Bar cutting plan
Enter the part lengths and quantities — the plan lays them out on stock bars, collapses identical bars into one row and shows how many bars to order and how much really goes to scrap. It downloads as a table and goes straight to the saw.
Short answer
The offcut does not depend on how much steel you need but on how the lengths fall on a bar. Six 2400 mm parts out of six-metre bars leave over 20 % waste; the same 2400 paired with a 1200 leaves almost none. That is why an allowance percentage is guesswork and a cutting plan is arithmetic: the calculator lays the parts out on bars and tells you how many bars to buy and how much really goes to scrap.
| No. | Part length, mm | Quantity |
|---|---|---|
| 1 | ||
| 2 | ||
| 3 | ||
| 4 | ||
| 5 | ||
| 6 |
How the layout is worked out
Fitting parts into stock bars is the bin packing problem, and it has no exact solution: trying every arrangement of forty parts will not finish in any useful time. So the plan uses First Fit Decreasing — the parts are sorted longest first and each goes into the first bar it fits.
The order is not a formality. Long parts go down first so that short ones can fill the remainders afterwards; laid out in the order you typed them, the same list takes noticeably more bars. One kerf is allowed for every part cut off — three millimetres across forty parts is twelve centimetres: not decisive, but not nothing either.
Finished bars are collapsed by identical layout, which is how a cutting card is written in a shop: “six bars, cut like this”, not six identical rows in a row.
The optimum: FFD gives a good plan, not the best one. A usable remnant: a 1.7 m offcut is counted as waste because the plan cannot know whether it goes in the corner or into the next job — and that is the foreman’s call, not the arithmetic’s. And a single stock length: if the yard carries both six- and twelve-metre bars, run both and compare.
What to do with the result
First, replace the percentage. The bill of materials takes an allowance blind, 5 % by default; here you get the real figure, and it is worth carrying back to where the mass and the cost are worked out.
Second, hand the card to the saw as it stands. A line reading “2 × 2400 + 1 × 1200” can be measured off without recalculating, and the bar count in the next column says how many times to repeat it.
Frequently asked questions
Why is this not the optimal cutting plan?
Because there is nothing to find the optimum with: bin packing is NP-hard, and an exhaustive search over a real parts list does not terminate. FFD guarantees a result no worse than 11/9 of the best plus one bar — in practice usually a difference of one bar, and in exchange the plan can be read by eye and reproduced with a tape.
Why are the long parts placed first?
Because a short part can always be tucked in somewhere, and a long one cannot. Start with the short ones and they take up the starts of the bars, leaving the long parts to open new ones. “Longest first” is not decoration on the method; it is the method.
Why is the remainder of a bar counted as waste?
Because the plan does not know your yard. A 1.7 m offcut is rarely thrown away in a real shop; it is put aside for the next job, and then the actual waste is lower than the calculation. But that call belongs to the person who can see what is stacked in the corner, not to a calculator.
How much does the kerf matter?
Less than people expect, but not so little that it can be dropped. Three millimetres across forty parts is twelve centimetres — a quarter of an average part. One kerf is allowed per part cut off; if your blade is thicker, change the figure in the field.
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