Pivoting Rules for the Revised Simplex Algorithm

Nikolaos Ploskas, Nikolaos Samaras

Pricing is a significant step in the simplex algorithm where an improving non- basic variable is selected in order to enter the basis. This step is crucial and can dictate the total execution time. In this paper, we perform a computational study in which the pricing operation is computed with eight different pivoting rules: (i) Bland’s Rule, (ii) Dantzig’s Rule, (iii) Greatest Increment Method, (iv) Least Recently Considered Method, (v) Partial Pricing Rule, (vi) Queue Rule, (vii) Stack Rule, and (viii) Steepest Edge Rule; and incorporate them with the revised simplex algorithm. All pivoting rules have been implemented in MATLAB. The test sets used in the computational study are a set of randomly generated optimal sparse and dense LPs and a set of benchmark LPs (Netlib- optimal, Kennington, Netlib-infeasible).