Inventory policies for all-or-nothing demand processes

When there is insufficient stock to meet a specific customer order, a common assumption is that the remaining stock will be used to satisfy the order partially while the balance of the order is backordered or lost – this is the ‘partial backorder’ or ‘partial lost sales’ assumption. In this paper we consider what happens when the nature of the demand process is such that orders must be met in full or not at all – this is the ‘all-or-nothing’ demand assumption. We concentrate, for the purpose of illustration, on the context of a continuous review model, with a Poisson customer arrival rate, with a fixed lead time and for which not more than one replenishment order may be outstanding at any time.