Conformal vector fields on compact connected homogeneous Finsler manifolds

Let $(M,F)$ be a compact connected homogeneous non-Riemannian Finsler manifold with $\dim M>1$. We prove that any conformal vector field on $(M,F)$ is a Killing vector field. Further more, we prove that $\rho F$ is a homogeneous Finsler metric on $M$ if and only if $\rho$ is a positive constant function.