A periodic-review inventory model in a fluctuating environment

We study a single-item periodic-review inventory model in a fluctuating environment with a fixed lead time of λ periods. The state of the environment at the beginning of each period is described by a homogeneous Markov chain. Ordering, holding, penalty costs and the distributions of random variables representing the customer's demand and the supplier's capacity level are state environment dependent. By using dynamic programming it is proved in the finite-horizon case that the optimal policy is of a base stock type. Its parameters are monotonic in the number of the periods making up the horizon and also in stochastically ordered random variables representing different supplier capacities. Similar results are proved for the infinite-horizon problem.