Surplus variable ($z=a^{T}x-b\ge 0$)

A surplus variable converts a lower-bound inequality $a^{T}x\ge b$ into $a^{T}x-z=b$, with $z\ge 0$. 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.