On the shortage control in a continuous review (Q, r) inventory policy using α_L service-level

Department of Industrial Engineering, Universidad Técnica Federico Santa María, Avenida Españ 1680, Valparaíso, Chile

^* Corresponding author: pablo.escalona@usm.cl

Received: 30 June 2020
Accepted: 14 August 2021

Abstract

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 α_L 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 (Q, r) policy. We show that explicitly controlling the frequency of replenishment cycle stockouts, using the α_L 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.