Paper Announcement: A Practical Approach to Replenishment Optimization with Extended (R, s, Q) Policy and Probabilistic Models

Zalando's ZEOS inventory optimization system combines probabilistic demand forecasting with discrete event simulation to solve the inventory paradox in e-commerce. The system extends the classical (R,s,Q) replenishment policy with lifecycle-aware parameters and uses Monte Carlo simulation to optimize under uncertainty. By modeling full probability distributions instead of point forecasts and optimizing for the 75th percentile cost, the system achieved 22.1% GMV uplift, 33.6% availability improvement, and 23.6% better demand fill rates compared to human decisions across 2 million articles over 12 months. The approach proves that explicitly embracing uncertainty through probabilistic forecasting and risk-aware optimization delivers substantial business value.