This paper addresses forecasting the volume of inventory units fulfilled from each warehouse and associated shipping costs. We model the joint distribution of outbound drain and costs across warehouses, conditioned on inventory positions and customer demand. A key challenge is ensuring the model is differentiable for use within reinforcement learning simulators, since actual production systems are too slow and non-differentiable for RL training. We propose a validation scheme leveraging production systems to evaluate model performance on counterfactual inventory states generated by RL policies, demonstrating accuracy in in-distribution settings.