# Scenario Predict-then-Optimize for Data-Driven Online Inventory Routing

arXiv: https://arxiv.org/abs/2401.17787 · HTML: https://mlsanity.com/paper/2401.17787/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2024.

## Built on by (most cited first, 7 of 7)

- [Sufficient Decision Proxies for Decision-Focused Learning](https://mlsanity.com/paper/2505.03953/) (2025)
- [Constrained Reinforcement Learning for the Dynamic Inventory Routing Problem under Stochastic Supply and Demand](https://mlsanity.com/paper/2503.05276/) (2025)
- [OTPTO: Joint Product Selection and Inventory Optimization in Fresh E-commerce Front-End Warehouses](https://mlsanity.com/paper/2505.23421/) (2025)
- [Simulating Classification Models for Ex-Ante Evaluation of Predict-Then-Optimize Methods](https://mlsanity.com/paper/2509.02191/) (2025)
- [Improving After-sales Service: Deep Reinforcement Learning for Dynamic Time Slot Assignment with Commitments and Customer Preferences](https://mlsanity.com/paper/2509.17870/) (2025)
- [BOCO: Bayesian Online Contextual Optimization for Decision-Focused Online Learning](https://mlsanity.com/paper/2511.20413/) (2025)
- [Learning Optimization Proxies for Sequential Contextual Stochastic Programs: An Order Fulfillment Application](https://mlsanity.com/paper/2606.25362/) (2026)

## Abstract (arXiv)

The real-time joint optimization of inventory replenishment and vehicle routing is essential for cost-efficiently operating one-warehouse, multiple-retailer systems. This is complex, as future demand predictions should capture correlation retailer demand, and based upon such predictions, replenishment and routing decisions must be taken. Traditionally, such decisions are made by either making distributional assumptions or using machine-learning-based point forecasts. The former approach ignores nonstationary demand patterns, while the latter approach only provides a point forecast ignoring the inherent forecast error. Consequently, in practice, service levels often do not meet their targets, and truck fill rates fall short, harming the efficiency and sustainability of daily operations. We propose Scenario Predict-then-Optimize. This fully data-driven approach for online inventory routing consists of two subsequent steps at each real-time decision epoch. The scenario-predict step exploits neural networks, specifically multi-horizon quantile recurrent neural networks, to predict future demand quantiles, upon which we design a scenario sampling approach. The subsequent scenario-optimize step then solves a scenario-based stochastic programming approximation. Results show that our approach outperforms the classic Predict-then-Optimize paradigm and empirical sampling methods. We show this both on synthetic data and real-life data. Our approach is appealing to practitioners. It is fast, does not rely on distributional assumptions, and does not face the burden of single-scenario forecasts. We show it is robust for various demand and cost parameters, enhancing the efficiency and sustainability of daily replenishment and routing decisions. Finally, Scenario Predict-then-Optimize is general and can be easily extended to account for other operational constraints, making it a useful tool in practice.