This paper is on the analysis of a single product, periodic review 
inventory model, where the distributions of demands vary with the 
state of the environment variable. The state of the environment is 
assumed to follow a discrete-time Markov chain. The optimal inventory 
policy to minimize the total  discounted expected cost is derived via 
dynamic programming. For the finite-horizon model, we show that an 
environmental-dependent base-stock policy is optimal, and derive some 
characteristics of the optimal policy. Under additional conditions, 
we further derive the monotonicity of the optimal policy.