  We generalize and study the Zermelo navigation problem on Hermitian manifolds
in the presence of a perturbation $W$ determined by a mild complex velocity
vector field $||W(z)||_h<||u(z)||_h$, with application of complex Finsler
metric of complex Randers type. By admitting space-dependence of ship's
relative speed $||u(z)||_h\leq1$ we discuss the projectively related complex
Finsler metrics, the geodesics corresponding to the solutions of Zermelo's
problem, in particular the conformal case and the connections between the
corresponding background Hermitian metric $h$, new Hermitian metric $a$ and
resulting complex Randers metric $F$. Moreover, we present some necessary and
sufficient conditions for the obtained locally projectively flat solutions. Our
findings are also illustrated with several examples.
