Order Crossover Research: A 60‐Year Retrospective to Highlight Future Research Opportunities

Abstract

We review the literature spanning 60 years of efforts to model the phenomenon of order crossover. The importance of this research has increased due to today's longer ocean supply chains, with their greater inherent uncertainty. The incidence of order crossover is higher in these supply chains, and ignoring it will result in overestimation of safety stock. The literature is grouped into four areas, which are described separately, and is mapped to reveal gaps. Gaps exist for combinations of lead time distributions, demand distributions, and inventory policies where extant methods do not address order crossover. The effective lead time approach has proven flexible enough to be used in a wide range of periodic review situations. However, our results show that its accuracy is undermined by bimodal skewed lead-time distributions, especially when lower bounds are nonzero. Future research needs to concentrate on exploring nonparametric methods or similar methods robust to different lead time distribution assumptions to provide a method of setting safety stock in “real world” situations where orders cross.

A nonparametric approach for setting safety stock levels

“…Second, compound-distribution approaches typically assume that LTD distributions follow standard distributional shapes, while in practice, LTD distributions can often exhibit high coefficients of variance, right skew, and multimodality (Das et al, 2014;Tyworth & O'Neill, 1997;Vernimmen et al, 2008). In practice, we observe right skew, multimodal, and generally nonstandard distributional forms for the LTD component distributions of demand (Bachman et al, 2016;Zhang et al, 2014) and lead time (Das et al, 2014;Saldanha et al, 2009), which result in nonstandard distributional forms of LTD (Mentzer & Krishnan, 1985;Saldanha & Swan, 2017;Tyworth & O'Neill, 1997). Third, operations managers often have to work with small sample sizes of lead time and/or demand to set inventory parameters that lead to significant errors in estimation for compound distribution approaches (Bai et al, 2012;Silver & Rahnama, 1986).…”

“…Similar to Zhou and Viswanathan (2011), the work in this literature stream assumes fixed lead times. As we have mentioned earlier, lead time can be highly variable and lead-time distributions encountered in practice are frequently nonstandard (Das et al, 2014;Saldanha et al, 2009), which results in nonstandard distributional forms of LTD (Mentzer & Krishnan, 1985;Saldanha & Swan, 2017;Tyworth & O'Neill, 1997). Bookbinder and Lordahl (1989) proposed and demonstrated the use of the classic Efron and Tibshirani (1986) univariate bootstrap quantile approach to estimate P 1 target ROPs from LTD data with nonstandard distributions.…”

“…Similar to Zhou and Viswanathan (2011), the work in this literature stream assumes fixed lead times. As we have mentioned earlier, lead time can be highly variable and lead‐time distributions encountered in practice are frequently nonstandard (Das et al., 2014; Saldanha et al., 2009), which results in nonstandard distributional forms of LTD (Mentzer & Krishnan, 1985; Saldanha & Swan, 2017; Tyworth & O'Neill, 1997).…”

The Impact of Lead Time Uncertainty on Supply Chain Performance Considering Carbon Cost

“…However, this study assumed that the supply chain is linear and that there are no order crossovers. In fact, an in-depth study by Saldanha et al [30] affirmed that the order crossover is a common phenomenon. Chaharsooghi et al [31] investigated the bullwhip effect in multi-echelon supply chain models and concluded that random lead time has a greater impact on bullwhip effect over fixed lead time.…”