Intermittent Demand

The foundational forecasting technique specifically designed for intermittent demand patterns. Unlike exponential smoothing, Croston's method decomposes the problem into two separate estimates:

• Demand interval: The time between non-zero demand occurrences
• Demand size: The magnitude of demand when it occurs

By updating these estimates independently only when demand occurs, Croston's method avoids the bias toward zero that plagues standard forecasting techniques during long periods of inactivity. The Syntetos-Boylan approximation later corrected an inherent positive bias in the original formulation.

Before applying any forecasting method, demand patterns must be categorized by intermittence and lumpiness. The standard classification uses two dimensions:

• Average Demand Interval (ADI): Mean time between non-zero demands. ADI > 1.32 indicates intermittent patterns
• Coefficient of Variation squared (CV²): Variance of non-zero demand sizes relative to their mean. CV² > 0.49 indicates lumpy, erratic demand

This creates four quadrants: smooth, intermittent, lumpy, and erratic. Each quadrant demands a different forecasting strategy, with intermittent and lumpy categories requiring Croston-type methods.

The asymmetric loss function that makes probabilistic intermittent demand forecasting possible. Pinball loss tilts the penalty depending on whether the forecast over-predicts or under-predicts:

• For a 95% quantile forecast, under-prediction is penalized 19x more than over-prediction
• For a 5% quantile, the asymmetry reverses

This property allows models to directly estimate prediction intervals for intermittent demand without assuming a parametric distribution. Modern deep learning approaches like DeepAR minimize pinball loss across multiple quantiles simultaneously, producing full forecast distributions even for SKUs with mostly zero demand.

In intermittent demand contexts, the distinction between these two metrics becomes critical for safety stock calculation:

• Cycle Service Level (CSL): Probability of no stockout during a replenishment cycle. A 95% CSL means stockouts occur in 5% of cycles regardless of magnitude
• Fill Rate: Proportion of total demand quantity satisfied from stock. A 95% fill rate means 5% of units are backordered

For intermittent, lumpy demand, a high CSL can mask catastrophically low fill rates because a single stockout event can represent a large quantity. Inventory optimization for spare parts typically targets fill rate rather than CSL to ensure operational continuity.

The discrete probability distribution that best models intermittent demand count data. Unlike the Poisson distribution, which assumes the mean equals the variance, the negative binomial accommodates overdispersion—the high variance-to-mean ratio characteristic of sporadic demand.

Key properties for supply chain modeling:

• Parameters: Mean demand rate and dispersion parameter
• Zero-inflated variants: Add a separate probability mass for excess zeros, common in spare parts where many periods have truly zero demand
• Compound distributions: Combine with a size distribution (e.g., gamma) to model both demand occurrence and magnitude

Modern probabilistic forecasting systems use the negative binomial as the output distribution for intermittent SKUs, generating complete demand probability profiles.

The classic single-period inventory model adapted for sporadic demand. The standard newsvendor balances overage cost (Co) against underage cost (Cu) to find the optimal critical fractile: Cu / (Co + Cu).

For intermittent demand, the model requires:

• Empirical demand distribution: Since parametric assumptions often fail with sparse data, bootstrapping historical non-zero demands and intervals generates a realistic distribution
• Compound distributions: Model the product of demand occurrence probability and demand size distribution
• Lead time integration: For intermittent items with long lead times, the demand distribution must compound over the entire protection period

The result is an optimal order-up-to level that explicitly accounts for the probability of zero demand during lead time.