On the number of solutions generated by Dantzig's simplex method for LP with bounded variables

Tomonari Kitahara, Tomomi Matsui, Shinji Mizuno

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We give an upper bound for the number of different basic feasible solutions generated by Dantzig's simplex method (the simplex method with the most negative pivoting rule) for LP with bounded variables by extending the result of Kitahara and Mizuno (2010). We refine the analysis by them and improve an upper bound for a standard form of LP. Then we utilize the improved bound for an LP with bounded variables. We apply our bound to the minimum cost flow problem and the maximum flow problem, and we obtain new results of bounds for Dantzig's simplex method.

Original languageEnglish
Pages (from-to)447-455
Number of pages9
JournalPacific Journal of Optimization
Volume8
Issue number3
Publication statusPublished - Jul 1 2012

Fingerprint

Simplex Method
Number of Solutions
Upper bound
Minimum Cost Flow
Costs
Maximum Flow
Scientific notation
Pivoting

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

Cite this

On the number of solutions generated by Dantzig's simplex method for LP with bounded variables. / Kitahara, Tomonari; Matsui, Tomomi; Mizuno, Shinji.

In: Pacific Journal of Optimization, Vol. 8, No. 3, 01.07.2012, p. 447-455.

Research output: Contribution to journalArticle

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