Cutting plan
Optimal cutting of profiles and battens from stock lengths and offcuts
How the calculation works
For each material and section enter the required parts (length and quantity), stock lengths with price and available quantity, existing offcuts, kerf width, end trims and the minimum usable offcut. Choose the goal – fewest new pieces, lowest cost or least waste. The calculator builds cutting patterns, draws the bars to scale and keeps an offcut register.
Formula and assumptions
For each piece: Σ parts + Σ cuts + start trim + remainder = piece length. There is one cut between adjacent parts, and a cut after the last part exists only if something remains. A remainder shorter than the minimum usable offcut is waste. Smaller lists are solved by an exact search with a proof of optimality, larger ones by a heuristic with improvements within the time limit.
Worked example
4 × 1200 mm and 6 × 850 mm from 4000 mm bars, 3 mm kerf: 3 bars (1200 + 1200 + 1200; 4 × 850; 1200 + 850 + 850), 10 cuts, 82.5 % utilisation, offcuts 1091, 588 and 391 mm, waste 30 mm (cuts only). Three bars is also the lower bound (9900 mm ÷ 4000 mm), so the solution is optimal.
More worked examples
- Three 2000 mm parts fit a 6000 mm bar without cutting a remainder only with a zero kerf; with a 3 mm kerf 6006 mm is needed, so two bars are required.
- Parts 700, 600, 500 and 3 × 400 mm from 1500 mm pieces: the exact search finds 2 pieces (700 + 400 + 400 and 600 + 500 + 400), while simple “first fit” packing gives 3.
How many parts fit a 6000 mm bar (3 mm kerf, no end trims)
| Part (mm) | Parts | Remainder (mm) |
|---|---|---|
| 500 | 11 | 467 |
| 1000 | 5 | 985 |
| 1200 | 4 | 1188 |
| 1500 | 3 | 1491 |
| 2000 | 2 | 1994 |
What affects real consumption
- Kerf width and trimming of factory ends.
- Available stock lengths, their price and existing offcuts.
- Minimum usable offcut – the larger it is, the more pieces end up as waste.
Common mistakes
- Ignoring the kerf width – ten 3 mm cuts lose 30 mm.
- Joining short offcuts into a longer part that must not be spliced.
- Using one plan for different sections or materials that must not be mixed.
Frequently asked questions
Why is the number of cuts not always the number of parts?
There is one cut between adjacent parts, and a cut after the last part is needed only if something remains. If the parts fit a piece exactly, the last cut is not needed; a start trim adds one cut.
When is the plan marked as optimal?
Only when the exact search has finished within the time limit. For larger lists the best solution found is shown, without claiming it is optimal.
Can I use offcuts from the site?
Yes – enter them as existing offcuts with a quantity. Their ends are not trimmed and they are used when that suits the chosen goal. Short offcuts are not joined into longer parts.