Abstract: In this paper we consider the homogenization of Non-homogneous Markov decision model with expected total reward criterion.denumerable state space and finite action spaces. We translate the non-homogeneous Markov decision processes into a homegeneous one by the method of extanding state space which is different from the usual one, and then we easily obtain the mail results obtained by usual method. Specially, the mail results obtained by K. Hinderer.

Key words: Markov decision processes, Non-homogeneous, Homogenization, Optimal policies