A cutting list, turned into which bar each piece comes off CUT

The obvious method costs you a bar, every job

Cutting stock to length is a packing problem, and packing problems punish the obvious method. What everybody does with a pencil is work down the list in the order it was written and start a new bar whenever the next piece does not fit. It is reliably one or two bars worse than sorting the pieces longest first and dropping each into the emptiest bar that will take it.

That difference is not academic. On a job of eighty cuts it is a length of steel, a length of timber or a length of pipe, per job, on every job, for as long as you do it that way. It is also invisible, because a plan that works looks like a plan that worked, and nobody sees the bar they did not have to buy.

The lower bound is printed alongside the answer: the total length you need divided by the bar length, rounded up. That is the number of bars no arrangement can beat. If the plan matches it, stop looking. If it is one over, you know exactly how much is left on the table, which is usually none: the bound is frequently unreachable because the pieces do not divide that way.

The kerf is what turns a plan into a shortage

A saw removes material. Three two-metre pieces do not come out of a six-metre bar, because with a three-millimetre blade they need six metres and six millimetres, and the third piece is six millimetres short.

This is the single most common error in a cutting list, it is always discovered at the saw, and by then the material is bought and someone is standing there. It is counted here on every cut, along with the end trim for the unusable material at the end of a bar, because both are real lengths that the arithmetic has to spend.

Measure your blade rather than guessing it. A thin-kerf circular saw blade and a standard one differ by a millimetre or more, a bandsaw is different again, and a plasma or laser cut has its own allowance. On a long list the difference compounds into a whole piece.

Read the offcuts before you cut anything

The plan lists what is left over on each bar, and flags the offcuts long enough to be worth keeping as stock. That list is worth a minute before you start, for two reasons.

First, it tells you whether a small change to the job buys you something. If three bars each finish with 800 mm left and you have an 850 mm piece coming next week, the arrangement is worth revisiting now. Second, an offcut that is nearly long enough for a piece on the same list means the pieces are close to fitting differently, and a millimetre off a tolerance somewhere may save a bar.

Then write the plan down and cut to it, in the order given. The savings come from the arrangement, and an arrangement abandoned halfway is just the pencil method with extra steps.

Nothing here is uploaded; the arithmetic runs in the tab. Nearby: PALLET packs boxes rather than lengths, SLING works out what a lift actually puts through each leg, and FIGURES handles the rounding so a tolerance does not quietly disappear.