A dynamic analysis of the single-item periodic stochastic inventory system with order capacity

Consider a single-item periodic review stochastic inventory system with positive setup cost and finite order capacity. Chen and Lambrecht showed that the optimal policy has a systematic pattern called the X–Y band structure. However there is no clear pattern for inventory positions between X and Y. Some properties of the optimal order policy are provided when the inventory position falls between X and Y. As a consequence of the analysis, an efficient algorithm is provided to compute the optimal ordering policy parameters.