Enhancing Symmetry and Memory in the Fractional Economic Growing Quantity (FEGQ) Model

In this paper, we present a novel approach to inventory management modeling, specifically tailored for growing items. We extend traditional economic growth quantity (EGQ) models by introducing the fractional economic growing quantity (FEGQ) model. This new approach improves the model’s symmetry and dynamic responsiveness, providing a more precise representation of the changing nature of inventory items. Additionally, the use of fractional derivatives allows our model to incorporate the memory effect, introducing a new dynamic concept in inventory management. This advancement enables us to select the optimal business policy to maximize profit. We adopt the fractional derivative in terms of Caputo derivative sense to model the inventory level associated with the items. To analytically solve the (FEGQ) model, we use the Laplacian transform to obtain an algebraic equation. As for the logistic function, known for its symmetrical S-shaped curve, it closely mirrors real-life growth patterns and is defined using fractional calculus. We apply an iterative approximation method, specifically the Adomian decomposition method, to solve the fractional logistic function. Through a sensitivity analysis, we delve for the first time into the discussion of the initial weights, which have a massive impact on the total profit level. The provided numerical data indicate that the firm began with a favorable policy. In the following years, several misguided practices were implemented that led to a decrease in profitability. The healing process began once again by selecting more effective strategies.