This paper develops a general [>Q, r) single item model, based on the usual assumptions of stationary, normally distributed probabilistic demand, but covering simultaneously all three types of shortage costs commonly dealt with in the literature; namely shortage costs proportional to the number of units short and to the duration of the shortage, or proportional to the number of units short, or proportional to the number of stockout occasions. The model considers that the item stocked is subject to throe different uses, each being linked with the different type of shortage cost.