On the estimation of on-hand stocks for base-stock policies and lost sales systems and its impact on service measures

Abstract

This paper focuses on computing on-hand stock levels at the beginning of a replenishment cycle for a lost sales inventory system with periodic reviews and discrete demand. A base-stock policy is used for replenishments. The literature provides an Exact method which requires a huge computational effort, and two closed-form approximate methods that arise from the backordering case, the Non-stockout and the Bijvank & Johansen. In this paper we propose three new and closed-form approaches that explicitly consider the lost sales assumptions: the Adjusted Non-stockout, the Polar Opposite and the 1-Step methods. Existing and proposed methods are evaluated in terms of their accuracy when computing the cycle service level and the fill rate. In this sense, results show that the Bijvank & Johansen and 1-Step methods provide similar performance but present different behaviours in terms of under or over estimating service measures that have different implications on the design of stock policies.

Keywords:

• inventory
• periodic review
• lost sales
• on-hand stock
• discrete demand

Acknowledgements

We gratefully acknowledge the help of Dr. John Boylan, University of Lancaster, and Dr. Marco Bijvank, University of Calgary, for providing useful comments and feedback to help improve this work. We also express our gratitude to the anonymous referees of this paper whose comments really have contributed to improve the quality of our work. All errors remain ours.