Vose SoftwareModelRisk Optimizer example · Venues and events
Stadium Egress: Gate-Lane Staffing
How many lanes to open at each gate so the crowd clears within 8 minutes on 95% of nights?
The optimisation problem
Lowest mean staffing cost
- Decide
- Open lanes at 6 gates, 1 to 12
- Goal
- Lowest mean staffing cost
- Limit
- Crowd clear within 8 minutes on 95% of nights
- Engine
- Vertex Detector
What the Optimizer found
| Starting plan | Optimizer’s plan | |
|---|---|---|
| Gate 1 | 3 | 2 |
| Gate 2 | 3 | 2 |
| Gate 3 | 3 | 1 |
| Gate 4 | 3 | 2 |
| Gate 5 | 3 | 2 |
| Gate 6 | 3 | 2 |
| Goal: Mean total staffing cost ($) | 1,710 | 1,045 |
| Limit: 95th percentile of evacuation time (min), at most 8 | 4.31 met | 7.54 met |
ModelRisk Optimizer run on 13 Oct 2026: the Vertex Detector engine, with Turbo simulation, tried 229 plans, each simulated with 10,000 samples, in 3 seconds. Both plans above were then simulated again with the same 10,000 samples.
What the workbook models
Six stadium gates each face an uncertain crowd surge (lognormal). Opening more lanes clears a gate faster but costs staff. Evacuation time is the slowest gate (a non-smooth MAX).
Decision, objective and constraint
- Decision
- 6 integer lane counts, each 1 to 12
- Objective
- Minimise Mean total staffing cost
- Hard constraint
- 95th-percentile evacuation time ≤ 8 minutes
The engine: Vertex Detector
Percentile of a non-smooth MAX over integer decisions then flat penalty wall; Auto then Vertex Detector.
The model
Open integer lanes at each gate so the 95th-percentile evacuation time stays within 8 minutes at least cost.
InputDecision (the Optimizer changes it)Calculated or uncertain (sampled each iteration)Objective
Parameters
| Staff cost per lane ($) | 95 |
|---|---|
| Crowd per gate (mean, k) | 7.00 |
| Lane throughput (k/min) | 1.10 |
Units (decision highlighted)
| Gate | Lanes (dec) | Crowd k (unc.) | Clear time min |
|---|---|---|---|
| Gate 1 | 3 | uncertain | calculated |
| Gate 2 | 3 | uncertain | calculated |
| Gate 3 | 3 | uncertain | calculated |
| Gate 4 | 3 | uncertain | calculated |
| Gate 5 | 3 | uncertain | calculated |
| Gate 6 | 3 | uncertain | calculated |
Results
| Total staffing cost ($): objective | calculated |
|---|---|
| Evacuation time (min): 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
- Evacuation time
- the clearance time of the slowest gate
Find similar models
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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.