Hybrid Demand Forecasting and Monte Carlo Simulation for Retail Supply Chain Inventory Optimization

Abstract

Retail inventory optimization must balance service levels against holding, ordering, and stockout costs under uncertain demand and lead time. We develop an integrated framework that couples hybrid demand forecasting with Monte Carlo simulation (MCS) to evaluate continuous‑review policies. Historical daily sales are modeled using statistical baselines (naive and exponential smoothing) and gradient‑boosted trees with quantile objectives to obtain distributional forecasts. Predictive means and residual‑based dispersion calibrate a Negative Binomial demand model; because lead-time is not present in the dataset, we treat it as a scenario parameter in the simulator (baseline mean ~2 days, SD ~1 day) and probe it via sensitivity analyses. Using a representative retail subset, we simulate 90‑day horizons with 300 replications per item across a grid of values. Results reveal a convex cost–service frontier: (15,120) minimizes total cost in the tested grid, while (25,140) achieves the highest fill rate. Sensitivity analyses show costs are most responsive to safety stock and lead‑time variability. The framework links forecast uncertainty to inventory policy selection, offering a reproducible, data‑driven tool for practitioners and a baseline for future multi‑echelon and decision‑focused extensions.