Vose SoftwareModelRisk Optimizer example · Energy and utilities
Wastewater Aeration: Blower Staging
How many blower steps per basin minimise the worst-case energy bill while keeping oxygen safe 95% of the time?
The optimisation problem
Lowest mean of the worst 10% of energy bills
- Decide
- Blower steps for 4 basins, 0 to 8
- Goal
- Lowest mean of the worst 10% of energy bills
- Limit
- At most a 5% chance any basin’s oxygen falls below 2.0 mg/L
- Engine
- Vertex Detector
What the Optimizer found
| Starting plan | Optimizer’s plan | |
|---|---|---|
| Basin 1 | 3 | 6 |
| Basin 2 | 3 | 7 |
| Basin 3 | 3 | 6 |
| Basin 4 | 3 | 6 |
| Goal: Mean of the highest 10% of energy cost ($) | 462 | 963 |
| Limit: Chance lowest basin O2 is at or below 2, at most 5% | 100% not met | 4.0% met |
ModelRisk Optimizer run on 13 Oct 2026: the Vertex Detector engine, with Turbo simulation, tried 350 plans, each simulated with 10,000 samples, in 3 seconds. Both plans above were then simulated again with the same 10,000 samples.
What the workbook models
Four aeration basins face an uncertain influent load (lognormal). Blowers add dissolved oxygen but draw energy whose price also varies. You choose integer blower steps per basin.
Decision, objective and constraint
- Decision
- 4 integer blower-step counts, each 0 to 8
- Objective
- Minimise the CVaR of energy cost: the mean of the worst 10% of bills
- Hard constraint
- probability that any basin's oxygen drops below 2.0 mg/L ≤ 5%
The engine: Vertex Detector
A tail-risk (CVaR) objective plus a chance constraint over integers then Auto then Vertex Detector.
The model
Stage integer blower steps per basin to minimise the upper-tail (CVaR) energy cost while keeping dissolved oxygen above the minimum 95% of the time.
InputDecision (the Optimizer changes it)Calculated or uncertain (sampled each iteration)Objective
Parameters
| Energy $/step | 34.00 |
|---|---|
| O2 transfer per step | 0.60 |
| Min dissolved O2 | 2.00 |
Units (decision highlighted)
| Basin | Blower steps (dec) | Influent load (unc.) | O2 delivered | Energy $ |
|---|---|---|---|---|
| Basin 1 | 3 | uncertain | calculated | uncertain |
| Basin 2 | 3 | uncertain | calculated | uncertain |
| Basin 3 | 3 | uncertain | calculated | uncertain |
| Basin 4 | 3 | uncertain | calculated | uncertain |
Results
| Energy cost ($): objective | calculated |
|---|---|
| Lowest basin O2: constraint | calculated |
Decision cells hold starting values: the workbook opens at the starting plan above, and the Optimizer finds its plan when you run it. The figures are illustrative.
Run it yourself. Open the workbook with ModelRisk, open the Optimizer from the ribbon (the saved task opens with it) and press Start.
Glossary
- CVaR
- conditional value-at-risk — the average of the worst-case tail of a distribution
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Download the workbook and run the Optimizer. It opens in Excel with ModelRisk.
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An illustrative example: the figures are invented for teaching. Last updated 9 October 2026.