AN UPPER BOUND FOR THE NUMBER OF DIFFERENT SOLUTIONS GENERATED BY THE PRIMAL SIMPLEX METHOD WITH ANY SELECTION RULE OF ENTERING VARIABLES

作者：Kitahara Tomonari^*; Mizuno Shinji

来源：Asia Pacific Journal of Operational Research, 2013, 30(3): 1340012.

DOI：10.1142/S0217595913400125

• Linear programming
• the number of basic solutions
• pivoting rule
• the simplex method

Recently, Kitahara, and Mizuno derived an upper bound for the number of different solutions generated by the primal simplex method with Dantzig%26apos;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.

• 出版日期2013-6