Plan with uncertainty
Stochastic Planning
Every operational variable is uncertain. Lead times vary. Yields fluctuate. Demand surprises. Autonomy plans with uncertainty, not despite it, and pairs it with conformal prediction to give every agent decision a calibrated likelihood score.
"The most significant shift in supply chain analytics is moving from point forecasts to probabilistic planning. Companies that plan with uncertainty outperform those that plan despite it."
"Stochastic optimization isn't about finding the optimal plan, it's about finding plans that perform well across the widest range of possible futures. That's a fundamentally different objective."
From One Signal to 1,000 Scenarios
Monte Carlo simulation fans a single demand signal into thousands of possible futures, revealing the full distribution of outcomes.
scenarios per simulation run
Monte Carlo engine
distribution types for real-world uncertainty
Beyond normal
percentile-based decision thresholds
Calibrated coverage
more robust than deterministic planning
McKinsey
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
Run 1,000+ scenarios through the full planning engine for stable, statistically reliable results.
Monte Carlo serves two critical purposes: 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 likelihood guarantees on every agent decision in the Decision Stream.
From Simulation to Calibrated Likelihood
The output of Monte Carlo simulation feeds directly into conformal prediction. Instead of raw percentiles, every KPI carries a mathematically guaranteed coverage bound: "P(cost < $2.6M) ≥ 85%" is not an estimate, it is a distribution-free guarantee that holds regardless of the underlying distribution. This is what makes autonomous agent decisions trustworthy.
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 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?"
"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."
of companies use probabilistic demand planning
Supply Chain Insights
coverage guarantee on KPI predictions
Conformal prediction
reduction in safety stock with stochastic methods
McKinsey
See stochastic planning in action
Run Monte Carlo simulation on your supply chain data, see calibrated conformal prediction intervals, and explore the probabilistic scorecard.