The Kondo lattice model and its SU(N) generalization have been the standard minimal models to understand the physics of the so-called heavy-fermion systems. Recent advances in experiments of ultra-cold alkaline-earth fermi gases paves a way to the experimental exploration of SU(N) "heavy fermion" physics. In this talk, I will discuss the phase diagram of the one-dimensional SU(N) Kondo lattice model with the local moments in the N-dimensional defining representation (an SU(N) generalization of spin-1/2). Specifically, I will rigorously show that when the Kondo coupling is large enough (whether positive or negative), ferromagnetic metal is stabilized in a finite window of the fermion filling. I will also discuss the emergence of supersymmetry SU(N|1) in a generalized Kondo lattice model and its physical implication.