Vose SoftwareModelRisk Optimizer example · Leisure
Snowmaking: Gun Allocation
How many snow guns per slope open most of the mountain on a marginal cold night at least cost?
The optimisation problem
Lowest mean water and power cost
- Decide
- Snow guns on 6 slopes, 0 to 20
- Goal
- Lowest mean water and power cost
- Limit
- At least 5 of 6 slopes open, with 90% assurance
- Engine
- Vertex Detector
What the Optimizer found
| Starting plan | Optimizer’s plan | |
|---|---|---|
| Slope 1 | 4 | 20 |
| Slope 2 | 4 | 16 |
| Slope 3 | 4 | 11 |
| Slope 4 | 4 | 20 |
| Slope 5 | 4 | 20 |
| Slope 6 | 4 | 11 |
| Goal: Mean total cost ($) | 1,680 | 6,860 |
| Limit: Chance slopes open (of 6) is below 5, at most 10% | 100% not met | 9.9% met |
ModelRisk Optimizer run on 13 Oct 2026: the Vertex Detector engine tried 147 plans, each simulated with 10,000 samples, in 302 seconds. Both plans above were then simulated again with the same 10,000 samples.
What the workbook models
Six slopes share a snowmaking budget. Each cold window has an uncertain wet-bulb temperature (normal) that sets how much snow a gun can make. A slope opens once it has enough snow.
Decision, objective and constraint
- Decision
- 6 integer gun counts, each 0 to 20
- Objective
- Minimise Mean water+power cost
- Hard constraint
- ≥90% assurance that at least 5 of 6 slopes open
The engine: Vertex Detector
A chance constraint on a count of open slopes over integers then Auto then Vertex Detector.
The model
Allocate integer snow guns per slope to minimise water+power cost while opening at least 5 of 6 slopes on 90% of cold windows.
InputDecision (the Optimizer changes it)Calculated or uncertain (sampled each iteration)Objective
Parameters
| Cost $/gun-night | 70 |
|---|---|
| Snow per gun (cm) | 5.00 |
| Open threshold (cm) | 30.00 |
Units (decision highlighted)
| Slope | Guns (dec) | Wet-bulb °C (unc.) | Snow made cm | Open? |
|---|---|---|---|---|
| Slope 1 | 4 | uncertain | calculated | calculated |
| Slope 2 | 4 | uncertain | calculated | calculated |
| Slope 3 | 4 | uncertain | calculated | calculated |
| Slope 4 | 4 | uncertain | calculated | calculated |
| Slope 5 | 4 | uncertain | calculated | calculated |
| Slope 6 | 4 | uncertain | calculated | calculated |
Results
| Total cost ($): objective | calculated |
|---|---|
| Slopes open (of 6): 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
- Wet-bulb temperature
- the temperature that controls how efficiently guns make snow
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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.