# Outbound Modeling for Inventory Management

arXiv: https://arxiv.org/abs/2507.10890 · HTML: https://mlsanity.com/paper/2507.10890/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 11 references that are in the map.
- First posted on arXiv 15 Jul 2025.

## Builds on (most cited first, 6 of 6)

- [A Multi-Horizon Quantile Recurrent Forecaster](https://mlsanity.com/paper/1711.11053/) (2017)
- [MQTransformer: Multi-Horizon Forecasts with Context Dependent and Feedback-Aware Attention](https://mlsanity.com/paper/2009.14799/) (2020)
- [GNN-based Probabilistic Supply and Inventory Predictions in Supply Chain Networks](https://mlsanity.com/paper/2404.07523/) (2024)
- [Bayesian quantile regression analysis for continuous data with a discrete component at zero](https://mlsanity.com/paper/1511.05925/) (2015)
- [Mid-quantile regression for discrete responses](https://mlsanity.com/paper/1907.01945/) (2019)
- [A Semiparametric Quantile Single-Index Model for Zero-Inflated Outcomes](https://mlsanity.com/paper/2503.21924/) (2025)

## Abstract (arXiv)

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.