A Practical Approach to Replenishment Optimization: Unifying One-Shot Inventory Policy Optimization with 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. 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 RsQ policy framework by Jansen (1996), adapting it to the specific demands of a distributed fulfillment network and highly seasonal assortments. Our ZEOS Inventory Optimization Tool unifies one-shot inventory policy optimization with the predictive power of probabilistic gradient-boosting models (LightGBM). This tool, currently deployed in production by a leading European e-commerce company (Zalando), extends the classical RsQ policy framework to accommodate distributed fulfillment networks and highly seasonal assortments. It optimizes replenishment decisions, including initial replenishment timing and quantities as well as subsequent order quantities, while respecting constraints such as lead times, safety stock requirements, and operational rules. The integration of gradient-boosting models, which excel at capturing complex temporal dynamics, provides a more nuanced and accurate representation of future demand compared to traditional deterministic models. 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.