Bayesian Forecasting for Retail Inventory in a Chain Store Network

Thesis Abstract

This study investigates the performance and reliability of Bayesian forecasting for retail inventory management within a national chain store network operating across 210 outlets and 18 regional warehouses, addressing persistent stockouts and excessive overstocks observed over the previous four fiscal years. The problem stems from the limitations of traditional forecasting approaches in handling demand volatility, promotional effects, and lead-time variability, which undermine service levels and inventory turnover. The aim is to develop a robust Bayesian forecasting framework that integrates hierarchical modeling, promotional lift, and supplier lead-time uncertainty to optimize stock levels across stores while maintaining feasible computational requirements for real-time decision support. Specific objectives are to (i) construct a hierarchical Bayesian state-space model that captures store- and region-level demand patterns, (ii) quantify the impact of promotions, price discounts, and seasonality on demand using dynamic regression components, (iii) incorporate lead-time uncertainty through stochastic process representations and meta-parameters informed by supplier performance data, (iv) compare the Bayesian approach with conventional ARIMA and exponential smoothing benchmarks in terms of forecasting accuracy, inventory turns, and stockout rates, and (v) develop an operational dashboard and decision rules for adaptive replenishment at store and warehouse levels. The methodology adopts a quantitative, action-oriented research design grounded in operations research and Bayesian statistics. The population comprises all retail SKUs with continuous replenishment across the 210 outlets, with a stratified random sample of 1,200 SKUs selected to cover category diversity and sales volume. A two-stage sampling approach is employed first, outlets are stratified by urban, suburban, and rural locations; second, SKUs are sampled within strata to ensure representation of high-velocity, mid-velocity, and slow-moving items. Data sources include point-of-sale (POS) transactions, weekly promotional calendars, supplier lead-time records, and stock-on-hand data for a 24-month training window and a 6-month out-of-sample validation window. Data collection instruments are integrated data extraction pipelines and a metadata catalog to ensure data quality, lineage, and timeliness. Model development uses a hierarchical Bayesian state-space framework with dynamic regression components for promotions, seasonality, and price effects, augmented by a stochastic lead-time model and a random-effects structure to capture inter-store heterogeneity. Posterior inference is obtained via Markov Chain Monte Carlo (MCMC) sampling implemented in Stan, with model comparison conducted through predictive likelihood and the Widely Applicable Information Criterion (WAIC). Baseline comparisons include ARIMA, Holt-Winters, and Bayesian structural time series (BSTS) models to establish relative performance. Model validation employs out-of-sample forecast accuracy metrics (MAE, RMSE, MAPE), inventory performance indicators (service level, stockout frequency, and average inventory on hand), and cost-based measures (inventory carrying cost, stockout loss). Expected findings include improved forecast accuracy at the store level through hierarchical pooling and shrinkage, better alignment of replenishment cycles with true demand, and reduced stockouts and excess inventory compared with benchmark methods. The study anticipates that incorporating marketing promotion signals and lead-time uncertainty within the Bayesian framework will yield quantifiable gains in service levels and total cost of ownership, particularly for fast-moving items during promotional periods. The contribution to knowledge lies in (i) demonstrating the viability and advantages of a fully Bayesian hierarchical state-space approach for multi-echelon retail inventory, (ii) detailing a practical method to integrate promotional lift and lead-time variability into forecast distributions, and (iii) delivering an operational decision-support toolkit that translates probabilistic forecasts into actionable replenishment policies, including threshold-based stock-reorder rules under uncertainty. The main conclusion is that Bayesian forecasting with hierarchical pooling and explicit uncertainty about promotions and lead times offers superior decision-support for inventory management in chain-store networks, compared with traditional methods. Recommendations address scaling the framework to additional SKUs, extending the model to incorporate shelf-space constraints and cross-category interactions, and embedding the forecasting system within an enterprise resource planning (ERP) platform to enable real-time, data-driven replenishment decisions.