14d • 💻 Technical Skills
3 stage stochastic optimization: New video
The attached slide shows a high-level summary of 2-stage and 3-stage stochastic optimization.
A new 65-minute video has been uploaded in the online course 116 (in the classroom) and the full Python code for a 3-stage stochastic optimization model, exactly as it is used in practice, has been uploaded.
In stochastic optimization, a stage is a point in time where you are forced to make a choice based only on the information you currently have. The future is uncertain.
On the left side of the slide, you see the most common framework used in operations research. It assumes uncertainty is revealed all at once in a single massive dump of information in the 2nd stage.
- Stage 1 (The "Here-and-Now"): The blue box in the attached slide. You must make a blind commitment before the uncertainty happens. (e.g., Bidding into a day-ahead electricity market at midnight).
- Uncertainty Resolution: The sun comes up, and the exact weather and electricity demand are fully revealed.
- Stage 2 (The "Recourse"): Now that you know exactly what happened, you take "wait-and-see" corrective actions to fix any imbalances. (e.g., Firing up a fast gas generator or discharging a battery to cover a solar shortfall).
- The scenario tree: One root, splitting directly into final scenarios.
On the right side, you see a more realistic model where information unfolds gradually over time, rather than all at once:
- Stage 1 (Initial Decision): The blue box. The first six hours of the day.
- First Resolution of uncertainty: You get a partial update. You now know the general weather for the day, but not the exact minute-by-minute fluctuations.
- Stage 2 (Intermediate Decisions): The orange boxes. You make mid-course corrections based on this partial knowledge (our 10 branches from Hours 6-15).
- Second Resolution: The evening arrives, and all remaining uncertainty is cleared up.
- Stage 3 (Final Recourse): You make your final, fine-tuned adjustments
- The Tree: This creates a deep scenario tree with multiple branching points.
Stochastic optimization is the absolute backbone of modern power system economics.
The electricity grid is ruled by uncertainties:
- Weather: Wind and solar PV output are highly unpredictable day-ahead.
- Demand: Human behavior (when people turn on ACs or plug in EVs) fluctuates constantly.
- Outages: Power plants or transmission lines can trip offline unexpectedly.
Grid operators use scenario trees exactly like the ones in the slide to minimize their expected operational costs.
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3 stage stochastic optimization: New video
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