The double pivot simplex method

Fabio Vitor () and Todd Easton ()
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Fabio Vitor: Kansas State University
Todd Easton: Kansas State University

Mathematical Methods of Operations Research, 2018, vol. 87, issue 1, No 5, 109-137

Abstract: 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.

Keywords: Linear programming; Simplex method; Block pivots; Multiple pivots; Double pivots; 90C05; 90C49 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00186-017-0610-4

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