Intermittent and Lumpy Demand
By MLAIA Data Science Ltd. · Published 13 July 2026
Intermittent demand is a demand pattern in which items are requested only sporadically, so that many time periods record zero demand. When the size of those occasional demands also varies greatly, the pattern is called lumpy demand. These patterns dominate spare parts, aftermarket components, and maintenance, repair and operations (MRO) inventories, and they defeat forecasting methods that assume regular, roughly normally distributed demand.
Definitions
- Intermittent demand
- Demand that occurs sporadically, with zero demand in many periods. The demand incidence (whether an order arrives) is irregular, while the sizes of the orders that do arrive are comparatively stable.
- Lumpy demand
- Intermittent demand whose non-zero order sizes are themselves highly variable. A part may sell nothing for months, then two units, then forty.
- Erratic demand
- Demand that occurs in most periods (low intermittency) but with highly variable sizes.
- Smooth demand
- Demand that occurs regularly with relatively stable sizes — the pattern most textbook forecasting methods implicitly assume.
The ADI–CV² classification
The standard way to classify a demand series uses two statistics, computed from its history:
- ADI (Average inter-Demand Interval) — the mean number of periods between successive periods with non-zero demand. ADI = 1 means demand occurs every period; ADI = 4 means demand appears, on average, once every four periods.
- CV² (squared coefficient of variation) — the variance of the non-zero demand sizes divided by the square of their mean: CV² = (σ / μ)². It measures how variable order sizes are, ignoring the zeros.
Syntetos, Boylan and Croston (2005) derived cutoff values for these two statistics by comparing the theoretical forecast errors of Croston's method and its bias-corrected variant across demand patterns. The resulting scheme, with cutoffs at ADI = 1.32 and CV² = 0.49, has become the de facto standard in both research and practice:
| CV² < 0.49 (stable sizes) | CV² ≥ 0.49 (variable sizes) | |
|---|---|---|
| ADI < 1.32 (frequent) | Smooth — regular timing, stable sizes | Erratic — regular timing, variable sizes |
| ADI ≥ 1.32 (sporadic) | Intermittent — sporadic timing, stable sizes | Lumpy — sporadic timing, variable sizes |
The cutoffs are pragmatic decision boundaries, not laws of nature: a series with ADI = 1.30 is not fundamentally different from one at 1.35. Their value is in giving a large item portfolio a consistent, automatable segmentation, which can then drive method selection per item.
Why intermittency breaks conventional forecasting
Most classical forecasting and inventory theory assumes demand per period is a well-behaved random variable — typically approximately normal, with observations in every period. Intermittent series violate this in several ways:
- Zero inflation. A large mass of the distribution sits exactly at zero, so the distribution is far from normal — it is discrete, non-negative, and often strongly right-skewed.
- The mean is misleading. An item that sells 12 units once a year has a mean of one unit per month, yet stocking one unit per month serves the actual demand pattern poorly. Point forecasts of a demand rate say nothing about when demand will arrive.
- Safety-stock formulas miscalibrate. The classic normal-based safety-stock formula maps a z-score to a service level through the normal distribution. On zero-inflated, skewed lead-time demand, that mapping can miss the intended service level badly in either direction.
- Error metrics degenerate. MAPE is undefined when the actual is zero, and period-by-period accuracy rewards forecasting zero every period. Scale-free metrics (such as MASE) or inventory-oriented evaluation are needed instead.
- Smoothing drifts. Simple exponential smoothing applied directly to an intermittent series spikes just after each demand and decays toward zero in between — it is highest exactly when replenishment is least needed. This observation motivated Croston's method.
Where intermittent demand occurs
Intermittent and lumpy patterns are the norm, not the exception, in several settings:
- Spare parts and service parts — demand arises from failures or maintenance events, which are irregular by nature. Studies of industrial spare-parts portfolios routinely find that a majority of SKUs are intermittent or lumpy.
- Aftermarket and B2B distribution — a long tail of slow-moving SKUs, punctuated by occasional large orders from fleet or project customers, produces lumpy histories.
- MRO inventories — consumables and repairables held against equipment uptime, where a stockout is costly but demand may not recur for months.
- Retail long tails — the bottom of most assortments sells sporadically even when the top sells daily.
Forecasting approaches
The established approaches to intermittent series fall into three families: dedicated statistical estimators (Croston's method and its SBA and TSB variants), empirical methods that resample the observed history (bootstrapping, following Willemain, Smart and Schwarz, 2004), and machine-learning models that pool information across many items. Which family is appropriate depends on the demand pattern, the data available, and the inventory decision the forecast feeds — a topic covered in Demand Classification for Forecasting.
Frequently asked questions
What counts as intermittent demand?
Demand is usually treated as intermittent when the average interval between periods with any demand (the ADI) is greater than about 1.32 periods — that is, when a substantial share of periods record zero demand. The exact threshold comes from the demand-categorization research of Syntetos, Boylan and Croston (2005).
What is the difference between intermittent and lumpy demand?
Both patterns have many zero-demand periods. Intermittent demand has relatively consistent order sizes when demand does occur (CV² of the non-zero sizes below about 0.49), while lumpy demand combines sporadic timing with highly variable order sizes (CV² at or above 0.49). Lumpy demand is the hardest standard pattern to forecast.
Why is MAPE a poor error metric for intermittent demand?
MAPE divides each error by the actual demand in that period. When many periods have zero actual demand, the division is undefined, and near-zero actuals produce exploding percentages. Scale-free alternatives such as MASE, or service-level-oriented measures, are generally preferred for intermittent series.
Can exponential smoothing or ARIMA be used on intermittent demand?
They can be computed, but simple exponential smoothing applied directly to an intermittent series is biased immediately after each demand occurrence and drifts toward zero in between, and ARIMA's Gaussian error assumption fits zero-inflated data poorly. Methods designed for intermittency — Croston's method, SBA, TSB, or bootstrapping — are the standard starting points.
References
- Croston, J. D. (1972). Forecasting and stock control for intermittent demands. Operational Research Quarterly, 23(3), 289–303.
- Syntetos, A. A., Boylan, J. E., & Croston, J. D. (2005). On the categorization of demand patterns. Journal of the Operational Research Society, 56(5), 495–503.
- Syntetos, A. A., & Boylan, J. E. (2005). The accuracy of intermittent demand estimates. International Journal of Forecasting, 21(2), 303–314.
- Willemain, T. R., Smart, C. N., & Schwarz, H. F. (2004). A new approach to forecasting intermittent demand for service parts inventories. International Journal of Forecasting, 20(3), 375–387.