Inventory turns and finite-horizon Little’s Laws

Over the past 30 years managers have increasingly focused on improving inventory management both within their own firms and across the supply chain. To this end, inventory turns metrics have been adopted as a popular tool for measuring flow velocity through the inventory and the efficiency of inventory-related asset utilization. There are multiple computational methods thereof currently used by practitioners, but each has some flaws. In particular, consensus is lacking as to (1) how to measure inventory flow and (2) how to measure the inventory level. Clearly, high-quality accounting information is essential for an accurate assessment of all inventory performance metrics. Unfortunately, when comparing efficiencies across firms or diagnosing and correcting intra-firm inefficiencies, choices of specific accounting rules and distortions between fair market values and corresponding accounting book values can lead to potentially misleading results. This paper presents finite-horizon versions of Little’s Law and elucidates their connection to inventory turns and restricted sojourn times in inventory, defined as the portion of the full sojourn time that falls within a prescribed time period. In particular, it explains when the reciprocal of sample inventory turns coincides with the sample average of restricted sojourn times. As such, the paper provides a unified prescriptive model for correctly relating inventory turns to sojourn times through an inventory system, thereby facilitating more accurate intra-firm and cross-firm comparisons.