Exact Computation of Optimal Inventory Policies Over an Unbounded Horizon

An inventory scheduling model with forbidden time intervals is analyzed. The objective is to minimize the long-term average cost per time unit. Unlike most of the literature on inventory theory, no restrictive assumptions are made a priori about the nature of optimal solutions. Rather it is proved that optimal policies exist, and that some of them are cyclic with cycles of a particular structure. It is then shown that such optimal policies can be computed and an algorithm is given.