Bland rule

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This is for pivot selection in the simplex method to avoid cycling:

  • If more than one (nonbasic) column has a negative (for minimization) reduced cost, choose the one with lowest index.
  • If more than one (basic) column has the same determining value to leave the basis, select the one with the lowest index.

Beale's example of cycling shows that Bland's Rule must apply to all candidates for entering the basis, not just those with most negative reduced cost, see the supplement on cycling. The fifth tableau is the first time Bland's Rule is needed to break the cycle. Variable LaTeX: x_1 is chosen to enter the basis rather than LaTeX: x_5.

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