Supply chain management is fundamentally a problem of decision-making under uncertainty: how much inventory to hold, when to reorder, where to position stock, and how to respond to demand signals. Traditional methods used point forecasts with ad hoc safety stock calculations, but Bayesian methods provide a coherent framework that propagates demand uncertainty through to inventory decisions, producing policies that are optimal with respect to the full posterior predictive distribution of future demand.
Bayesian Demand Forecasting
Demand for products is driven by trend, seasonality, promotions, price, competitor actions, weather, and countless other factors, many of which are imperfectly observed. Bayesian structural time-series models decompose demand into interpretable components — local level, local trend, seasonal patterns, regression on covariates — with posterior distributions over each component. This decomposition enables both forecasting and causal attribution (how much did the promotion increase demand?).
μₜ = μₜ₋₁ + δₜ₋₁ + η_μ,ₜ [local level]
δₜ = δₜ₋₁ + η_δ,ₜ [local trend]
γₜ = −Σⱼ₌₁ˢ⁻¹ γₜ₋ⱼ + η_γ,ₜ [seasonality]
All variance parameters have inverse-gamma priors
β ~ N(β₀, Σ₀) [regression coefficients]
The posterior predictive distribution of future demand — not just a point forecast and error band — feeds directly into inventory optimization. The probability that demand exceeds a given level determines the required safety stock for a target service level, and the full distribution enables optimization of order quantities under arbitrary cost functions.
Intermittent and Lumpy Demand
Many industrial and spare parts supply chains face intermittent demand — long periods of zero demand punctuated by occasional orders of varying size. Traditional forecasting methods (exponential smoothing, Croston's method) handle this poorly. Bayesian models like the Bayesian variant of the Croston method and zero-inflated Poisson models naturally accommodate the dual uncertainty of whether demand will occur and how large it will be, with posterior distributions that honestly represent the high uncertainty inherent in intermittent demand.
When a product is newly launched, historical demand data do not exist. Bayesian methods shine in this setting by incorporating prior information from analogous products, expert judgment on expected demand levels, and early sales signals that rapidly update the forecast. The posterior predictive distribution starts wide (reflecting high uncertainty) and narrows as data accumulate, providing honest uncertainty bounds throughout the product lifecycle. This is vastly superior to deterministic forecasts that create an illusion of precision when little data exists.
Bayesian Inventory Optimization
Given the posterior predictive distribution of demand, Bayesian inventory optimization determines order quantities and reorder points that minimize expected total cost — holding costs, ordering costs, and stockout penalties — integrated over demand uncertainty. Newsvendor models with Bayesian demand posteriors produce analytically tractable solutions, while more complex multi-echelon and multi-period problems use simulation-based optimization with posterior samples.
"The supply chain does not need better point forecasts — it needs better uncertainty quantification. A forecast that says 'demand will be 100 units' is far less useful than one that says 'demand has a 90% chance of falling between 70 and 140 units.'" — Supply chain analytics maxim
Demand Sensing and Real-Time Updating
Bayesian demand sensing updates forecasts in real time as point-of-sale data, web traffic, and other demand signals arrive. The Kalman filter and its nonlinear extensions provide the computational framework for sequential Bayesian updating of demand state estimates. Each new observation revises the posterior, enabling supply chains to respond to demand shifts within days rather than the monthly planning cycles of traditional systems.
Multi-Product and Hierarchical Forecasting
Retail and distribution supply chains manage thousands of products across hundreds of locations. Bayesian hierarchical models estimate demand parameters at multiple levels — individual SKU, product category, store cluster, region — with information flowing between levels through the hierarchical prior. A new product with no history borrows demand patterns from its category; a store with sparse data borrows from similar stores. This hierarchical borrowing of strength is the Bayesian solution to the curse of dimensionality in large-scale demand forecasting.