Surplus variable
= Surplus variable
{title2=$z=a^Tx-b\ge0$}
A surplus variable converts a lower-bound inequality $a^Tx\ge b$ into $a^Tx-z=b$, with $z\ge0$. This is the lower-bound counterpart of a <slack variable>. When the original coefficients, right-hand side and decision variables are integer, the surplus variable is integer as well; that fact permits it to appear in an all-integer <Gomory fractional cut> row.