Vose SoftwareModelRisk Optimizer example · Pharma and biotech
Cold-Chain Vaccine Micro-Depot
How many coolers and backup batteries per depot keep temperature excursions to essentially zero?
The optimisation problem
Lowest mean capital cost
- Decide
- Coolers and backup batteries for 4 depots, 0 to 6
- Goal
- Lowest mean capital cost
- Limit
- 90th percentile of excursion hours no more than 0
- Engine
- Vertex Detector
What the Optimizer found
| Starting plan | Optimizer’s plan | |
|---|---|---|
| Depot 1 · coolers | 2 | 0 |
| Depot 1 · batteries | 2 | 3 |
| Depot 2 · coolers | 2 | 0 |
| Depot 2 · batteries | 2 | 3 |
| Depot 3 · coolers | 2 | 3 |
| Depot 3 · batteries | 2 | 1 |
| Depot 4 · coolers | 2 | 0 |
| Depot 4 · batteries | 2 | 3 |
| Goal: Mean total capex ($) | 24,000 | 17,400 |
| Limit: 90th percentile of worst excursion hours, at most 0 | 0 met | 0 met |
ModelRisk Optimizer run on 13 Oct 2026: the Vertex Detector engine, with Turbo simulation, tried 350 plans, each simulated with 1,200 samples, in 3 seconds. Both plans above were then simulated again with the same 10,000 samples.
What the workbook models
Four vaccine micro-depots must ride through uncertain grid outages (lognormal). Coolers hold cold longer and batteries run coolers during an outage. An excursion (warming) occurs when the outage outlasts the backup.
Decision, objective and constraint
- Decision
- 4×2 integer counts (coolers, batteries), each 0 to 6
- Objective
- Minimise Mean total capex
- Hard constraint
- 90th-percentile of the worst excursion hours ≤ 0 (a cold-chain integrity limit)
The engine: Vertex Detector
A 90th-percentile constraint over integers is a thin, noisy feasible boundary; Auto then Vertex Detector.
The model
Size the coolers and backup batteries so temperature excursions happen on fewer than 1 day in 10 (90th-percentile ≤ 0 hours).
InputDecision (the Optimizer changes it)Calculated or uncertain (sampled each iteration)Objective
Parameters
| Cooler capex ($/unit) | 1,800 |
|---|---|
| Battery capex ($/unit) | 1,200 |
| Grid-outage hours (mean) | 4.00 |
| Cooling hours per battery | 3.00 |
Units (decision highlighted)
| Site | Coolers (dec) | Batteries (dec) | Outage h (unc.) | Excursion h |
|---|---|---|---|---|
| Depot 1 | 2 | 2 | uncertain | calculated |
| Depot 2 | 2 | 2 | uncertain | calculated |
| Depot 3 | 2 | 2 | uncertain | calculated |
| Depot 4 | 2 | 2 | uncertain | calculated |
Results
| Total capex ($): objective | calculated |
|---|---|
| Worst excursion hours: 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
- Excursion
- time a vaccine spends above its safe temperature
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.