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

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 because future demand predictions should capture (auto)correlation and lumpy retailer demand, and based upon such predictions, inventory replenishment and vehicle-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, whereas the latter approach provides only 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 two-stage stochastic programming approximation. Results show that our approach outperforms a classic sequential learning and (stochastic) optimization approach, distributional approaches, empirical sampling methods, residuals-based sample average approximation, and a state-of-the-art integrated learning and (stochastic) optimization approach. We show this on both synthetic data and large-scale real-life data from our industry partner. Our approach is appealing to practitioners. It is fast, does not rely on any distributional assumption, and does not face the burden of single-scenario forecasts. It also outperforms residuals-based scenario generation techniques. We show that it is robust for various demand and cost parameters, enhancing the efficiency and sustainability of daily inventory replenishment and truck-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. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2024.0613 .