Lower bounds for the maximum number of solutions generated by the simplex method

Kitahara and Mizuno 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 a paper by the authors 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 explain and prove the properties of the variant more precisely. We also show a new lower bound by using a simple example of LP.


Journal of the Operations Research Society of Japan, vol. 54, no.4, December 2011, pp. 191--200.