Order crossover research: A 60-year retrospective to highlight future research opportunities

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.