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.

Fuzzy modeling approach to on-hand stock levels estimation in (R, S) inventory system with lost sales

“…As can be seen, the proposed fuzzy method properly estimates the fill rate in all the cases, even when the fill rate level is lower than 90%. Normally, approximations in the literature present good performance when the fill rate is high (see Cardós et al, 2017). This behaviour is logical due to the fact that, with high levels of fill rate, the system satisfies almost all the demand so the number of stockouts are low.…”

“…The difficulty of this expression is that it requires a huge computational effort (especially for high levels of S) which also hinders its implementation in practical environments. In the literature we find other works (Babiloni, Cardós & Guijarro-Tarradellas, 2011;Bijvank & Johansen, 2012;Cardós, Guijarro & Babiloni, 2017) that propose different approximations to calculate the on-hand stock levels in the lost sales context, however, none of them introduces the uncertainty of the demand in the model. To overcome these drawbacks, this paper proposes the application of fuzzy set techniques on the on-hand stock estimation that introduce the uncertainty of the demand and dramatically reduce computational efforts.…”

“…However, these approaches may incur some risks when they are used to determine the base-stock levels. As is detailed explained by (Cardós et al, 2017), some of them can lead to an increase of the stock level and, consequently, of holding costs, whereas other approaches can underestimate the base-stock level which implies that the target fill rate is not achieved and the system is actually less protected against stockout occasions than might be expected.…”

Exploring the nonlinear dynamics of the lost-sales order-up-to policy

“…Interestingly, Karlin and Scarf (1958) showed that the optimal reorder quantity with backlogs can be derived from a single number (the sum of inventory-on-hand and on-order), but in the lost-sales systems this quantity is a relatively complex function of the on-hand inventory as well as the timing and quantity of all outstanding orders. Since then, several works have mined this research vein, searching for (near-)optimal inventory policies and deriving bounds of optimal order quantities under various cost assumptions; including Morton (1969), Johansen (2001), Chen, Ray, and Song (2006), Bijvank and Vis (2012), Johansen (2013), Goldberg et al (2016), Cardós, Guijarro, andBabiloni (2017) and Godichaud and Amodeo (2019). We refer readers to Bijvank and Vis (2011) for a detailed literature review of replenishment policies for lost-sales systems.…”

Spare parts demand forecasting: a review on bootstrapping methods

“…Two service level measures have been considered in the bootstrapping inventory literature: the cycle service level and the fill rate (e.g. Dolgui and Pashkevich 2005;Porras and Dekker 2008;Syntetos and Boylan 2008;Teunter and Duncan 2009;Babai, Syntetos, and Teunter 2010;Syntetos, Babai, and Altay 2012;Syntetos, Babai, and Gardner 2015;Cardos, Guijarro, and Babiloni 2017). However, the cycle service level is the most used service measure in the literature.…”