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The double pivot simplex method

Author

Listed:
  • Fabio Vitor

    (Kansas State University)

  • Todd Easton

    (Kansas State University)

Abstract

The simplex method, created by George Dantzig, optimally solves a linear program by pivoting. Dantzig’s pivots move from a basic feasible solution to a different basic feasible solution by exchanging exactly one basic variable with a nonbasic variable. This paper introduces the double pivot simplex method, which can transition between basic feasible solutions using two variables instead of one. Double pivots are performed by identifying the optimal basis in a two variable linear program using a new method called the slope algorithm. The slope algorithm is fast and allows an iteration of DPSM to have the same theoretical running time as an iteration of the simplex method. Computational experiments demonstrate that DPSM decreases the average number of pivots by approximately 41% on a small set of benchmark instances.

Suggested Citation

  • Fabio Vitor & Todd Easton, 2018. "The double pivot simplex method," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(1), pages 109-137, February.
    • Handle: RePEc:spr:mathme:v:87:y:2018:i:1:d:10.1007_s00186-017-0610-4
    DOI: 10.1007/s00186-017-0610-4
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    Cited by:

    1. Fabio Vitor & Todd Easton, 2022. "Projected orthogonal vectors in two-dimensional search interior point algorithms for linear programming," Computational Optimization and Applications, Springer, vol. 83(1), pages 211-246, September.

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