On the number of solutions generated by the dual simplex method

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On the number of solutions generated by the dual simplex method

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Lower Bounds for the Maximum Number of Solutions Generated by the Simplex Method

Kitahara and Mizuno [3] get upper bounds for the maximum number of different basic feasible solutions generated by Dantzig’s simplex method. In this paper, we obtain lower bounds of the maximum number. Part of the results in this paper are shown in Kitahara and Mizuno [4] as a quick report without proof. They present a simple variant of Klee-Minty’s LP and get a lower bound. In this paper, we e...

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A bound for the number of different basic solutions generated by the simplex method

In this short paper, we give an upper bound for the number of different basic feasible solutions generated by the simplex method for linear programming problems having optimal solutions. The bound is polynomial of the number of constraints, the number of variables, and the ratio between the minimum and the maximum values of all the positive elements of primal basic feasible solutions. When the ...

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ژورنال

عنوان ژورنال: Operations Research Letters

سال: 2012

ISSN: 0167-6377

DOI: 10.1016/j.orl.2012.01.004