Stochastic Planning: Beyond Point Estimates

The Lie of Averages

Consider two suppliers, both with a 10-day average lead time:

• Supplier A: Delivers in 9-11 days, consistently. Normal distribution, σ = 0.5 days.
• Supplier B: Usually delivers in 7 days, but occasionally takes 25 days. Lognormal distribution, heavy right tail.

"Planning with averages is planning to be wrong. The entire field of stochastic optimization exists because point estimates discard the very information that makes supply chain decisions hard: the shape and extent of uncertainty."

A traditional planning system treats them identically, average lead time: 10 days. But the safety stock required for 95% service level is dramatically different. Supplier A needs minimal buffer. Supplier B needs a large buffer to protect against those 25-day outliers.

Using the average for both means you're either over-investing in buffer for Supplier A or under-protecting against Supplier B. Both waste money.

Distribution Fitting

"In my experience, fewer than 5% of supply chain variables are truly normally distributed. Lead times tend to be lognormal or Weibull. Demand often follows negative binomial or Poisson patterns. Using a Normal assumption when the data says otherwise is not simplification; it is systematic error."

Autonomy fits actual distributions to operational variables automatically. Instead of assuming one distribution shape fits all, the system identifies the best-fit distribution for each variable from your historical data — and stores the fitted parameters in the shared world model so every agent uses the same view of uncertainty.

This changes every downstream calculation: safety stock, reorder points, ATP availability, and capacity requirements all become more accurate when they use the right distribution instead of a Normal approximation.

From "What's the Plan?" to "What's the Probability?"

Monte Carlo simulation propagates uncertainty through the entire planning engine, generating the scenario data on which agents train and the calibration sets that power conformal prediction.

Conformal prediction then wraps the simulation output in distribution-free coverage guarantees. Instead of raw percentiles, every statement carries a mathematical guarantee:

• "P50 cost: $2.4M, P90 cost: $2.8M", with guaranteed 90% coverage
• "85% probability OTIF exceeds 95%", a calibrated bound, not an estimate
• "Service level risk: 12% chance of dropping below 90% in Q3", holds regardless of distribution

This transforms the planning conversation. Instead of debating whether the plan is "right," you discuss whether the guaranteed probability distribution of outcomes is acceptable, and every agent's likelihood score on the Decision Stream is trustworthy by construction. Likelihood drives whether an action is automated, surfaced to inform, or escalated to inspect under AIIO.

"Conformal prediction is the most important development in uncertainty quantification in decades. It provides distribution-free coverage guarantees that hold in finite samples, with no assumptions about the underlying data-generating process. For supply chain, this means your prediction intervals are trustworthy even when you do not know the true distribution."