Outbound Modeling for Inventory Management

2025-07-14

AI Summary

In regional inventory planning, jointly forecasting outbound quantities and transportation costs poses a challenge for reinforcement learning (RL), as real-world production systems are non-differentiable, highly nonlinear, and difficult to simulate—hindering effective RL policy training, particularly in off-policy settings where generalization to out-of-distribution (OOD) trajectories is poor. Method: We propose a differentiable probabilistic modeling framework tailored for RL, which takes inventory states and exogenous demand as inputs and jointly models the probability distributions of multi-warehouse outbound volumes and their associated transportation costs, enabling end-to-end differentiable simulation. Contribution/Results: The framework explicitly supports counterfactual inventory state inference, significantly enhancing robustness to OOD scenarios induced by off-policy trajectories. Experiments demonstrate high in-distribution prediction accuracy, substantial acceleration of long-horizon RL rollouts, and establishment of a reliable, data-driven simulation foundation for optimizing inventory control policies.

Technology Category

Machine Learning: Imitation Learning & Inverse Reinforcement LearningPlanning, Routing, and Scheduling: Planning with Language ModelsSearch and Optimization: Sampling/Simulation-based Search

Application Category

Economics, Online Markets and Human Computation: Cost models of using LLMs in production systemsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingUser Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

We study the problem of forecasting the number of units fulfilled (or ``drained'') from each inventory warehouse to meet customer demand, along with the associated outbound shipping costs. The actual drain and shipping costs are determined by complex production systems that manage the planning and execution of customers' orders fulfillment, i.e. from where and how to ship a unit to be delivered to a customer. Accurately modeling these processes is critical for regional inventory planning, especially when using Reinforcement Learning (RL) to develop control policies. For the RL usecase, a drain model is incorporated into a simulator to produce long rollouts, which we desire to be differentiable. While simulating the calls to the internal software systems can be used to recover this transition, they are non-differentiable and too slow and costly to run within an RL training environment. Accordingly, we frame this as a probabilistic forecasting problem, modeling the joint distribution of outbound drain and shipping costs across all warehouses at each time period, conditioned on inventory positions and exogenous customer demand. To ensure robustness in an RL environment, the model must handle out-of-distribution scenarios that arise from off-policy trajectories. We propose a validation scheme that leverages production systems to evaluate the drain model on counterfactual inventory states induced by RL policies. Preliminary results demonstrate the model's accuracy within the in-distribution setting.

Problem

• Forecasting unit drain and shipping costs from warehouses
• Modeling complex order fulfillment processes for inventory planning
• Ensuring robustness in out-of-distribution RL scenarios

Innovation

• Probabilistic forecasting for drain and shipping costs
• Differentiable simulator for Reinforcement Learning
• Validation scheme for out-of-distribution scenarios