Board Cut List Optimizer

How it works

Cutting parts from stock boards is a one-dimensional bin-packing problem: every part has to come from some board, and the aim is to use as few boards as possible. Finding the true minimum is computationally hard in general, so the calculator uses first-fit decreasing, a standard rule that is fast and has a proven worst-case bound.

The parts are sorted longest first. Each part goes into the first board that still has room for it, and a new board is started only when none does. A part fits when the length already used, plus one saw kerf for the cut that separates it, plus the part itself, is no more than the usable length: the stock length minus the end trim.

Long parts are placed first because they are the hardest to fit; short parts then fill the gaps they leave. The table shows which parts come from each board and the offcut left over once the cut that frees it (one more kerf) is made. The defect allowance adds a percentage of extra boards, rounded up, for knots, splits and other defects that make part of a board unusable.

Formula

usable length = stock length − end trim
sort parts longest first; place each in the first board where
  used + kerf + part ≤ usable length   (an empty board takes any part ≤ usable length)
offcut left = max(0, usable length − used − kerf)
boards with allowance = ceil(boards × (1 + allowance ÷ 100))
yield = total part length ÷ (boards × stock length)

Example

A project needs two 36 in parts, four at 30 in, four at 22.5 in and six at 14 in, cut from 8 ft (96 in) boards with a 1/8 in kerf and 1 in of end trim, leaving 95 in usable on each board.

First-fit decreasing lays them out on 4 boards: 36, 36 and 22.5 on the first (94.75 in used including kerfs, leaving a 0.125 in offcut after the last kerf); 30, 30 and 30 on the second; 30, 22.5, 22.5 and 14 on the third; and 22.5 with five 14s on the fourth. The 366 in of parts come from 4 × 96 = 384 in of stock, a yield of 95.3%. A 10% defect allowance raises the count to ceil(4 × 1.1) = 5 boards.

Assumptions and limitations

• First-fit decreasing is a heuristic: for some part lists it uses more boards than the true minimum (at most 11/9 of the minimum plus 6/9 of a board). It never uses fewer boards than the total length of the parts allows.
• One kerf is counted between adjacent parts; the end trim covers the cuts that square the board's ends.
• All stock boards are the same length and parts are cut across the board only. Width, ripping and grain matching are not considered.
• The kerf, end trim and defect allowance are typical shop values you can change. Defects in real boards fall where they fall, so the allowance is a rough margin, not a layout.

Frequently asked questions