AI-Integrated Probabilistic Optimization for Inventory Control Under Stochastic Demand

The identification and operationalization of increasingly nonstationary and volatile demand patterns challenge the conduct of inventory management in contemporary supply chains. The classical models, especially EOQ and static policies, rest on the stability of demand assumptions, either deterministically or distributionally, and are hence less apt under real-world uncertainty. In view of these limitations, the present study puts forward an integrated and modular framework that merges AI-driven adaptive forecasting with probabilistic inventory optimization. The proposed forecasting module uses LSTM networks with exogenous inputs and online learning in order to capture evolving demand structures. Residual analysis and nonparametric error distributions quantify forecast uncertainty. These estimates of uncertainty are embedded within a quartile-based safety stock formulation and eventually allow for risk-aware replenishment decisions in a rolling horizon setting. The empirical evaluation based on both synthetic and real retail data illustrates that the proposed system outperforms the classical model and state-of-the-art baselines in terms of forecast accuracy and holding cost reduction as well as service level improvement. In theory, the convexity of the expected cost function is established, and the sensitivity of optimal order quantities to forecast error variance is analyzed. This is followed by a discussion of the main model assumptions and practical limitations, comprising data requirements and a single-echelon scope. Overall, the findings position the proposed framework as a robust, adaptive, and implementable solution to inventory control in environments characterized by high uncertainty in demand.