Atlas/Planning & Forecasting/Intermittent demand

Intermittent demand

Definition

Intermittent demand is a profile where most periods are zero, interspersed with rare spikes of variable size. Typical of spare parts, end-of-life or niche products, it defeats classic forecasting methods and demands dedicated treatment, whose historical reference is Croston's method.

Why it matters

The Achilles' heel of statistical forecasting.

An industrial spare part may be ordered only once every few months, and in a quantity that varies each time. Applying classic exponential smoothing to this series produces an aberration: the method averages all the zeros and yields a tiny, constant forecast, something like 0.3 units a week, that matches no orderable reality. You then permanently under-stock, to the point of a stockout at the worst moment, or over-stock in reaction, tying up capital on parts that sleep.

The problem is far from marginal. In heavy industry, aerospace, defense, automotive, after-sales service, a majority of references follow this intermittent profile. They are often critical parts: their absence idles a machine, grounds a plane, stops a line. The financial stake of a stockout there is out of all proportion to the price of the part itself. Forecasting the intermittent well is therefore no statistical refinement, it is a matter of operational availability and controlled holding cost.

The underlying difficulty is that the useful information is drowned in zeros. An intermittent series actually carries two distinct signals: how much, when demand occurs, and how often it occurs. Mixing them, as any method treating the series as a block does, destroys the information. Croston's breakthrough, in 1972, was to understand these two signals must be separated and forecast independently.

Business impact

The business stake goes beyond the forecast itself: it directly touches safety stock sizing. Croston showed from the outset that classic smoothing applied to the intermittent produces inappropriate stock levels, potentially double what is truly needed. That is frozen capital, at scale, on thousands of dormant references.

An even more insidious trap threatens large portfolios: silent obsolescence. When a part definitively stops being demanded, classic Croston keeps forecasting a small residual demand indefinitely, because it only updates its estimates when a demand occurs. On tens of thousands of automatically managed references, dead parts thus keep generating phantom replenishment. The TSB variant, which smooths the demand probability, was designed precisely to detect this decline and let the forecast trend toward zero.

The mechanism

Separate the size and the rhythm.

Croston's intuition is to decompose the intermittent series into two simpler series, each regular in its own way, then forecast them separately before recombining them.

On the chart, the raw series is made of long stretches of zeros (the gray dots) and rare spikes (the bars). Croston extracts two pieces of information. First the size of demand: the height of each spike when it occurs, independent of when it occurs. Then the interval: the number of periods between two successive spikes. Two series far more regular than the original, each lending itself to classic exponential smoothing.

The subtle, decisive point is the timing of the update. Croston refreshes its two estimates only when a demand occurs. During zero periods, it merely increments the interval counter, without touching the estimates. This is what stops it from diluting the information in the zeros, unlike classic smoothing which updates every period and lets itself be dragged down by each zero.

The final forecast per period is then the quotient of the two: expected average size divided by expected average interval. If a part is ordered on average in lots of 6 every 3 periods, expected demand per period is 2. This number, unlike the aberrant forecast of classic smoothing, has physical meaning and serves as a sound basis for safety stock and reorder point.

intervalsize periods (mostly zero) →
Demand spike (size)Interval between demands

Figure 1. An intermittent series: zeros (dots) and rare spikes (bars). Croston separates spike size and the interval between them, and forecasts them independently. Illustrative schematic.

Forecast per period = smoothed size  ẑtsmoothed interval  p̂t
t smoothed average size of demand when it occurs  ·  t smoothed average interval between two non-zero demands. Croston's method applies exponential smoothing separately to these two quantities, and only when a demand occurs (zero periods only increment the interval counter). Dividing size by interval gives the expected demand per period. Expert refinement: Croston slightly over-forecasts; the Syntetos-Boylan approximation (SBA) corrects this bias by multiplying by (1 − α/2). To handle obsolescence, the TSB variant smooths the demand probability rather than the interval.

The traps

Three errors on the intermittent.

The intermittent first traps those who fail to recognize it and apply the tools of the regular.

01

Applying classic smoothing to it

This is the founding error. Simple smoothing averages the zeros and yields a tiny, constant, uninterpretable forecast that mechanically skews safety stock. Recognizing a series as intermittent, via its average interval and the variability of its sizes, is the absolute prerequisite to choosing the method.

02

Ignoring Croston's bias

The original Croston method slightly over-forecasts, a bias demonstrated and quantified by research. On a large portfolio, this systematic bias inflates stock. The Syntetos-Boylan approximation (SBA) corrects it with a simple multiplicative factor; ignoring it means accepting a known, avoidable overstock.

03

Not managing obsolescence

Classic Croston keeps forecasting residual demand on parts that no longer sell, generating phantom replenishment invisible at scale. On portfolios where references die out constantly, the TSB variant is needed, which tracks demand probability and lets the forecast decline toward zero.

Computing it

Four steps from series to replenishment.

Treating the intermittent follows a clear sequence, from recognizing the profile to sizing the stock.

Recognize the intermittent profile

Measure the average interval between demands and the variability of sizes. A classification (like Syntetos-Boylan's) points to Croston, SBA or a variant depending on whether demand is intermittent, erratic, or lumpy. This diagnosis conditions everything.

Decompose into size and interval

Extract the two components from the series: the sizes of non-zero demands on one side, the intervals separating them on the other. You get two regular series, each ready to be smoothed.

Smooth separately and recombine

Apply exponential smoothing to each component, updating only when a demand occurs, then divide the smoothed size by the smoothed interval (see formula). Apply the SBA correction to remove the bias if the portfolio warrants it.

Size the stock accordingly

Use this per-period forecast, with its variability, to compute a safety stock and reorder point suited to intermittency, usually very different from those of regular demand. This is where the right method turns into euros saved and stockouts avoided.

Neighboring concepts

Read next.

The intermittent is a limit case of smoothing and is measured with suitable metrics.

From knowledge to action

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