A Stochastic-Conformable Fractional Framework for Inventory Systems with Memory-Dependent Deterioration

Abstract

Managing inventory for perishable goods remains a persistent operational challenge, largely because conventional exponential decay models struggle to capture the irregular deterioration patterns observed in practice. This paper develops the Reliable Fractional Derivative (RFD) frame work, which incorporates memory effects i nto t he modeling of product decay through a time-shifted kernel. Unlike standard approaches that assume constant deterioration, this formulation accommodates both accelerating and decelerating patterns depending on product characteristics and storage conditions. We derive closed-form expressions for optimal ordering quantities under both deterministicand stochastic demand, then test the framework’s perfor mance through numerical experiments spanning two thousand parameter combinations. The analysis reveals that RFD models deliver the greatest improvements when de
terioration rates are steep, holding costs are substantial, or storage horizons are extended—conditions under which switching from conventional methods yields average cost reductions approaching nineteen percent, with substantially larger gains in certain cases. A pharmaceutical application confirms savings between 3.6 and 9.1 percent relative to misspecified traditional models. These findings connect with recent industry movements toward more sophisticated safety-stock practices, offering managers a principled basis
for selecting inventory policies aligned with actual product behavior rather than assuming decay conforms to simpler theoretical forms