Dynamic Heterogeneous Graph Learning and Task-Conditioned Meta-Learning for Cold-Start Demand Forecasting in Multi-Warehouse Supply Chains

New products have little sales history, which makes short-horizon demand forecasting difficult. This study tests whether a product–store–time graph can provide pre-origin relational context and whether task-conditioned meta-learning can adapt a forecasting model from limited support observations. IGEML combines a dynamic heterogeneous graph encoder with a task-conditioned model-agnostic meta-learning adapter. The cold-start graph contains product, store, and time-window nodes; user–product interactions are excluded at the forecast origin. In the 14-day evaluation, IGEML achieves MSE = 0.2345, MAE = 0.1532, and MAPE = 0.1206. In the k = 1 setting, IGEML achieves MAE = 0.1269, with an online adaptation time of 2.8 ms per SKU. The framework defines product-level forecasting tasks, maps engineered features to graph and adaptation modules, and controls the information available at the forecast origin. Conditioning task adaptation on pre-origin relational information enables cold-start forecasting without target-period demand or post-origin user interactions.