BIZOMAT MAKEOS · Money
Learning-Curve Quote (Batch Hours, Cost and Price per Unit)
With the learning curve, how many hours will this batch take, what does each unit cost, and does the price I am offered give my margin?
Quote for a batch where labour time falls with repetition: time for the first and last unit, cumulative and average hours on the unit learning curve (as the learning curve tool), set-up, labour and machine cost at your hourly rate, material per unit, overhead, total and unit cost, the price per unit for your margin, and the margin the offered price gives.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Hours for the first unit | h | Hours the first unit takes (estimate or prototype record). |
| Learning rate | % | Learning rate: each doubling of quantity multiplies the unit time by this (80–90% typical for manual assembly). |
| Units in the batch | Units in the batch. | |
| Set-up hours | h | Set-up hours for the batch. |
| Labour and machine rate | $/h | Hourly rate for labour plus machine (for example from the machine hour rate tool). |
| Material per unit | $ | Material and bought-in parts per unit. |
| Overhead on cost | % | Overhead added to the direct cost. |
| Margin wanted on price | % | Margin you want as a share of the selling price. |
| Price offered per unit | $ | Price per unit the customer offers. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Hours for the first unit
- What it is
- The hours needed to make the very first unit, from a prototype record or an estimate; the starting point of the learning curve.
- Units and format
- Enter a number in h: hours. The form accepts 0.000001 h to 100000 h. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 h as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Every unit’s hours, and so labour cost, scale in direct proportion.
What this means: Learning rate
- What it is
- The learning rate: each time the cumulative quantity doubles, the time per unit becomes this percentage of what it was.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 50% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 85% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A lower rate cuts the hours for later units and so lowers the unit cost.
- Get it right
- A lower percentage means faster learning. Base it on similar past jobs.
What this means: Units in the batch
- What it is
- The number of units in this batch. The tool counts them from the first unit ever made.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 100000. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- The curve starts at unit 1, so a repeat batch is costed as if no learning carried over from earlier batches.
What this means: Set-up hours
- What it is
- The one-off hours to prepare for the batch, such as machine set-up, tooling and first-off inspection, charged at the same hourly rate.
- Units and format
- Enter a number in h: hours. The form accepts 0 h to 100000 h. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6 h as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Labour and machine rate
- What it is
- The cost of one hour of labour plus machine time, applied to both production and set-up hours.
- Units and format
- Enter a number in $/h: money per hour. The form accepts $0/h to $10000/h. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with $105/h as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Material per unit
- What it is
- The cost of material and bought-in parts for one unit.
- Units and format
- Enter a number in $: an amount of money; use one currency for every money input. The form accepts $0 to $10000000. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with $40 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Overhead on cost
- What it is
- Overhead added as a percentage on top of the direct labour, machine and material cost.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 200%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Margin wanted on price
- What it is
- The profit you want as a percentage of the selling price; the price is unit cost ÷ (1 − margin).
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 90%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Margin on price, not markup on cost; the two give different prices for the same percentage.
What this means: Price offered per unit
- What it is
- The price per unit the customer has offered, compared with your unit cost to show the margin it gives.
- Units and format
- Enter a number in $: an amount of money; use one currency for every money input. The form accepts $0 to $100000000. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with $900 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Method and formulas
- Unit time T_x = T₁ x^b with b = log₂(learning rate); cumulative hours = Σ T_x (as the learning curve tool).
- Cost = (cumulative + set-up) × rate + material × n, plus overhead.
- Price for margin m = unit cost ÷ (1 − m); margin offered = 1 − unit cost ÷ offer.
- Example: 50 units take 255.13 h; unit cost 676.63, price for 20% margin 845.79; the offer gives 24.819%.
Limitations
- Unit learning curve (Crawford); the cumulative-average (Wright) model gives different numbers.
- Learning stops at a floor set by machine time; check later units against standard times.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Quote a first production batch
- Decide whether an offered price is acceptable
- Show how cost falls with batch size
Who it is for
- Estimators
- Production managers
- Business owners
What you get
- Unit and cumulative hours
- Cost in total and per unit
- Price for the margin and the offered margin
Interpreting the result
- The first units cost far more than the average: quote small first batches with care.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 146, 134–146. Topic reference; no source tables or recommended settings are reproduced.
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Open the Learning-Curve Quote (Batch Hours, Cost and Price per Unit) calculator