The one-for-one (S-1,S) inventory policy, which calls for a replenishment order after each demand equal in magnitude to the size of the demand, is often advocated for controlling the stock levels of expensive, slow-moving items. In particular, this policy has frequently been promoted for use in recoverable-item inventory systems. An important managerial question is: When is the (S-1,S) policy optimal? Results in this article provide guidance for the selection of this policy. Conditions under which it is not economical to batch demands are developed, provided the renewal function of the renewal process of demand sizes is concave. This includes the important case of unit-sized demands. The inventory system considered is one with continuous review, constant lead times, general interarrival and discrete demand distributions, complete backlogging, and linear holding and penalty costs per unit per unit time. Examples are given for the special case when the demand process is Poisson and when the demand process is a particular compound Poisson distribution known as the stuttering Poisson distribution.
