Using a Gaussian Mixture Model to measure transit time bimodality and its impact on inventory decisions

Companies make inventory decisions based on well-established safety stock methodologies. In these methodologies, a key assumption is that transit times are normally distributed. Although previous studies have shown a nonnormality in transit time distributions in ocean freight, it is still unclear how transit time is distributed in land freight and how much less inventory a company could hold if transit time estimates were more accurate. Moreover, while safety stock methodologies are accepted practice, the inputs used in them are sometimes sourced from static and unsophisticated transit timetables. To address these limitations, this study conducted a distribution analysis and hypothesis testing on geolocation data captured by the sponsoring company, project44, a supply chain visibility provider. The analysis revealed differences in day- of-the-week transit time distributions. Using a Gaussian Mixture Model, this research also studied day-of- the-week transit time bimodality in detail. It was found that the majority of the first distribution had low dispersion around the mean and the second distribution grouped all long-tail transit times, with typically higher standard deviations as a result. This trend is particularly strong in intrastate full truck load shipping. Furthermore, Monday and Tuesday transit times show lower spread in means and have less variation across transit times. In contrast, the rest of the week has considerably higher spread in transit time distributions. This study shows that the full truck load freight is bimodal. Companies accounting for day of the week and transit time bimodality could reduce safety stock and therefore lower inventory cost by up to 16% through forward planning and making orders earlier in the week.

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