Vose SoftwareModelRisk Optimizer example · Agriculture and food
Greenhouse: CO₂ Enrichment vs Cost
What CO₂ set-point maximises yield without breaching the daily enrichment budget?
The optimisation problem
Highest mean yield
- Decide
- One CO₂ set-point, 400 to 1,200 ppm
- Goal
- Highest mean yield
- Limit
- Enrichment cost no more than $150 a day
- Engine
- BFGS
What the Optimizer found
| Starting plan | Optimizer’s plan | |
|---|---|---|
| CO₂ set-point (ppm) | 700 | 977 |
| Goal: Expected yield index | 22.4 | 35.7 |
| Limit: Enrichment cost ($/day), at most 150 | 78 met | 150 met |
ModelRisk Optimizer run on 13 Oct 2026: the BFGS engine, with Turbo simulation, tried 137 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
A greenhouse enriches CO₂ to lift yield (a smooth concave, diminishing-returns curve) but pays for the gas. Yield carries day-to-day noise (normal).
Decision, objective and constraint
- Decision
- 1 continuous CO₂ set-point, 400 to 1200 ppm
- Objective
- Maximise the Mean yield index
- Hard constraint
- enrichment cost ≤ $150/day
The engine: BFGS
A single continuous variable WITH a hard constraint then Method=Auto routes to the quasi-Newton BFGS line-search engine (not the unconstrained 1-D Brent).
The model
Set the single CO₂ set-point to maximise expected yield subject to a hard enrichment-cost cap.
InputDecision (the Optimizer changes it)Calculated or uncertain (sampled each iteration)Objective
| CO₂ set-point (ppm): decision | 700.00 |
|---|---|
| Cost per 100 ppm ($/day) | 26.00 |
| Cost cap ($/day) | 150 |
| Expected yield index: objective | calculated |
| Enrichment cost ($/day): 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
- Enrichment
- adding CO₂ above ambient (400 ppm) to accelerate photosynthesis
Find similar models
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- Uses
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.