Estimating the reorder point for a fill-rate target under a continuous review policy in the presence of non-standard lead-time demand distributions

Skewed and multimodal lead-time demand (LTD) distributions can be present in supply chains. Under these conditions, logistics managers find that conventional approaches, which assume standard LTD distribution shapes, yield unreliable estimates of a single item's reorder point (ROP) in relation to meeting fill-rate targets under a continuous review inventory policy. Furthermore, logistics managers have limited data available from which to determine the true shape of the underlying LTD distribution. In this study, I present a non-parametric bootstrap approach to set a least-biased estimate of the ROP. In addition, to deriving bootstrap expressions for non-standard LTD shapes, I derive expressions for standard distribution shapes to estimate the ROP across a range of fill rates. Thus, eliminating the double counting of stockouts with conventional fill-rate measures. Using Monte Carlo simulation experiments, I show that in comparison to the conventional state-of-the-art approaches the non-parametric bootstrap approach yields the least biased ROP estimates robust to both the shape of the LTD distribution and the sample size. This research offers more accurate ROP estimators, which can serve as a basis for expanding the scope of future inventory management research and enabling logistics managers to reduce inventory while maintaining and even improving fill rates.