The global economy relies on the flow of goods over supply chain networks, with nodes as firms and edges as transactions between firms. While we may observe these external transactions, they are governed by unseen production functions, which determine how firms internally transform the input products they receive into output products that they sell. In this setting, it can be extremely valuable to infer these production functions, to improve supply chain visibility and to forecast future transactions more accurately. However, existing graph neural networks (GNNs) cannot capture these hidden relationships between nodes' inputs and outputs. Here, we introduce a new class of models for this setting by combining temporal GNNs with a novel inventory module, which learns production functions via attention weights and a special loss function. We evaluate our models extensively on real supply chains data and data generated from our new open-source simulator, SupplySim. Our models successfully infer production functions, outperforming the strongest baseline by 6%-50% (across datasets), and forecast future transactions, outperforming the strongest baseline by 11%-62%