Introduction

  • TL;DR: AI Sales Forecasting becomes valuable only when it drives ordering decisions. Build a lead-time (or protection-period) demand distribution, pick the right service metric (CSL vs fill rate), and set reorder point/order-up-to levels using quantiles. Avoid “adding daily P95s” to get a lead-time P95—use sample-path aggregation. For reliable uncertainty, calibrate prediction intervals (e.g., conformal forecasting).

Why it matters: Forecast accuracy is not the objective; meeting service targets at minimal total cost is.

1. Prerequisites

  • Sales history (SKU×location), calendar/promotions
  • Lead time (mean + variability) measured from actual PO/receipts
  • Ordering constraints (MOQ, case pack, lot size)
  • Inventory state: on-hand, on-order, backorders/committed

Why it matters: Wrong definitions (lead time, inventory position) break replenishment even with good forecasts.

2. Choose the service metric first: CSL vs Fill Rate

  • CSL (Cycle Service Level): probability of no stockout per replenishment cycle
  • Fill Rate: fraction of demand served immediately; reflects stockout magnitude

Why it matters: A “95% service level” means different inventory levels depending on the metric.

3. Pick an inventory policy: (s,Q), (s,S), (R,S), or Newsvendor

Inventory position (IP) is commonly defined as: IP = on-hand + on-order − backorders − committed

  • (s,Q): if IP ≤ s, order fixed Q
  • (s,S): if IP ≤ s, order (S − IP)
  • (R,S): every R periods, order (S − IP)
  • Newsvendor (single period): order to the critical fractile quantile

Why it matters: Periodic review typically needs more safety stock because protection spans review interval + lead time.

4. The core workflow: Lead-time demand distribution → quantile → s/S

  1. Generate probabilistic demand forecasts for horizons within lead time
  2. Aggregate via sample paths to form the lead-time demand distribution (DLT)
  3. Set s (ROP) to a target quantile (for CSL targets, a common approximation is ROP ≈ Quantile_α(DLT))
  4. Safety stock = ROP − E[DLT] (conceptually)
  5. For (s,S)/(R,S): order quantity = S − IP when ordering is triggered

Why it matters: Replenishment is a tail-risk problem over cumulative demand, not a single-step forecast problem.

5. Single-period ordering: Newsvendor as a quantile rule

Critical fractile form (one common statement): P(Demand ≤ q*) = Cu / (Cu + Co)

Why it matters: When underage is more expensive than overage, the “optimal” order is intentionally above the mean.

6. Validation & monitoring

  • Realized CSL / fill rate vs targets
  • Prediction-interval coverage: if 95% PI doesn’t contain ~95% of outcomes, reorder points will drift
  • Consider conformal forecasting for calibration with coverage guarantees under minimal assumptions

Why it matters: Miscalibrated uncertainty is a direct path to chronic stockouts or chronic overstock.

Conclusion

  • Build a lead-time/protection-period demand distribution and use quantiles to set s/S.
  • Decide CSL vs fill rate up front; they optimize different outcomes.
  • Use the correct inventory-position definition and apply constraints (MOQ/case packs).
  • Calibrate uncertainty (e.g., conformal) to keep service levels stable.

Summary

  • Forecasts become actionable when translated into policy parameters (s, S) using lead-time demand quantiles.
  • Don’t add per-day quantiles; aggregate sample paths.
  • Monitor service outcomes and PI calibration continuously.

References

  • (Transportation Procurement in the Digital Age (ESD.260 Lect11), 2006-01-01)[https://ocw.mit.edu/courses/esd-260j-logistics-systems-fall-2006/8b53c45fd26ffff706d815131e8d177e_lect11.pdf]
  • (Introduction to Inventory Models (ESD.260 Lect10), 2006-01-01)[https://ocw.mit.edu/courses/esd-260j-logistics-systems-fall-2006/0a08c590d54287e2188088c3b5382d65_lect10.pdf]
  • (Understanding safety stock and mastering its equations, 2011-07-01)[https://web.mit.edu/2.810/www/files/readings/King_SafetyStock.pdf]
  • (Reorder Point Defined: Formula & How to Use, 2022-04-08)[https://www.netsuite.com/portal/resource/articles/inventory-management/reorder-point-rop.shtml]
  • (Safety Stock: What It Is & How to Calculate, 2025-04-01)[https://www.netsuite.com/portal/resource/articles/inventory-management/safety-stock.shtml]
  • (Reorder Point Formula with Practical Examples, 2025-12-13)[https://www.ism.ws/logistics/reorder-point-formula-and-examples/]
  • (Conformal Time-Series Forecasting, 2021-12-01)[https://proceedings.neurips.cc/paper/2021/file/312f1ba2a72318edaaa995a67835fad5-Paper.pdf]
  • (Conformal Prediction (StatsForecast tutorial), 2026-02-10)[https://nixtlaverse.nixtla.io/statsforecast/docs/tutorials/conformalprediction.html]
  • (Tutorial for time series (MapieTimeSeriesRegressor), 2026-02-10)[https://mapie.readthedocs.io/en/v0.8.1/examples_regression/4-tutorials/plot_ts-tutorial.html]
  • (Newsvendor model, 2026-02-10)[https://en.wikipedia.org/wiki/Newsvendor_model]