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Linear Programming pp 23–47Cite as

The Simplex Algorithm

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Part of the book series: Modern Birkhäuser Classics ((MBC))

Abstract

Designed in 1947 by G. Dantzig, the Simplex Algorithm was the method of choice used to solve linear programs for decades. Though not a polynomial-time algorithm in the worst case, the Simplex Algorithm is remarkably fast in practice. Problems with thousands of variables and constraints are routinely solved by the Simplex Algorithm. Only since the appearance of Karmarkar’s Algorithm in 1984 and the more recent interior-point methods have contenders for “best practical linear programming algorithm” existed.

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Bibliography

  1. I. Adler, “The Expected Number of Pivots Needed to Solve Parametric Linear Programs and the Efficiency of the Self-Dual Simplex Method,” manuscript, Dept. of Industrial Engineering and Operations Research, University of California, Berkeley, 1983.

    Google Scholar 

  2. I. Adler, R. M. Karp and R. Shamir, “A Family of Simplex Variants Solving an m x d Linear Program in Expected Number of Pivots Depending on d Only,” Mathematics of Operations Research 11 (1986), 570-590.

    Article  MATH  MathSciNet  Google Scholar 

  3. I. Adler, R. M. Karp and R. Shamir, “A Simplex Variant Solving an m X d Linear Program in O (min(m 2, d 2)) Expected Number of Pivot Steps,” Journal of Complexity 3 (1987), 372-387.

    Article  MATH  MathSciNet  Google Scholar 

  4. I. Adler and N. Megiddo, “A Simplex Algorithm Whose Average Number of Steps is Bounded Between Two Quadratic Functions of the Smaller Dimension,” Journal of the ACM 32 (1985), 871-895.

    Article  MATH  MathSciNet  Google Scholar 

  5. D. Avis and V. Chvátal, “Notes on Bland’s Pivoting Rule,” Mathematical Programming Study 8 (1978), 24-34.

    Google Scholar 

  6. R. G. Bland, “New Finite Pivoting Rules for the Simplex Method,” Mathematics of Operations Research 2 (1977), 103-107.

    Article  MATH  MathSciNet  Google Scholar 

  7. K. H. Borgwardt, The Simplex Method: A Probabilistic Analysis, Springer-Verlag, New York, NY, 1987.

    MATH  Google Scholar 

  8. G. Brassard and P. Bratley, Algorithmics: Theory and Practice, Prentice Hall, Englewood Cliffs, NJ, 1988.

    MATH  Google Scholar 

  9. J. E. Calvert and W. L. Voxman, Linear Programming, Harcourt Brace Jovanovich, New York, NY, 1989.

    Google Scholar 

  10. V. Chvátal, Linear Programming, Freeman, New York, NY, 1983.

    MATH  Google Scholar 

  11. G. B. Dantzig, Linear Programming and Extensions, Princeton University Press, Princeton, NJ, 1963.

    MATH  Google Scholar 

  12. S. I. Gass, Linear Programming Methods and Applications, fourth edition, McGraw-Hill, New York, NY, 1975.

    MATH  Google Scholar 

  13. A. M. Glicksman, An Introduction to Linear Programming and the Theory of Games, Wiley, New York, NY, 1963.

    MATH  Google Scholar 

  14. G. Hadley, Linear Programming, Addison-Wesley, Reading, MA, 1962.

    MATH  Google Scholar 

  15. A. J. Hoffman, “Cycling in the Simplex Algorithm,” Report No. 2974, National Bureau of Standards, Washington, DC, 1953.

    Google Scholar 

  16. R. G. Jeroslow, “The Simplex Algorithm with the Pivot Rule of Maximizing Criterion Improvement,” Discrete Mathematics 4 (1973), 367-377.

    Article  MATH  MathSciNet  Google Scholar 

  17. L. G. Khachiyan, “A Polynomial Algorithm for Linear Programming” (in Russian), Doklady Akademiia Nauk USSR 244 (1979), 1093-1096. A translation appears in Soviet Mathematics Doklady 20 (1979), 191-194.

    MATH  MathSciNet  Google Scholar 

  18. V. Klee and G. J. Minty, “How Good is the Simplex Algorithm?”, in Inequalities-III, 0. Shisha, ed., Academic Press, New York, NY, 1972, 159-175.

    Google Scholar 

  19. H. W. Kuhn, class notes, Princeton University, Princeton, NJ, 1976.

    Google Scholar 

  20. C. H. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity, Prentice Hall, Engle-wood Cliffs, NJ, 1982.

    MATH  Google Scholar 

  21. R. Shamir, “The Efficiency of the Simplex Method: A Survey,” Management Science 33 (1987), 301-334.

    Article  MATH  MathSciNet  Google Scholar 

  22. M. Simonnard, Linear Programming, Prentice Hall, Engle-wood Cliffs, NJ, 1966.

    MATH  Google Scholar 

  23. S. Smale, “The Problem of the Average Speed of the Simplex Method,” in Mathematical Programming: The State of the Art (Bonn 1982), A. Bachem et al., eds., Springer-Verlag, Berlin, 1983, 530-539.

    Google Scholar 

  24. S. Smale, “On the Average Number of Steps in the Simplex Method of Linear Programming,” Mathematical Programming 27 (1983), 241-262.

    Article  MATH  MathSciNet  Google Scholar 

  25. G. Strang, Linear Algebra and Its Applications, third edition, Harcourt Brace Jovanovich, San Diego, CA, 1988.

    Google Scholar 

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Author information

Authors and Affiliations

  1. College of Computing, Georgia Tech, Atlanta, GA, 30332, USA

    Howard Karloff

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  1. Howard Karloff
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© 2009 Birkhäuser Boston, a part of Springer Science+Business Media, LLC

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Karloff, H. (2009). The Simplex Algorithm. In: Linear Programming. Modern Birkhäuser Classics. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4844-2_2

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  • DOI: https://doi.org/10.1007/978-0-8176-4844-2_2

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-0-8176-4843-5

  • Online ISBN: 978-0-8176-4844-2

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