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