BIZOMAT MAKEOS · Fabrication
Three-Size Stock Cut Planner
How can these pieces fit into equal-length stock bars?
Build a feasible longest-first plan for three part lengths, with end trims, kerf, offcuts and bars to purchase.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Stock bar length | mm | Purchased full-length stock before end trims; all bars use this length. |
| End trim at each end | mm | Length removed at each end, including any trim-cut loss not covered by per-piece kerf. |
| Kerf per finished piece | mm | One kerf per finished piece including the last piece: deliberately conservative. |
| Part 1: finished length | mm | Required cut length including any later machining allowance. |
| Part 1: required pieces | pieces | Whole pieces of this length, up to 100; use 0 to omit this part. |
| Part 2: finished length | mm | Required cut length including any later machining allowance. |
| Part 2: required pieces | pieces | Whole pieces of this length, up to 100; use 0 to omit this part. |
| Part 3: finished length | mm | Required cut length including any later machining allowance. |
| Part 3: required pieces | pieces | Whole pieces of this length, up to 100; use 0 to omit this part. |
| Bars already available | bars | Identical full-length bars already available; shorter offcuts are excluded. |
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: Stock bar length
- What it is
- The full length of each bar you buy or hold, before any end trims are cut off. Every bar in the plan is assumed to be this length.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Longer bars fit more pieces each and can reduce the bars required.
- Get it right
- Measure actual bar length; mill lengths can vary from the nominal order length.
What this means: End trim at each end
- What it is
- The length cut off and discarded at each end of a bar to remove damaged, uneven or out-of-square ends.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Each bar’s usable length falls by twice this value.
- Get it right
- This is per end: the tool removes it twice from every bar.
What this means: Kerf per finished piece
- What it is
- The material lost to the saw cut for each finished piece, set by the blade or cutting process width.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Each piece takes its length plus one kerf from the usable bar.
- Get it right
- Measure the actual cut width; one kerf is reserved for every piece including the last, which is deliberately conservative.
What this means: Part 1: finished length
- What it is
- The length each piece of this part must be cut to, including any machining or squaring allowance you will remove later.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 250 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Longer pieces use more bar and can raise the number of bars needed.
- Get it right
- Add later facing or machining stock to the cut length; the kerf is handled separately.
What this means: Part 1: required pieces
- What it is
- How many pieces of this length the job needs in total, across all bars.
- Units and format
- Enter a number in pieces: pieces. The form accepts 0 pieces to 100 pieces. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6 pieces as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More pieces add length to the plan and can add bars.
- Get it right
- Enter 0 to leave this part out of the plan; include spares or test pieces if you need them.
What this means: Part 2: finished length
- What it is
- The length each piece of this part must be cut to, including any machining or squaring allowance you will remove later.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 180 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Longer pieces use more bar and can raise the number of bars needed.
- Get it right
- Add later facing or machining stock to the cut length; the kerf is handled separately.
What this means: Part 2: required pieces
- What it is
- How many pieces of this length the job needs in total, across all bars.
- Units and format
- Enter a number in pieces: pieces. The form accepts 0 pieces to 100 pieces. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 pieces as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More pieces add length to the plan and can add bars.
- Get it right
- Enter 0 to leave this part out of the plan; include spares or test pieces if you need them.
What this means: Part 3: finished length
- What it is
- The length each piece of this part must be cut to, including any machining or squaring allowance you will remove later.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 90 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Longer pieces use more bar and can raise the number of bars needed.
- Get it right
- Add later facing or machining stock to the cut length; the kerf is handled separately.
What this means: Part 3: required pieces
- What it is
- How many pieces of this length the job needs in total, across all bars.
- Units and format
- Enter a number in pieces: pieces. The form accepts 0 pieces to 100 pieces. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 pieces as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More pieces add length to the plan and can add bars.
- Get it right
- Enter 0 to leave this part out of the plan; include spares or test pieces if you need them.
What this means: Bars already available
- What it is
- How many full-length bars of this stock you already have on hand, used to work out how many more to buy.
- Units and format
- Enter a number in bars: bars. The form accepts 0 bars to 100000 bars. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 bars as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- It does not change the plan, only the number of bars to purchase.
- Get it right
- Count only full-length bars; shorter offcuts are not used by this plan.
Method and formulas
- Enter lengths to at most three decimals in millimetres; calculations use integer micrometres. Usable length is stock minus two end trims.
- Sort pieces longest first and place each into the first bar with room for its length plus one kerf, starting another bar when necessary.
- The ceiling of total piece-plus-kerf length divided by usable bar length is a material lower bound. Matching this bound proves minimum bar count in this model; otherwise the plan is only feasible.
- Example: 1000 mm stock, 5 mm each end and 2 mm kerf, with six 250 mm, four 180 mm and four 90 mm pieces needs 3 bars. Parts = 2580 mm, kerf = 28 mm, trims = 30 mm, offcuts = 362 mm. With 2 bars available, purchase 1.
Limitations
- At most three lengths and 100 pieces each. Mixed stock sizes, mitres, defects, clamping length, shared cuts and reusable offcut inventory are excluded.
- First-fit decreasing is a heuristic. A plan above the lower bound is not claimed optimal.
- One kerf is reserved per finished piece, including the last. End trims include their own cutting loss.
- Default values are worked examples, not recommended settings or material properties.
Typical uses
- cut stock
- saw cutting plan
- material yield
Who it is for
- Fabricators
- Estimators
- Workshop planners
What you get
- Per-bar cutting list
- Required bars and purchase quantity
- Parts, kerf, trims, offcuts and yield
Interpreting the result
- Check each pattern, stock specification and machine allowances before cutting.
- Yield is finished part length/gross stock length. No reuse value is assigned to offcuts.
References
- Method: original first-fit decreasing implementation with integer length accounting and a material lower bound.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Cutting bars with least waste
In Shop Floor Optimisation by the Numbers
What it covers: Cut a list of tube or bar lengths from stock with the fewest bars: the material lower bound, the first-fit decreasing rule in the BIZOMAT stock cut planner, cutting patterns, offcuts and stock length.
BIZOMAT tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.