# Tolerance approach

This is an approach to sensitivity analysis in linear programming that expresses the common range that parameters can change while preserving the character of the solution. In particular, suppose $LaTeX: B$ is an optimal basis and rim data changes by $LaTeX: (Db, Dc).$ The tolerance for this is the maximum value of $LaTeX: t$ for which $LaTeX: B$ remains optimal as long as $LaTeX: \textstyle |Db_i| \le t$ for all $LaTeX: i$ and $LaTeX: \textstyle |Dc_j| \le t$ for all $LaTeX: j.$ The tolerance for the basis, $LaTeX: B,$ can be computed by simple linear algebra, using tableau information.