The Gamma Distribution and Inventory Control: Disruptive Lead Times Under Conventional and Nonclassical Conditions

Abstract

Background: Foundational research on the gamma distribution and inventory control highlighted its flexibility and practicality for managing fast-moving finished goods. Nonetheless, concerns remain about conventional statistical approximations of lead-time demand (LTD) distributions. Real-world lead times often result in nonstandard LTD forms, and traditional methods may introduce parameter mismatches under nonclassical conditions. Despite these challenges, this research demonstrates that a gamma LTD approximation is an effective method for managing these goods. Methods: This study employs numerical experiments to assess accuracy at high service levels, focusing on errors in system cost and product availability. Three propositions are validated: (1) a standard distribution generally characterizes the demands of fast-moving items; (2) demand variability systematically modifies the form of nonstandard LTD distributions, enhancing accuracy; (3) nonclassical conditions generally improve the accuracy of properly parameterized gamma approximations. A purposive sample of disruptive lead-time distributions found in global maritime supply chains drives numerical experiments. Results: Externally validated evidence provides the following findings within our study context: (1) a nonstandard lead-time distribution does not necessarily result in a similar LTD distribution, as it also depends on demand variability; (2) demand variability positively affects the form of a nonstandard LTD distribution under conventional conditions, with nonclassical conditions enhancing this effect; (3) the shape transformations almost always improve the accuracy of a gamma approximation. Conclusions: A gamma LTD approximation can manage inventory for fast-moving finished goods effectively, even with disruptive lead times under both conventional and nonclassical conditions.