Inventory management plays a very important role in the process of business operation, providing favorable backing for the smooth operation of production and sales. In this paper, LightGBM and PSO-LSTM models in big data technology are combined to improve inventory management and demand forecasting in supply chains. Then, the relationship between inventory, order, and forecast is elaborated, the two-level inventory cost components and the relationship between them are analyzed, the model constraints are formulated, and a mathematical model for two-level multi-cycle inventory control is constructed. Finally, the single demand forecasting model is compared with the improved model to explore the optimization effect of inventory management after the application of the LightGBM-PSO-LSTM model. The LightGBMPSO-LSTM model is the best fit and can be used for actual demand forecasting. After the optimization of inventory management, the inventory turnover ratio of Company H increased from 8.2 in 2022 to the maximum value of 9.2 in 2023, and the OTIF achievement rate of sales orders increased from 97.9% in 2022 to 99.3% in 2023. This paper provides a successful example of optimizing supply chain inventory management using big data analytics.