A practical approach to replenishment optimization with extended (R, s, Q) policy and probabilistic models

Effective inventory management is crucial for businesses operating across diverse sales channels, particularly in the dynamic e-commerce landscape. Balancing the need to minimize inventory costs while ensuring sufficient stock availability to meet fluctuating demand presents a significant challenge, further compounded by the complexities of external partnerships and distributed fulfillment networks. These factors introduce uncertainties in demand, returns, and lead times, impacting overall profitability. Recent literature has advanced optimization techniques for production and supply chain systems, often focusing on complex analytical objectives related to imperfect quality, typically solved using meta-heuristics. However, these sophisticated optimization models often rely on deterministic or simplified demand assumptions. This study presents a novel approach to replenishment optimization with a two-fold contribution. First, we aim to bridge the gap through the systematic integration of probabilistic demand forecasting with advanced inventory policy optimization techniques, bridging a critical gap between predictive modeling and practical replenishment decisions. Second, we introduce a significant extension to the classical policy framework by Jansen (1996), adapting it to the specific demands of a distributed fulfillment network and highly seasonal assortments. Our Zalando E-commerce Operating System (ZEOS) Inventory Optimization Tool unifies one-shot inventory policy optimization with the predictive power of probabilistic gradient-boosting models (LightGBM). In a backtest covering the full one-year period, the system achieved an aggregate in both Gross Merchandise Value (GMV) and GMV after fulfilment costs uplift compared to the human baseline of and outperformed all classical inventory-theory baselines (Tuned , periodic base-stock, and Myopic newsvendor), with average operational availability and demand fill rate maintained at and , respectively. Ablation analyses show that probabilistic forecasts with a percentile-based objective yield the most robust performance. Further, horizon sensitivity analysis identifies a 12-week window as optimal for balancing responsiveness and profit stability. This research represents a pioneering effort in bridging the gap between probabilistic demand forecasting and policy optimization techniques, resulting in a practical tool that addresses the challenges of inventory management in an e-commerce setting, contributing to improved efficiency, reduced costs, and enhanced profitability.