Author ORCID Identifier
Document Type
Article
Publication Date
9-23-2017
Publication Title
Mathematical Methods of Operations Research
Volume
87
First Page
109
Last Page
137
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.
Recommended Citation
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.
Comments
This is a post-peer-review, pre-copyedit version of an article published in Mathematical Methods of Operations Research. The final authenticated version is available online at: https://doi.org/10.1007/s00186-017-0610-4.