two applications of the IBM cardprogrammed electronic calculator. Proc. Indust. Comput. Seminar (1950) (IBM, New York) 62–65Google Scholar
  • Morgenstern O., Morgenstern O. Experiments and large scale computation in economics. Economic Activity Analysis (1954) (John Wiley and Sons, New York) 483–549Google Scholar
  • Motzkin T. S. New techniques for linear inequalities and optimization. Symposium on Linear Inequalities and Programming (1952) (Headquarters, U.S. Air Force, Washington, D.C.) Google Scholar
  • Motzkin T. S., Schoenberg I. J. The relaxation method for linear inequalities. Canadian J. Math. (1954) 6:393–404CrossrefGoogle Scholar
  • Motzkin T. S., Raiffa H., Thompson G. L., Thrall R. M., Kuhn H. W., Tucker A. W. The double description method. Contributions to the Theory of Games, Vol. II, Annals of Mathematics Study 28 (1953) (Princeton University Press, Princeton, NJ) 51–73CrossrefGoogle Scholar
  • Murphy F. H., Panchanadam V. Understanding linear programming modeling through an examination of the early years on model formulation. Oper. Res. (1999) 45:341–356LinkGoogle Scholar
  • National Bureau of Standards SEAC determines low bidders. Tech. News Bull. (1954) 38:179Google Scholar
  • Opler A. Some applications of the Monte Carlo method. Proc. Indust. Comput. Sem. (1950) (IBM, New York) 94–95Google Scholar
  • Orchard-Hays W. The RAND code for the simplex method. (1954) (The RAND Corporation, Santa Monica, CA) . RM1269Google Scholar
  • Orchard-Hays W. History of the development of LP solvers. Interfaces (1990) 20:61–73LinkGoogle Scholar
  • Orden A. Application of the simplex method to a variety of matrix problems. Sympos. Linear Inequalities Programming (1952a) (Headquarters, U.S. Air Force, Washington, D.C.) 28–55Google Scholar
  • Orden A. Solution of systems of linear inequalities on a digital computer. (1952b) (Headquarters, U.S. Air Force, Washington, D.C) . (Presented at the meeting of the Association for Computing Machinery, May 2, 1952, Pittsburgh, PA), Directorate of Management AnalysisGoogle Scholar
  • Orden A., Ralston A., Wilf H. S. Matrix inversion and related topics by direct methods. Mathematical Methods for Digital Computers (1960) (John Wiley and Sons, New York) 39–55Google Scholar
  • Orden A. LP from the '40s to the '90s. Interfaces (1993) 23:2–12LinkGoogle Scholar
  • Petrie G. W. Matrix inversion and solution of simultaneous algebraic equations with the IBM Type 604 electric calculating punch. Proc. Comput. Sem. (1951) (IBM, New York) 105–111Google Scholar
  • Pollack S. Optimization in linear programming. (1952) (National Bureau of Standards, Washington, D.C.) . Internal ReportGoogle Scholar
  • Riley V., Gass S. I.Linear Programming and Associated Techniques (1954) (Johns Hopkins University Press, Baltimore, MD) Google Scholar
  • Schell E. D. Project SCOOP. Systems for Modern Management (1953) xvii(5):7–835Google Scholar
  • Stanley E. D., Honig D. P., Gainen L. Linear programming in bid evaluation. Naval Res. Logist. Quart. (1954) 1:48–54CrossrefGoogle Scholar
  • Stiefel E. L.An Introduction to Numerical Mathematics (1963) (Academic Press, New York) Google Scholar
  • Stifler W. W.High-Speed Computing Devices (1950) (McGraw-Hill, New York) Google Scholar
  • Strang G.Linear Algebra and Its Applications (1988) 3rd ed.(Harcourt Brace Jovanovich, San Diego, CA) Google Scholar
  • Symonds G. H.Linear Programming: The Solution of Refinery Problems (1955) (Esso Standard Oil Co., New York) Google Scholar
  • Turing A. M. Rounding-off errors in matrix processes. Quart. J. of Mechanics Appl. Math. (1949) 1:287–308CrossrefGoogle Scholar
  • USAF The mathematical computation branch: Origins, functions, and facilities. (1953) (DCS/Comptroller, U.S. Air Force, Washington, D.C.) Google Scholar
  • von Neumann J., Goldstine H. H. Numerical inverting of matrices of high order. Bull. Amer. Math. Soc. (1947) 53:1021–1099CrossrefGoogle Scholar
  • Wagner H. M. Matrix inversion on an automatic calculator by row and column partition. (1953) (The RAND Corporation, Santa Monica, CA) . Report P-417Google Scholar
  • Washburn A. A new kind of fictitious play. Naval Res. Logist. Quart. (2001) 48:270–280CrossrefGoogle Scholar
  • Wood M. K., Dantzig G. B. Programming of interdependent activities I, general discussion. Project SCOOP Report Number 5. (1949) (Headquarters, U.S. Air Force, Washington, D.C.) 193–199Also published in T. C. Koopmans, ed. Activity Analysis of Production and Allocation. John Wiley and Sons, New York, 1951, 15, 18 and Econometrica 17(3&4) July-October, 1949Google Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.