Iтеративна оптимiзацiя попиту з використанням методу дискретних функцiональних частинок

This article addresses the challenge of assortment planning in retail under uncertain demand and operational constraints. It develops a hybrid methodology that integrates SARIMAX time-series forecasting with the Discrete Functional Particle Method (DFPM) for optimisation, enabling both strategic (long-term) and tactical (monthly) decision support.The proposed framework combines statistical forecasting with iterative optimisation in order to balance predictive accuracy and operational feasibility. In the forecasting stage, a SARIMAX model with exogenous regressors captures seasonality, promotions, and demand fluctuations, while a safeguard mechanism prevents excessively pessimistic predictions. In the optimisation stage, DFPM is applied to a quadratic objective under linear constraints, with parameters tuned using eigenvalue analysis of the risk matrix. A novel operational risk metric—the Inventory Efficiency Ratio—is introduced, defined as the ratio of leftover stock value to revenue, and used to construct the covariance structure for optimisation.A hybrid strategy blends the mathematically optimal allocation with a baseline derived from historical sales shares, ensuring both practical stability and data-driven improvements. Tactical adjustments refine this strategic solution by incorporating seasonal indices and business constraints such as minimum and maximum category weights.The framework is implemented in Python and evaluated on real-world retail data from a Ukrainian anti-stress toy retailer. Results demonstrate a 25% reduction in operational risk and a threefold increase in inventory turnover, while maintaining realistic revenue forecasts.Overall, the work contributes a flexible and reproducible decision-support methodology that unifies modern forecasting and optimisation techniques, providing practitioners with a tool for improving assortment decisions in dynamic retail environments.