Title: Learning to Solve an Order Fulfillment Problem in Milliseconds with Edge-Feature-Embedded Graph Attention. Abstract: The order fulfillment problem is one of the fundamental combinatorial  optimization problems in supply chain management and it is  required to be solved in real-time for modern online retailing. Such a problem is computationally hard to address by exact mathematical programming methods.  In this paper, we propose a machine learning method to solve it in milliseconds by  formulating a tripartite graph and learning the best assignment policy through the proposed edge-feature-embedded graph attention mechanism. The edge-feature-embedded graph attention considers the high-dimensional edge features and accounts for the heterogeneous information, which are important characteristics of the studied  optimization problem. The model is also size-invariant for problem instances of any scale, and it can address cases that are completely unseen during training. Experiments show that our model substantially outperforms the baseline heuristic method in optimality. The online inference time is milliseconds, which is thousands of times faster than the exact mathematical programming methods.