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An upper bound for the number of different solutions generated by the primal simplex method with any selection rule of entering variables

Tomonari Kitahara (kitahara.t.ab***at***m.titech.ac.jp)
Shinji Mizuno (mizuno.s.ab***at***m.titech.ac.jp)

Abstract: Kitahara and Mizuno (2011a) obtained an upper bound for the number of different solutions generated by the primal simplex method with Dantzig's (the most negative) pivoting rule. In this paper, we obtain an upper bound with any pivoting rule which chooses an entering variable whose reduced cost is negative at each iteration. The bound is applied to special linear programming problems. We also get a similar bound for the dual simplex method.

Keywords: Linear programming; the number of basic solutions; pivoting rule; the simplex method.

Category 1: Linear, Cone and Semidefinite Programming (Linear Programming )

Citation: To appear in Asia-Pacific Journal of Operational Research (APJOR)

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Entry Submitted: 02/15/2012
Entry Accepted: 02/15/2012
Entry Last Modified: 05/08/2012

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