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Simplex-type algorithms perform successive pivoting operations (or iterations) in order to reach the optimal solution. The choice of the pivot element at each iteration is one of the most critical steps in simplex-type algorithms. The flexibility of the entering and leaving variable selection allows to develop various pivoting rules. This chapter presents six pivoting rules used in each iteration of the simplex algorithm to determine the entering variable: (i) Bland’s rule, (ii) Dantzig’s rule, (iii) Greatest Increment Method, (iv) Least Recently Considered Method, (v) Partial Pricing rule, and (vi) Steepest Edge rule. Each technique is presented with: (i) its mathematical formulation, (ii) a thorough numerical example, and (iii) its implementation in MATLAB. Finally, a computational study is performed. The aim of the computational study is twofold: (i) compare the execution time of the presented pivoting rules, and (ii) highlight the impact of the choice of the pivoting rule in the number of iterations and the execution time of the revised simplex algorithm.
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