optimization under uncertainty

**Optimization Under Uncertainty** in semiconductor manufacturing is the **formulation and solution of optimization problems that explicitly account for variability and uncertainty** — finding solutions that are not just optimal on average but remain robust when process parameters, equipment states, and demand fluctuate. **Key Approaches** - **Stochastic Programming**: Optimize the expected value over a set of scenarios (scenario-based). - **Robust Optimization**: Optimize worst-case performance over an uncertainty set (conservative). - **Chance Constraints**: Ensure constraints are satisfied with high probability (e.g., yield ≥ 90% with 95% confidence). - **Bayesian Optimization**: Use probabilistic surrogate models to optimize expensive, noisy functions. **Why It Matters** - **Process Windows**: Find process conditions that maximize yield while remaining robust to variation. - **Robust Recipes**: Recipes optimized under uncertainty maintain performance despite day-to-day drifts. - **Capacity Planning**: Account for demand uncertainty and equipment reliability in tool investment decisions. **Optimization Under Uncertainty** is **planning for the unpredictable** — finding solutions that work well not just on paper but in the face of real-world manufacturing variability.