Menglei Jia | Searcharxiv

arXiv2026

The Distributionally Robust Cyclic Inventory Routing Problem

We study the cyclic inventory routing problem that involves joint decisions on vehicle routing and inventory replenishment on an infinite, cyclic horizon. It considers a single warehouse and a set of geographically dispersed retailers. We model retailer demand as random variables with uncertain distributions belonging to a moment-based ambiguity set. We develop a distributionally robust optimization formulation that minimizes the worst-case expected cost over the ambiguity set, while ensuring service reliability through a distributionally robust chance constraint. Our main results are that we prove that the worst-case expected inventory cost is attained under a multi-point distribution, which can be identified a posteriori via linear programming, and that the distributionally robust chance constraint can be reformulated into near-equivalent deterministic forms. This yields a deterministic reformulation of the original problem. To solve it, we design a nested branch-and-price framework, in which the first level partitions retailers into clusters, and the second level concerns routing and replenishment decisions within each cluster. Computational experiments on both synthetic instances and real-world data from SAIC Volkswagen Automobile Co., Ltd. demonstrate the effectiveness and efficiency of the proposed approach.

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arXiv2024

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, 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.

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