Forecast intermittent demand by separating order size from the gap between orders

A business may sell no replacement kits for several weeks and then receive an order for twelve. A forecast that focuses only on the latest week's zero can miss the recurring requirement, while a forecast based only on order sizes can ignore how infrequently orders arrive.

Croston's method separates those two features. Hyndman and Athanasopoulos describe smoothing the positive demand quantities and the intervals between them, then dividing the estimated quantity by the estimated interval. The result is a demand-rate forecast for the selected time period.

This is one candidate method for intermittent demand, not a universal solution for every sparse sales history. The decision still needs to distinguish genuinely irregular demand from missing records, stockouts, a scheduled purchase program or a product approaching retirement.

Imagine an invented weekly demand series with orders of eight units in week two, twelve in week six and six in week nine, with zero demand in the intervening weeks. The positive quantities are eight, twelve and six. The observed gaps after the first event are four weeks and three weeks.

Retain the complete weekly calendar even though the quantity series includes only positive events. Removing zero weeks from the original record without preserving the gaps would make infrequent orders appear to occur every observation period.

The interval before the first observed order requires an initialization convention because the available history may start after an earlier event. Document that convention. A short history with only two gaps provides little evidence about a stable long-run arrival pattern, regardless of how precisely the spreadsheet displays the result.

Assume a hypothetical model currently estimates eight units per positive demand event and a four-week interval, giving a rate of two units per week. A new order of twelve units arrives five weeks after the previous positive demand event.

Use a smoothing weight of 0.2 for both components in this illustration. The updated quantity estimate is 0.2 times twelve plus 0.8 times eight, or 8.8 units. The updated interval estimate is 0.2 times five plus 0.8 times four, or 4.2 weeks.

The new forecast rate is 8.8 divided by 4.2, or approximately 2.095 units per week. The larger order raises the quantity estimate, while the longer gap partly offsets that increase. Smoothing the two components separately is different from simply averaging the individual event rates.

The 2.095-unit forecast does not mean a customer will purchase two units every week. The observed business may continue to have zero weeks and larger orders. The rate summarizes that intermittent pattern rather than supplying a calendar of individual events.

For a twelve-week planning horizon, multiplying the rate by twelve gives approximately 25.14 units. At an assumed $40 purchase cost per unit, that corresponds to about $1,005.71 of modeled demand-related cost before other purchasing rules.

That amount is not yet a purchase order or a dated cash payment. Existing stock, supplier pack sizes, lead times, minimum orders and payment terms determine the actual purchasing schedule. Keep the demand forecast as an input to that schedule instead of rounding every week's rate into a separate order.

In the basic event-updated method described here, the smoothed size and interval estimates change when another positive event arrives. The forecast can therefore remain unchanged through a prolonged sequence of zeros. The longer completed interval enters the update only when the next event occurs.

That behavior matters if demand is disappearing. A product with no future market can retain a positive forecast while the method waits for an event that never arrives. Review product status and customer evidence rather than interpreting the unchanged number as proof that demand remains intact.

Alternative intermittent-demand methods handle occurrence and obsolescence differently. Compare suitable methods on the actual decision and data instead of modifying zeros until the preferred model produces a desired answer. A planned product retirement may require an explicit operating assumption outside a purely historical rate estimate.

Hyndman and Athanasopoulos note that the original Croston method does not correspond to a full statistical model and that its forecasts are known to be biased. Its point output does not, by itself, supply prediction intervals or a probability that demand will exceed a stock level.

A service-level stock decision needs information about demand over the replenishment lead time, including its distribution and the lead-time uncertainty. Two demand patterns can share the same average rate while requiring different inventory to achieve a chosen availability objective.

If a software package displays confidence bounds with an intermittent-demand forecast, identify the model or approximation used to produce them. Do not assume that selecting the Croston label establishes a particular coverage probability. Validate the uncertainty output separately from the point forecast.

Check whether recorded zero sales represent zero demand. An unavailable item can have unobserved demand, and a missed data import can create artificial gaps. Returns or corrections may also need separate treatment before constructing a positive-demand event series.

Evaluate forecasts over the horizon relevant to purchasing or budgeting. Weekly accuracy alone may not reflect a supplier's six-week lead time. Use error measures that remain defined when actual demand is zero, and examine the cost of shortages and excess stock under the proposed ordering policy.

Keep known scheduled orders outside an unexplained statistical average. If a customer has confirmed a specific quantity and date, incorporate that evidence with a documented rule that avoids counting it again within the historical demand-rate assumption.

Show the estimated positive order size, estimated interval, smoothing choices, last observed event and resulting rate. Those components explain whether a revision came from larger orders, shorter gaps or both.

The purchasing owner can then compare the forecast with customer activity and supplier constraints. The method is useful when it preserves the intermittent nature of demand while making the budget assumption inspectable, without pretending that a smooth weekly number describes the dates on which orders or payments will occur.