In many small and medium enterprises, inventory systems still function primarily as transaction-recording tools and provide limited support for anticipatory replenishment. This study introduces the Cognitive Inventory Management System (CIMS), a progressive web application that integrates mobile stock validation, tenant-isolated data management, machine-learning-driven demand forecasting, and economic order quantity (EOQ) ordering logic. Guided by design science principles, CIMS was evaluated over six months using anonymized primary operational inventory records from Indonesia, covering 35 warehouses, 2,184 stock-keeping units (SKUs), and 186,420 inventory transactions. A pre-post comparison was supplemented with a matched-pair robustness check, a paired t-test, a Wilcoxon signed-rank test, bootstrap confidence intervals, and multiple sensitivity analyses to assess the stability of the findings. Compared with the previous reorder-point practice, the system reduced monthly stockouts by 24.7%, decreased days sales of inventory by 31.2%, and shortened order-to-delivery cycles by 18.5%. Random Forest achieved lower mean absolute percentage error (MAPE) than naive, moving-average, and autoregressive integrated moving average (ARIMA) benchmarks, while the alert mechanism generated stockout warnings 7.3 days in advance on average. The main contribution is an empirically validated architecture that connects interpretable inventory rules with tenant-specific predictive signals in resource-constrained operational settings. The results also indicate that the fully integrated workflow outperforms separate use of forecasting, validation, or EOQ-based rules.