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The double pivot simplex method

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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.

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Authors and Affiliations

  1. Department of Industrial and Manufacturing Systems Engineering, Kansas State University, 2061 Rathbone Hall, Manhattan, KS, 66506, USA

    Fabio Vitor & Todd Easton

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  1. Fabio Vitor
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  2. Todd Easton
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Correspondence to Fabio Vitor.

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Vitor, F., Easton, T. The double pivot simplex method. Math Meth Oper Res 87, 109–137 (2018). https://doi.org/10.1007/s00186-017-0610-4

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