Time series and forecasting · insight-0221
Pick the forecast quantile from the ratio of under- and over-forecast costs
- Evidence type
- documented fact
- Difficulty
- medium
- Roles
- Data scientist, Data analyst
- Industries
- aviation, retail, logistics
Summary: situation, action, reason, boundary
Situation
Operations asks for 'the forecast' to set meal loads per flight, where running out costs more than waste.
Action
Estimate the unit cost of a shortfall and of an excess, set the target quantile to shortfall cost divided by the sum of both costs, and forecast that quantile directly or from a predictive distribution.
Reason
Under asymmetric piecewise linear loss, the optimal point forecast is a quantile whose level is set by the relative costs of under- and over-prediction.
Boundary
Inventory, catering, staffing, overbooking buffers, cloud capacity.
Symptom or risk
Using the mean or median forecast ignores the cost asymmetry and systematically under-provisions.
Exceptions
When costs are not linear (penalties after a threshold, service-level contracts), solve the decision by simulation instead.
Trade-offs
High quantiles need good tail estimates, which are data hungry.
Pitfalls
Asking the model team to pick the quantile; the costs belong to the business owner.
Example
Hypothetical costs: shortfall 12, excess 3 per meal, so the target quantile is 12 / 15 = 0.8.
Lessons and concepts
Claims and their sources
Quantiles are optimal point forecasts under generalized piecewise linear losses, with the quantile level set by the costs of under- and overprediction.