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.

"Most planning systems treat uncertainty as noise to be eliminated. The breakthrough is treating it as signal to be exploited, every distribution tells you something about where to focus."

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

The system automatically selects the best-fit distribution for each variable from your historical data.

Monte Carlo Simulation, The Data Engine

1,000+ scenarios run through the digital twin, not through the planning engine. The direction matters, and it is the one thing on this page worth getting exactly right.

We do not Monte Carlo a plan. Sampling futures at decision time would put fabricated spread on top of measured spread, and it would replace a number we can check with one we cannot. Simulation runs upstream: it produces the calibration data, conformal turns that into a band, and the plan reads the band. At decision time nothing is being simulated (how agents learn).

So Monte Carlo serves two purposes, both of them before the plan exists: it generates the rich scenario data on which agents train, and it produces the calibration sets that power conformal prediction. The simulation output is not an end in itself, it is the foundation for calibrated, distribution-free coverage guarantees on every agent decision in the Decision Stream.

From Simulation to Calibrated Achievability

The output of Monte Carlo simulation feeds directly into conformal prediction. Instead of raw percentiles, every KPI carries a calibrated coverage bound: "P(cost < $2.6M) ≥ 85%" holds without assuming the shape of the underlying distribution, without assuming the model is correctly specified, and without assuming the errors behave.

Distribution-free is not assumption-free. The guarantee rests on exchangeability: that the data it was calibrated on and the thing being predicted come from the same process. A supply chain whose rules genuinely change violates that, and no amount of calibration reaches it. What makes the bound trustworthy is not the guarantee alone: it is that the substrate is built to check realised coverage against the promise on a schedule, so the day the assumption stops holding is a day the number reports rather than a day nobody notices. See Conformal Prediction.

Probabilistic Balanced Scorecard

Every KPI is a probability distribution with conformal coverage guarantees, organized into four perspectives:

• Financial, E[Total Cost], P(Cost < Budget), P10/P50/P90 cost distribution
• Customer, E[OTIF], P(OTIF > 95%), fill rate achievability
• 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 "how achievable is it, and how fragile does it get once the error grows?"

"Only 12% of companies model demand as a probability distribution. The rest are making billion-dollar decisions based on a single number. That's not planning, it's guessing."