Modeling memory-driven inventory dynamics using fractional calculus: an approach to decision-making under uncertainty

This study aims to address the gap in operations research (OR) by focusing on ensuring cost efficiency, decreasing stockouts, and enhancing the overall stability of system behaviors by investigating whether incorporating memory effects through fractional calculus (FC) can improve inventory management compared to classical models. In this study, FC was used to develop a fractional inventory model that incorporates both memory-dependent demand and non-exponential deterioration. Relative to classical models, the fractional model reduces cost estimation error by 18–22% and yields up to a 28% increase in the optimal order quantity Q∗. The method of this study includes considering a classical model as a standard and then creating an inventory model that employs FC to determine memory-dependent demand and deterioration. The developed model was treated numerically via a finite-difference scheme in Python. Findings of this study signify that lower fractional orders α increase inventory deterioration and present substantial memory effects, yielding a nonlinear association between α and both Q∗ and total cost. The study recommends that employing FC can improve model flexibility compared to classical approaches while remaining computationally manageable. This study provides a practical implication for inventory modeling and assists in developing scalable numerical tools for practical OR applications.