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

Tomonari Kitahara, Shinji Mizuno

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3 Citations (Scopus)

Abstract

Recently, Kitahara, and Mizuno derived 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 upper bound is applied to a linear programming problem with a totally unimodular matrix. We also obtain a similar upper bound for the dual simplex method.

Original languageEnglish
Article number1340012
JournalAsia-Pacific Journal of Operational Research
Volume30
Issue number3
DOIs
Publication statusPublished - Jun 1 2013
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Management Science and Operations Research

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