The infinite horizon non-stationary stochastic multi-echelon inventory problem and near-myopic policies

A dynamic multi-echelon inventory problem with nonstationary demands is studied in this paper. It is known that in the single-location nonstationary inventory problem, near-myopic policies are sufficiently close to the optimal one in cost. We show that this property also holds for the multi-echelon inventory problem. In order to show this, we derive error bounds of the near-myopic policies for the optimal one and evaluate them with a number of numerical experiments. On the other hand, we pay attention to weak ergodicity of inventory processes under base-stock policies, and find that weak ergodicity makes the error bounds of the near-myopic policies much tighter.