||A well known stochastic extension of the classical economic order quantity (EOQ) inventory model bases the reorder decision on the stock level. When lead times are stochastic and independently distributed, it is not always possible to establish that there is at most one outstanding order. Consideration is presented of a continuous deterministic-demand, stochastic lead-time inventory model such that the individual unit demands are non-interchangeable. Equations are derived that define the optimal values of the 2 decision variables: 1. order size, and 2. timing. This model is demonstrated to be a stochastic lead-time generalization of the EOQ model with backlogging of demand. An illustrative example is included. A lower bound which is independent of the order size is derived for the optimal ordering time. Figure.