- The Foundations of Supply Chain (Lecture 1.1)
- The Quantitative Supply Chain in a Nutshell (Lecture 1.2)
- Product-Oriented Delivery for Supply Chain (Lecture 1.3)
- Programming Paradigms for Supply Chain (Lecture 1.4)
- 21st Century Trends in Supply Chain (Lecture 1.5)
- Quantitative Principles for Supply Chain (Lecture 1.6)
- Bullwhip effect
- Containers
- Copacking
- Cross-docking
- Drop shipping
- Decision-driven optimization
- DDMRP
- Deliverables (Quantitative SCM)
- Economic Drivers (Quantitative SCM)
- Initiative (Quantitative SCM)
- Kanban
- Lean SCM
- Manifesto (Quantitative SCM)
- Micro fulfilment
- Product Life-cycle
- Resilience
- Sales and Operations Planning (S&OP)
- Success (Quantitative SCM)
- Supply Chain Management (SCM)
- Supply Chain Scientist
- Test of Performance
- Third Party Logistics (3PL)
- Backorders
- Bill of Materials (BOM)
- Economic order quantity (EOQ)
- Fill Rate
- Inventory accuracy
- Inventory control
- Inventory costs (carrying costs)
- Inventory Turnover (Inventory Turns)
- Lead demand
- Lead time
- Min/Max inventory method
- Minimum Order Quantity (MOQ)
- Phantom inventory
- Prioritized ordering
- Reorder point
- Replenishment
- Service level
- Service level (optimization)
- Stock-Keeping Unit (SKU)
- Stockout
- Accuracy
- Accuracy (financial impact)
- Accuracy gains (Low Turnover) Formula
- Backtesting
- Continuous Ranked Probability Score (CRPS)
- Cross-entropy
- Forecast Value Added
- Generalization
- Pinball loss function (quantile loss)
- Probabilistic forecasting
- Quantile regression
- Seasonality
- Time-series
- ABC analysis (Inventory)
- ABC XYZ analysis (Inventory)
- Erlang C (call center staffing)
- Time-series forecasting
- Prioritized Inventory Replenishment
- Safety stock
- Supply Chain Antipatterns
- Devil's advocate
- The Non-Euclidian Horror
- The 100% service level
- The Jedi initiation
- Naked forecasts

*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.