Vose SoftwareModelRisk Optimizer example · Healthcare
Radiotherapy: Beam-Weight Plan
What beam weights maximise a robust (P10) tumour dose while keeping the organ within tolerance 95% of the time?
The optimisation problem
Highest 10th-percentile tumour dose
- Decide
- 5 beam weights, 0 to 5
- Goal
- Highest 10th-percentile tumour dose
- Limit
- At most a 5% chance the organ dose exceeds 26 Gy
- Engine
- Vertex Detector
What the Optimizer found
| Starting plan | Optimizer’s plan | |
|---|---|---|
| Beam 1 | 2 | 5 |
| Beam 2 | 2 | 0 |
| Beam 3 | 2 | 5 |
| Beam 4 | 2 | 5 |
| Beam 5 | 2 | 5 |
| Goal: 10th percentile of tumour dose (Gy) | 29.0 | 59.3 |
| Limit: Chance organ dose (Gy) is above 26, at most 5% | 0.01% met | 0.29% met |
ModelRisk Optimizer run on 13 Oct 2026: the Vertex Detector engine, with Turbo simulation, tried 302 plans, each simulated with 1,500 samples, in 4 seconds. Both plans above were then simulated again with the same 10,000 samples.
What the workbook models
Five treatment beams deposit dose in the tumour and, unavoidably, in a nearby organ. Daily setup error is uncertain (normal). You choose an integer weight 0 to 5 per beam.
Decision, objective and constraint
- Decision
- 5 integer beam weights, each 0 to 5
- Objective
- Maximise the 10th-percentile tumour dose (a robust dose)
- Hard constraint
- probability the organ dose exceeds 26 Gy ≤ 5%
The engine: Vertex Detector
A percentile objective plus a chance constraint over integer weights then Auto then Vertex Detector.
The model
Pick integer weights for each beam to maximise the 10th-percentile tumour dose while sparing the organ at risk with 95% assurance.
InputDecision (the Optimizer changes it)Calculated or uncertain (sampled each iteration)Objective
Parameters
| Organ tolerance (Gy) | 26.00 |
|---|---|
| Setup error σ | 0.60 |
Units (decision highlighted)
| Beam | Weight (dec 0-5) | Tumour k | Organ k | Tumour dose | Organ dose |
|---|---|---|---|---|---|
| Beam 1 | 2 | 3.10 | 1.20 | uncertain | uncertain |
| Beam 2 | 2 | 2.70 | 1.60 | uncertain | uncertain |
| Beam 3 | 2 | 3.40 | 0.90 | uncertain | uncertain |
| Beam 4 | 2 | 2.90 | 1.40 | uncertain | uncertain |
| Beam 5 | 2 | 3.20 | 1.10 | uncertain | uncertain |
Results
| Tumour dose (Gy): objective | calculated |
|---|---|
| Organ dose (Gy): 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
- P10 dose
- the tumour dose achieved on the worst 10% of days — a robustness measure
Find similar models
- Product
- Type
- Application
- Uses
Download the workbook and run the Optimizer. It opens in Excel with ModelRisk.
Related example models
- ModelChoice★★★★★Hospital Equipment DecisionBuy premium or standard imaging equipment, lease it, or share it with a partner hospital?Two decisions and four chance events, driven by linked inputs. Best first decision: Buy Premium Equipment, expected value $44.8m.
- ModelRiskOptimizer★★★★★Snowmaking: Gun AllocationHow many snow guns per slope open most of the mountain on a marginal cold night at least cost?Spreads snow guns over six slopes at the lowest water and power cost, with five slopes open with 90% assurance.
- ModelRiskOptimizer★★★★★Stadium Egress: Gate-Lane StaffingHow many lanes to open at each gate so the crowd clears within 8 minutes on 95% of nights?Staffs the lanes at six gates at the lowest mean cost, so the crowd clears within eight minutes on 95% of nights.
An illustrative example: the figures are invented for teaching. Last updated 9 October 2026.