A periodic review replenishment model with a refined delivery scenario

This paper considers a single-item replenishment problem where every n periods the buyer plans for the quantity delivered for each upcoming period. Assuming that demand not filled immediately is backlogged, we suggest that the quantity delivered in the immediately upcoming period be of any size and the quantity delivered in each of the subsequent (n-1) periods be equal to or smaller than a fixed quantity Q. We derive the average cost per n periods and compute the optimal order-up-to level for the proposed replenishment policy. Next, assuming a fixed cost for reviewing inventory and planning deliveries, we obtain the optimal n by minimizing the expected cost per period. Finally, the optimal Q can also be determined. The proposed periodic review policy is easy to implement.