To tackle the challenges of inventory models in practical applications, this paper introduces a grey forecasting modeling approach to uncover the inventory differential equation and subsequently develops an inventory optimization model. Firstly, for deteriorating products with price-dependent demand, this article formulates a differential equation to describe inventory levels by analyzing the inventory system and develops an optimization model aimed at maximizing inventory profits. Based on the idea of grey forecasting modeling, this article discusses the problem description of identifying the inventory differential equation. Then, by using the cumulative generation operator, the parameter estimation of the inventory differential equation is transformed into a regression problem. A numerical example is presented to illustrate the steps of grey forecasting modeling. The simulation results validate the feasibility of the grey forecasting modeling in the simulation case.