Vose SoftwareModelRisk example · Pharmaceuticals and biotech
Batch Yield and Manufacturing Capacity
How many batches must we plan to make enough drug substance for the launch year?
From the model’s saved run
How many batches?
Drug substance made and the chance of meeting the 120 kg needed, by campaign size.
Line chart: Failure rate uncertain, Failure rate taken as known.
| Campaign | Cost US$m | Expected kg | 1 in 20 kg (P5) | Demand met rate uncertain | Demand met rate known |
|---|---|---|---|---|---|
| 22 batches (22 + 0 contract) | 13.2 | 110.2 | 92.5 | 14.6% | 16.2% |
| 23 batches (23 + 0 contract) | 13.8 | 115.2 | 96.9 | 36.1% | 42.0% |
| 24 batches (24 + 0 contract) | 14.4 | 120.2 | 101.3 | 56.6% | 67.6% |
| 25 batches (24 + 1 contract) | 15.8 | 125.2 | 105.8 | 72.4% | 84.8% |
| 26 batches (24 + 2 contract) | 17.2 | 130.2 | 110.6 | 83.4% | 93.9% |
| 27 batches (24 + 3 contract) | 18.6 | 135.2 | 115.1 | 90.5% | 97.7% |
| 28 batches (24 + 4 contract) | 20.0 | 140.3 | 119.6 | 94.7% | 99.1% |
| 29 batches (24 + 5 contract) | 21.4 | 145.2 | 123.7 | 97.0% | 99.7% |
| 30 batches (24 + 6 contract) | 22.8 | 150.3 | 128.3 | 98.2% | 99.9% |
Demand met: the chance that the batches needed are no more than the campaign (VoseSimProbability).
Green: at least the 95% wanted. Rate known: the failure rate taken as exactly 3 in 40.
The business question
A biotech company is preparing to launch a monoclonal antibody and needs 120 kg of drug substance in the launch year. Each batch runs in a 2,000-litre bioreactor. The titre at harvest is between 3 and 5 grams a litre, and purification recovers 60–75% of it — about 5.5 kg a batch.
But batches fail: contamination or a result out of specification costs the whole batch, and 3 of the plant's last 40 batches failed. The plant can run 24 batches in the year at about US$0.6 million each; more must be booked now at a contract manufacturer at US$1.4 million each. On the average figures 24 batches make 120 kg exactly.
How many should the company plan?
- Who it is for
- Manufacturing and supply planning, CMC and technical operations teams, launch planning.
- Main outputs
- For 22 to 30 batches: the cost of the campaign, the drug substance expected and the chance of meeting demand — with the failure rate uncertain and with it taken as known · the batches needed for the confidence you set (95% as shipped) · the failure rate's uncertainty.
How the model works
Three sheets after this one, read from left to right. Each one feeds the next.
Inputs sheet
The drug substance needed; the bioreactor volume and the low, most likely and high titre and recovery; the number of batches run and failed in the plant's record. The plant's capacity and the cost of a batch in the plant and at the contract manufacturer.
Batches sheet
The failure rate is drawn from a Beta distribution: 3 failures in 40 batches with a uniform prior. Each batch draws a uniform number that decides whether it succeeds — once with the uncertain rate and once with the rate taken as known, 3 in 40 — and a titre and recovery that give its yield.
Cumulative output shows what a campaign of any size would make, and the batches needed are the batches until it reaches the demand.
Results sheet
For each campaign size from 22 to 30 batches: cost, drug substance and the chance of meeting demand both ways — the chance that the batches needed are no more than the campaign. The batches needed for the confidence on the Inputs sheet; the uncertainty in the failure rate.
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The results in detail
The failure rate
What the plant's record says — and does not say — about the next batches.
Histogram of Batch failure rate from the saved simulation.
| Measure | Unit | Value |
|---|---|---|
| Failure rate taken as known (3 in 40) | share | 7.5% |
| Failure rate: mean of the Beta | share | 9.5% |
| …90th percentile | share | 15.6% |
| Batches for 95% confidence, rate uncertain | batches | 29 |
| Batches for 95% confidence, rate taken as known | batches | 27 |
The percentile of the batches needed: the smallest campaign that meets demand with that confidence.
How to read these results
- A successful batch yields about 5.5 kg and about one batch in ten fails, so the plant's 24 batches make about 120 kg on average — exactly the demand. That gives only a 57% chance of meeting it.
- Every batch beyond the plant's 24 must be booked now at the contract manufacturer, at US$1.4 million. A 95% chance of 120 kg takes 29 batches — five at the contract manufacturer, US$21.4 million in all against US$14.4 million for the plant's 24.
- A spreadsheet that takes the failure rate as exactly 3 in 40 (7.5%) would plan 27 batches, and overstate its confidence: 27 batches meet demand about 90% of the time, not 98%. A record of 40 batches cannot pin the rate down — the Beta averages 9.5% and exceeds 15.6% one time in ten.
- Failures matter more than the batch-to-batch variation in titre and recovery, because each one costs a whole batch. Learning the failure rate better — every batch adds to the record — or cutting it, through a root-cause study of the three failures, reduces the batches needed most.
See it move. Open the workbook, change an input on the Inputs sheet and run the simulation: every table and chart on this page updates in Excel.
Inputs and assumptions
Every assumption in the model, with its uncertainty and where it comes from. The figures are illustrative.
Demand 2 inputs
| Assumption | Unit | Value |
|---|---|---|
| Drug substance needed in the launch yearLaunch stock and the first year's sales. | kg | 120 |
| Confidence wanted of meeting demandThe campaign should meet demand with at least this chance. | probability | 95% |
Batch yield 3 inputs
Yield of a successful batch = volume × titre × recovery.
| Assumption | Unit | Uncertainty | Low | Most likely | High |
|---|---|---|---|---|---|
| Bioreactor working volume | litres | Fixed | 2,000 | ||
| Titre at harvestDrawn for each batch on the Batches sheet. | g / litre | PERT · drawn elsewhere | 3.0 | 4.0 | 5.0 |
| Purification recoveryDrawn for each batch on the Batches sheet. | of harvest | PERT · drawn elsewhere | 60% | 70% | 75% |
The plant's record 2 inputs
Batch failures: contamination or a result out of specification.
| Assumption | Unit | Value |
|---|---|---|
| Batches runThe last two years. | batches | 40 |
| Batches failed | batches | 3 |
Capacity and costs 3 inputs
| Assumption | Unit | Value |
|---|---|---|
| Batches the plant can run in the year | batches | 24 |
| Cost of a batch in the plantMedia, resins, labour, testing. | US$m | 0.60 |
| Cost of a batch at the contract manufacturerBooked now, paid whether needed or not. | US$m | 1.40 |
Units and conventions
- Quantities
- Drug substance in kg; titre in grams per litre.
- Money
- US$ million (US$m).
- Campaign
- The batches planned for the year: the plant's first, then the contract manufacturer's.
- Rate known
- The failure rate taken as exactly 3 in 40, as a spreadsheet with a single number would.
Key assumptions and limitations
- Batches
- Independent given the failure rate; a failed batch yields nothing; titre and recovery vary from batch to batch.
- Failure rate
- The same in the plant and at the contract manufacturer; a uniform prior before the record.
- Timing
- All planned batches complete within the year; a failed batch is not replaced.
- Data
- The company, the product and all figures are invented for this example.
How to use it
- Enter your demand, batch size, titre and recovery ranges on the Inputs sheet.
- Enter your plant's record — batches run and failed — and its capacity and costs.
- Run a simulation from the ModelRisk ribbon (10,000 samples with a fixed seed are set).
- Set the confidence you need on the Inputs sheet (95% as shipped): Results shows the campaign size that reaches it. Book the extra batches.
ModelRisk functions used
- VoseBeta
- The batch failure rate from the plant's record, with its uncertainty.
- VoseBernoulli
- Whether each batch succeeds; its U argument shares one uniform draw between the two versions.
- VoseUniform
- The uniform draw of each batch.
- VoseOutput, VoseSimMean, VoseSimPercentile, VoseSimProbability
- Outputs and their statistics on the Results sheet: the chance that the batches needed are no more than a campaign is VoseSimProbability.
- VosePERT
- Titre and recovery of each batch, drawn on the Batches sheet.
Further reading
- Monte Carlo simulation explained (Vose guide)
- Shukla, A. A. & Thömmes, J. (2010). Recent advances in large-scale production of monoclonal antibodies. Trends in Biotechnology 28(5), 253–261.
- Vose, D. (2008). Risk Analysis: A Quantitative Guide, 3rd edition. Wiley — the Beta distribution for a probability estimated from data.
Download the workbook and run it yourself. It opens in Excel with ModelRisk. The free trial runs every example model.
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An illustrative example: the figures are invented for teaching and do not describe a real company, project or asset. Last updated 9 October 2026.