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.

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

Autonomy fits actual distributions to operational variables using maximum likelihood estimation with KS tests and AIC/BIC model selection. Instead of assuming Normal, the system identifies whether lead times are Weibull, demand is Lognormal, or yields follow a Beta distribution.

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. Instead of a single-point supply plan, you get a distribution of outcomes:

• "P50 cost: $2.4M, P90 cost: $2.8M"
• "85% probability OTIF exceeds 95%"
• "Service level risk: 12% chance of dropping below 90% in Q3"

This transforms the planning conversation. Instead of debating whether the plan is "right," you discuss whether the probability distribution of outcomes is acceptable.