Robustness of Static and Rolling (s, S) Inventory Policies under Negative Binomial Demand

Abstract

Effective inventory management for Indonesian e-commerce MSMEs is challenged by extreme demand shocks driven by platform-specific promotional events (tanggal kembar). While operations research often suggests adaptive rolling horizon frameworks to handle non-stationarity, these dynamic models frequently rely on standard formulas assuming normally distributed demand. This study evaluates the robustness of the continuous-review  inventory control policy under deliberate model misspecification. Using a 6-month daily transactional dataset from a fashion footwear MSME, empirical daily sales were fitted to a Negative Binomial distribution, while lead times followed a stochastic Triangular distribution. A 180-day discrete-event Monte Carlo simulation framework replicated across 2,500 iterations evaluated a global Parametric Static policy against an Adaptive Rolling Horizon policy ( to 60 days). Counter-intuitively, the simpler Parametric Static policy dominated, maintaining a superior Cycle Service Level (CSL) of 96.7% and a Fill Rate of 95.0%. Conversely, the adaptive framework failed to reliably satisfy the 95% target, yielding lower CSL ranges (94.2%–95.5%) and Fill Rates (90.9%–93.1%) due to sampling errors and localized variance instability caused by forcing a symmetric Normal assumption onto highly skewed data. For resource-constrained MSMEs, these findings reveal that dynamic parameter updates can lead to operational self-disruption, indicating that a stable, long-term static policy serves as a highly robust and administratively efficient buffer against promotional volatility.