Stochastic Planning

Why Stochastic?

Traditional planning systems use point estimates: average demand, standard lead time, nominal yield. But averages lie. A supplier with a 10-day average lead time that varies from 5 to 25 days behaves very differently from one that consistently delivers in 9-11 days — even though the averages are identical.

Autonomy distinguishes between operational variables (inherently uncertain: lead times, yields, capacities, demand) and control variables (deterministic: inventory targets, costs, policy parameters). Uncertainty is modeled explicitly, not swept under the rug.

20 Distribution Types

Not all uncertainty is normal. Autonomy supports the distributions that actually match real-world supply chain behavior:

• Normal / Lognormal — Demand with symmetrical or right-skewed variation
• Gamma / Weibull — Lead times, time-to-failure
• Beta — Yields and fill rates (bounded 0-1)
• Exponential — Inter-arrival times
• Triangular — Expert estimates (min, most likely, max)
• Mixture models — Bimodal patterns, seasonal shifts
• Empirical — When no parametric distribution fits, use the actual histogram

Distribution fitting uses maximum likelihood estimation with KS tests and AIC/BIC ranking to automatically select the best-fit distribution for each variable.

Monte Carlo Simulation

Run 1,000+ scenarios through the full planning engine with variance reduction techniques (common random numbers, antithetic variates, Latin hypercube sampling) for stable results with fewer samples.

The output is not a single plan but a distribution of outcomes. Instead of "projected cost: $2.4M," you see "P50 cost: $2.4M, P90 cost: $2.8M, 85% probability cost stays under $2.6M."

Probabilistic Balanced Scorecard

Every KPI is a probability distribution, organized into four perspectives:

• Financial — E[Total Cost], P(Cost < Budget), P10/P50/P90 cost distribution
• Customer — E[OTIF], P(OTIF > 95%), fill rate likelihood
• Operational — E[Inventory Turns], E[Days of Supply], bullwhip ratio distribution
• Strategic — Flexibility scores, supplier reliability, concentration risk

This transforms planning conversations from "what's the plan?" to "what's the probability the plan delivers the outcomes we need?"