Time series and forecasting · insight-1206
Score lead-time demand as a cumulative quantity when the decision covers the whole lead time
- Evidence type
- practitioner heuristic
- Difficulty
- medium
- Roles
- Data scientist, Data analyst
- Industries
- retail, logistics, aviation
Summary: situation, action, reason, boundary
Situation
A replenishment or seat-allocation decision commits stock for the next four days; the team reports daily MAPE for horizons 1 to 4.
Action
Sum forecasts and actuals over the lead time at each origin and score that cumulative error with the metric and quantile the decision uses. Report the daily profile separately for diagnosis.
Reason
The decision responds to total demand over the exposure window. Signed errors on adjacent days partly cancel (and may be correlated), so the cumulative error has its own size and distribution.
Boundary
Inventory, crew and capacity decisions with a lead time or review period longer than one step.
Symptom or risk
Daily error says little about the cumulative shortfall that causes stock-outs, and the daily numbers look worse than the decision-relevant ones when errors partly cancel.
Exceptions
If each step triggers its own irrevocable decision, per-step error is the right level.
Trade-offs
Cumulative scoring hides which day was wrong; keep both views.
Pitfalls
Summing per-step quantiles to get a cumulative quantile (see the insight on quantile sums).
Example
Hypothetical: independent daily errors with sd 10 on daily demand of 100 give 8% mean absolute percentage error, while the four-day total (sd 20 on 400) gives 4%.