A Periodic-Review Base-Stock Inventory System with Sales Rejection

We consider a system in which an order is placed every T periods to bring the inventory position up to the base stock S. We accept demand until the inventory position reaches a sales rejection threshold M. Our objective is to find the optimal values of S and M that minimize the long-run average cost per period. We establish the stationary distribution of our system and develop structural properties of the optimal solution that facilitate computation. In particular, we show that in an optimal solution, the optimal value of M is nonnegative under some reasonable conditions. Hence, in our model a mixture of backorders and lost sales may occur. Additionally, we compare our system against traditional systems in which demand during stockouts is either fully backordered or lost.