On the shortage control in a continuous review (Q, r) inventory policy using α<inf>l</inf>service-level

<jats:p>Popular measures of product availability in inventory systems seek to control different aspects of stock shortages. However, none of them simultaneously control all aspects of shortages, because stock shortages in inventory systems are complex random events. This paper analyzes the performance of<jats:italic>α</jats:italic><jats:sub><jats:italic>L</jats:italic></jats:sub>service measure, defined as the probability that stockouts do not occur during a replenishment cycle, to cover different aspects of stock shortages when used to design an optimal continuous review (<jats:italic>Q</jats:italic>,<jats:italic>r</jats:italic>) policy. We show that explicitly controlling the frequency of replenishment cycle stockouts, using the<jats:italic>α<jats:sub>L</jats:sub></jats:italic>service-level, allows to implicitly control the size of the stockouts at an arbitrary time, the size of accumulated backorders at an arbitrary time, and the duration of the replenishment cycle stockouts. However, the cost of controlling the frequency of replenishment cycle stockouts is greater than the cost of controlling the size of stockouts and the duration of the replenishment cycle stockouts.</jats:p>