Guide · How it works
How Bar and Tube Cutting Optimization Software Works
What happens between typing a cut list and getting a buy list: the cutting stock problem, the two search methods this planner uses, how kerf and miters enter the arithmetic, and what to expect from browser and desktop tools.
The problem
The cutting stock problem in plain words
You need a list of pieces and can buy bars of one or more lengths. Every piece must come out of some bar, every cut costs a blade width, and the bar ends are trimmed square. Find the purchase that costs least, and the order of cuts in each bar. Mathematicians call this the one-dimensional cutting stock problem.
It was described by Kantorovich in 1939 and given its classic pattern model by Gilmore and Gomory in 1961. It is NP-hard, so no known method is fast on every instance, but shop-sized lists, a few hundred pieces of up to a few dozen lengths, are usually small enough to solve exactly in a browser.
Algorithm
First-fit decreasing, then exact search to the lower bound
- Lower bound
- Add every piece plus one kerf and divide by the usable length of the longest bar. Here that is 3 bars; no plan can do better.
- First-fit decreasing
- Sort pieces longest first; put each into the first open bar where it fits, else start a new bar. Fast; its proven worst case is 11/9 of the optimum plus a fraction of a bar (Dósa, 2007).
- Exact search
- List every pattern, a set of pieces that fits one bar, then search over remaining demand for the cheapest combination of patterns. When it finishes, the plan is proven best.
- Fallback
- Lists with more than 20,000 patterns, 400,000 demand states or a fixed work cap fall back to first-fit decreasing, and the summary says Best found instead of Optimal.
On the machine frame both methods reach 3 bars, equal to the bound, so the summary shows Optimal. Ties are broken by fewer cuts, then by keeping drops long, so leftovers are more likely to be reusable.
Objective
Cost, bar count and length with mixed stock
| 2 × 2900 mm, goal | Buys | Bars | Yield | Cost |
|---|---|---|---|---|
| Lowest purchase cost | 2 × 3000 mm | 2 | 96.7% | $80.00 |
| Fewest bars | 1 × 6000 mm | 1 | 96.7% | $96.00 |
| Least stock length | 1 × 6000 mm | 1 | 96.7% | $96.00 |
With one stock length every goal gives the same plan. When the per-metre price differs, the goal decides: two short bars are cheaper here, one long bar is less handling. Cost is the default because it matches the invoice. On the 80/20 frame it buys a 3000 mm bar for the last pieces, $42.00 less than 6000 mm bars only.
Geometry
Kerf and miter arithmetic
Square cuts are simple: each piece takes its length plus one kerf. Angled ends need two more facts, the profile width W and the angle a. An end reaches d = W · cot a past the centerline, and the blade slot measured along the bar is k ÷ sin a.
When two neighbours have parallel ends, one cut serves both and the triangle between them disappears. The search can turn pieces over to create those parallel pairs. On the window preset that takes the job from 6 to 5 bars and 40 to 25 cuts; see the miter cut length optimizer for the drawings.
Determinism
Same input, same plan
The engine uses no random numbers and no time limits that depend on your machine. The same cut list, settings and stock always produce the same bars in the same order, so a share link, a re-import or a Pro export rebuilds exactly the plan you checked on screen. The linear material yield calculator guide shows how its yield figure is computed.
Shop needs
What a shop needs from the software
| Output | Why it matters | Here |
|---|---|---|
| Purchase list | How many bars of each length and material to order or pull from the rack | Free, on screen |
| Stop marks | Tape readings from one zero for every piece, kerf included | Free on screen; full list in the Pro PDF and CSV |
| Shop traveler | One block per bar with a scale drawing, angles and flip flags | Pro PDF |
| Labels | Part ID, length, angles and bar number on each piece | Pro PDF, Avery sheets |
| CAD file | Bars drawn 1:1 for checking, CNC saw prep or archiving | Pro DXF + SVG |
| Spreadsheet | BOM, cut schedule and remnant ledger back in Excel | Pro CSV pack (3 files) |
Compare
Browser planner vs installed desktop tools
| Capability | This browser planner | Typical installed desktop tool |
|---|---|---|
| Install | None: a web page; works on Windows, macOS, Linux, tablets | Installer, usually Windows only |
| Where the cut list is processed | In your browser; Pro files built in memory and not stored | On your computer |
| Excel input | Paste rows, or import CSV, TSV, job JSON (5 MB) | Varies: import, paste or manual entry |
| Mixed stock lengths and prices | Yes, cheapest mix, fewest bars or least length | Common |
| Mitered ends and shared cuts | 90/45/60/30° ends, complementary flip switch | Varies by product |
| Offcut inventory | Yes, used first at $0 when switched on | Common in paid editions |
| Barcode labels | Pro: Avery 5160 / L7160, Code-128 per piece and offcut | Varies; often a higher edition |
| DXF export | Pro: 1:1 R12 DXF on 6 layers + SVG | Varies |
| Price model | Free planner; Pro $4.99 for 7 days, $7.99/month or $19.99 once | One-time license; one benchmarked Windows tool lists $173 per seat |
A desktop tool makes sense when you need offline use on a locked-down shop PC or a direct link to a CNC saw controller. A browser planner suits estimators and small shops who want an answer now, on whatever device is at hand, and only pay when shop-floor files are needed.
Privacy: the nesting runs in your browser. Imported files are never uploaded. A Pro export sends the job JSON once to this site, the file is built in memory and returned, and nothing is stored. Start on the 1D nesting optimizer, or the pipe and aluminum tools.