*By Joannes Vermorel, Last revised November 2014*The

*lead demand* (also called

*lead time demand*) is the total demand between now and the anticipated time

*for the delivery after the next one* if a reorder is made now to

replenish the inventory. This delay is named the

lead time. Since lead demand is a

*future* demand (not yet observed), this value is typically forecasted using

time series analysis.

The

*lead demand* concept applies, among others, to retail, wholesale and manufacturing businesses, where inventory is kept in order to serve clients.

In the classical

safety stock analysis, the

reorder point is the sum of the lead demand and the safety stock component. The

*median* lead demand can be interpreted as the demand estimate that has 50% chances to be above or below the future demand when looking ahead for N days where N is the lead time. Thus, if the lead demand is used as reorder point with a zero safety stock, the expected service level would be of 50%.

However, with the more modern

quantile viewpoint, a purposefully biased estimation of the lead demand is directly calculated through a quantile forecasts. From the quantile viewpoint, the reorder point is nothing but a purposefully biased estimate of the lead demand. The bias is adjusted to match the desired service level.

In both cases (classic or quantile), the

accurate estimation of the lead demand is critical in order to achieve a good level of inventory optimization, that is, to use the minimal amount of inventory to reach specific

service level objectives.

## Lokad's gotcha

The most natural way of thinking about the future demand is an

**aggregated** future demand

**per day, week or month**. Through this aggregation, the forecast is just the extension of the past demand curve into the future. Then, once a lead time is specified, the lead demand is calculated as the sum of the forecasted values for the next N periods.

However, this

**indirect approach** is not optimal because the criterion being optimized (i.e. per period forecast) is not the one impacting inventory (i.e. per lead time forecast). This discrepancy introduced by the aggregation itself also explains why we observe more accurate forecasts when leveraging a

quantile forecasting technology as opposed to a classic forecasting technology.