  By combining the algebraic Bethe ansatz and the off-diagonal Bethe ansatz, we
investigate the trigonometric SU(3) model with generic open boundaries. The
eigenvalues of the transfer matrix are given in terms of an inhomogeneous T-Q
relation, and the corresponding eigenstates are expressed in terms of nested
Bethe-type eigenstates which have well-defined homogeneous limit. This exact
solution provides a basis for further analyzing the thermodynamic properties
and correlation functions of the anisotropic models associated with higher rank
algebras.
