Vose SoftwareModelRisk example · Manufacturing
Capacity Expansion Decision
How many presses should we add? Seasonal, growing, uncertain demand against capacity, overtime and a subcontractor.
From the model’s saved run
How many presses?
Five-year cost of each option (US$k): new presses net of what is left of them, fixed costs, overtime and subcontracting premiums, and lost contribution.
| Option | Plan average forecast | Mean simulated | 90th pct 1 time in 10 | Demand met, mean | Chance cheapest |
|---|---|---|---|---|---|
| No new press | 426 | 920 | 2,313 | 93.7% | 47% |
| One new press | 471 | 765 | 1,437 | 98.0% | 35% |
| Two new presses | 887 | 994 | 1,190 | 99.4% | 14% |
| Three new presses | 1,326 | 1,364 | 1,398 | 99.8% | 5% |
| Mean five-year cost by component (US$k) | No new press | One new press | Two new presses | Three new presses | Saved by one press |
|---|---|---|---|---|---|
| New presses, net of what is left of them | – | 264 | 528 | 792 | −264 |
| Their fixed costs | – | 174 | 348 | 522 | −174 |
| Overtime premium | 72 | 40 | 20 | 11 | 32 |
| Subcontracting premium | 168 | 65 | 26 | 14 | 103 |
| Lost contribution | 681 | 222 | 72 | 25 | 458 |
| Five-year cost | 920 | 765 | 994 | 1,364 | 156 |
S-curve (cumulative probability) of No new press, One new press, Two new presses, Three new presses from the saved simulation.
The business question
A moulder makes plastic housings for air-conditioning units on four injection-moulding presses. Demand averages about 78,000 parts a month, peaks in late spring at 15% above the average, and is expected to grow about 6% a year — but a new customer programme could add more, and a lost one could stop growth.
The presses make about 80,000 parts a month; Saturday overtime adds up to 10%, and a subcontractor can take up to 10,000 parts a month at a premium. The housings are made to order for each customer's model, so the plant cannot build stock ahead of the peak: what cannot be made in its month is lost.
A new press costs US$400,000 installed and takes about six months to arrive. The plan, built on the average forecast, finds overtime and the subcontractor cheaper than a new press. Is it right — and if a press is needed, one or two?
- Who it is for
- Operations and plant managers, capacity planners, manufacturing finance and capital committees.
- Main outputs
- The five-year cost of each option — new presses net of their remaining value, fixed costs, overtime, subcontracting and lost sales — on the plan and simulated: mean, 1 time in 10 and the chance each option is cheapest · the share of demand met · monthly demand against capacity · what drives the value of a new press.
How the model works
Three sheets after this one, read from left to right. Each one feeds the next.
Inputs sheet
Today's demand before seasonality, its growth (uncertain) and volatility; twelve monthly seasonal factors; the presses, their output at full efficiency and the plant's OEE. The limits and costs of overtime and subcontracting; the contribution lost on a lost sale. The price, fixed cost, delivery time and remaining value of a new press; the discount rate.
Capacity sheet
VoseTimeSeasonalGBM draws sixty months of demand, and each month's OEE is drawn around the plant's level. Each option — no new press, one, two or three — is the same block of rows: the presses make what they can in regular time. Overtime, then the subcontractor, take what they can of the shortfall; the rest is lost.
The block ends with the option's five-year cost by component, discounted to today. The plan runs the same blocks on the average forecast.
Results sheet
Each option's five-year cost on the plan and in the simulation. The share of demand it meets and the chance it is cheapest; where the cost comes from; the saving from one press and the protection from a second; monthly demand against capacity; what drives the saving.
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The results in detail
What the plan misses
The average forecast against the simulated futures.
Line chart: 90th percentile, Median, Mean, 10th percentile, Most it can supply today, …with one new press.
| Measure | Unit | Value |
|---|---|---|
| Cost of no new press: simulated mean ÷ plan | ratio | 2.16 |
| Saving from one new press, on the plan | US$k | −45 |
| Saving from one new press, simulated mean | US$k | 156 |
| Chance that one new press saves money | 53.4% | |
| A second press: extra mean cost | US$k | 230 |
| A second press: lower 1-in-10 cost | US$k | 247 |
What decides the value of a press?
Lowest and highest mean saving from a new press over ten equal groups of each input (VoseSimSensitivityMean), drawn from the overall mean.
Tornado chart: the inputs ranked by how far the mean output moves across each input’s range.
The ranking as a table 3 inputs
| Input (ranked by influence) | Lowest mean | Highest mean | Rank |
|---|---|---|---|
| Growth in demand | −152 | 540 | 1 |
| Plant OEE, sustained | 54 | 266 | 2 |
| Delivery and installation | 141 | 172 | 3 |
How to read these results
- On the plan — demand growing steadily at 6% a year, the presses at 80% OEE every month — overtime and the subcontractor absorb the peaks for two summers, and only the last three summers lose some sales. Doing nothing costs about US$426,000 over five years, US$45,000 less than a new press: the plan says wait.
- Across the simulated futures, doing nothing costs about US$920,000 on average — more than twice the plan — and more than US$2.3 million one time in ten. The plan's flaw is its averages: a shortfall costs up to US$2.20 a part, while spare capacity costs nothing extra, so a strong summer or a month of low OEE costs far more than a weak one saves.
One new press has the lowest average cost, about US$765,000: it saves about US$156,000 on average and keeps 98% of demand, against 94% without it. Yet it saves money in only 53% of futures, and doing nothing is the cheapest option in 47% of them — when growth is slow, the press stands partly idle.
Its value is that it cuts the bad futures: the 1-in-10 cost falls from US$2.3 million to US$1.4 million.
- Where the saving comes from (the table by component): the press costs about US$264,000 net of what is left of it, plus US$174,000 of fixed costs. In return it cuts the lost contribution by about US$458,000 and the overtime and subcontracting premiums by about US$135,000.
- A second press costs about US$230,000 more on average and lowers the 1-in-10 cost by about as much: it is insurance against strong growth, worth buying only if a lost customer would cost more than the contribution on the parts not delivered. A third press costs the most on average and is the cheapest option in only 5% of futures.
Growth drives the value of a press: the mean saving runs from a loss of about US$150,000 in the tenth of futures with the slowest growth to US$540,000 in the tenth with the fastest. A lower OEE makes it more valuable. The delivery time hardly matters, because the shortages come in later summers.
Before buying a second press, try cheaper flexibility on the Inputs sheet: a larger subcontractor, or more overtime.
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 3 inputs
Demand for the housings and its growth.
| Assumption | Unit | Uncertainty | Low | Most likely | High |
|---|---|---|---|---|---|
| Demand today, before seasonalityThe average month of the last twelve. | k parts / month | Fixed | 78 | ||
| Growth in demandSales plan 6%; a new customer programme could add more, a lost one could stop growth. | per year | PERT | 0.0% | 6.0% | 15.0% |
| Volatility of the demand levelChanges that persist: a month's change carries into the following months. | per month | Fixed | 3.0% | ||
Seasonality 13 inputs
Each month's demand as a multiple of the average month.
| Assumption | Unit | Value | Uncertainty |
|---|---|---|---|
| JanuaryFrom the last three years' sales; the twelve factors average 1. | × average month | 0.85 | Fixed |
| February | × average month | 0.88 | Fixed |
| March | × average month | 0.98 | Fixed |
| April | × average month | 1.04 | Fixed |
| May | × average month | 1.10 | Fixed |
| June | × average month | 1.15 | Fixed |
| July | × average month | 1.12 | Fixed |
| August | × average month | 1.05 | Fixed |
| September | × average month | 1.02 | Fixed |
| October | × average month | 0.98 | Fixed |
| November | × average month | 0.95 | Fixed |
| December | × average month | 0.88 | Fixed |
| Average of the twelve factorsMust be 1.00. | 1.00 | Calculated |
The presses 5 inputs
Today's presses and their efficiency.
| Assumption | Unit | Uncertainty | Low | Most likely | High |
|---|---|---|---|---|---|
| Presses today | presses | Fixed | 4 | ||
| Output of one press at full efficiencyTwo shifts, five days a week. | k parts / month | Fixed | 25 | ||
| Plant OEE, sustainedOverall equipment effectiveness: availability × speed × quality. Last year 79%. | of full efficiency | PERT | 72% | 80% | 85% |
| A bad month: OEE up to … below the plant's levelBreakdowns, material problems, absences. | points | Fixed | 10% | ||
| A good month: OEE up to … above the plant's level | points | Fixed | 4% | ||
Overtime, subcontracting and lost sales 5 inputs
Used in this order when demand exceeds regular output.
| Assumption | Unit | Value |
|---|---|---|
| Overtime: extra output at mostSaturday shifts. | of regular output | 10% |
| Overtime: extra costThe overtime pay premium. | US$ per part | 0.30 |
| Subcontractor: capacityA moulder with spare presses; the tools are already qualified. | k parts / month | 10 |
| Subcontractor: extra costIts price less our own variable cost. | US$ per part | 0.80 |
| Lost sale: contribution lostPrice less variable cost: the customer buys elsewhere. | US$ per part | 2.20 |
New presses 4 inputs
Ordered now.
| Assumption | Unit | Uncertainty | Low | Most likely | High |
|---|---|---|---|---|---|
| Price of a press, installed | US$k | Fixed | 400 | ||
| Fixed cost of a pressMaintenance, energy and floor space, from the month it works. | US$k / month | Fixed | 4.0 | ||
| Delivery and installationRounded to whole months; the press makes parts from the month after. | months | PERT | 4.0 | 6.0 | 10.0 |
| Value left after five yearsA ten-year life: after five years the press is half used. | of the price | Fixed | 50% | ||
Finance 1 input
| Assumption | Unit | Value |
|---|---|---|
| Discount rateCost of capital. | per year | 8.0% |
Units and conventions
- Parts
- Thousand parts a month.
- Money
- US$ thousand (US$k), today's prices; costs per part in US$.
- Months
- Month 1 is January next year; costs are discounted monthly to today.
- Five-year cost
- New presses at their price less the present value of what is left of them after five years, plus their fixed costs, the overtime and subcontracting premiums, and the contribution lost on lost sales — all discounted.
- Plan
- The same calculation with growth at its most likely rate and no volatility, OEE at its most likely level every month, and delivery at its most likely time.
Key assumptions and limitations
- Demand
- A seasonal geometric Brownian motion: changes in the level persist, and the seasonal pattern repeats every year.
- Supply
- Regular time first, then overtime, then the subcontractor; demand that cannot be met in its month is lost, not carried forward.
- Presses
- All presses identical; new presses are ordered now and make parts from the month after delivery; after five years a press is worth half its price.
- Data
- The company and all figures are invented for this example.
How to use it
- Enter your demand, its growth and its seasonal pattern on the Inputs sheet.
- Enter your presses and their efficiency, and the limits and costs of overtime, subcontracting and lost sales.
- Run a simulation from the ModelRisk ribbon (10,000 samples with a fixed seed are set).
- Compare the options on the mean cost and on bad years; try a larger subcontractor or a faster delivery.
Simulate this model with ModelRisk’s classic engine: it does not run in Turbo mode yet.
ModelRisk functions used
- VoseTimeSeasonalGBM
- Sixty months of demand: a growing, uncertain level with a repeating seasonal pattern (array function).
- VosePERT
- The plant's sustained OEE, each month's OEE around it, the growth of demand and the delivery time.
- VoseInput, VoseOutput
- Mark the uncertain inputs, and the outputs recorded at every sample.
- VoseSimMean, VoseSimPercentile, VoseSimProbability
- Statistics of the simulation for the tables and charts on the Results sheet.
- VoseSimSensitivityMean
- The tornado chart: every VoseInput ranked by how far the mean saving from a press moves across its range.
Further reading
- Sensitivity analysis in Excel: a tornado chart step by step (Vose guide)
- Stevenson, W. J. (2021). Operations Management, 14th edition. McGraw-Hill — strategic capacity planning.
- Savage, S. L. (2009). The Flaw of Averages. Wiley.
- de Neufville, R. & Scholtes, S. (2011). Flexibility in Engineering Design. MIT Press.
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.