Workshop
Bar cutting optimizer
In short
A bar cutting plan packs parts into bars of a given length, each cut removing a saw kerf e: a bar takes parts while Σ (L + e) ≤ C + e, with C the bar length less the end trim. The calculation compares two packings (FFD and BFD) with the bound B = ⌈ Σ(L + e) / (C + e) ⌉.
Calculation
Example calculated with the tool’s default values.
Inputs
- Bar length
- 6000 mm
- Saw kerf
- 3 mm
- End trim per bar
- 0 mm
- Minimum reusable offcut
- 300 mm
- Piece 1: length
- 2000 mm
- Piece 1: quantity
- 3
Results
- Bars to cut
- 2of 6000 mm
Worked example
Every value in this section belongs to the example, calculated with the tool’s default values.
Other results of the example
- Lower bound
- 2optimum proven
- Waste rate
- 50.0%
- Total waste
- 6.00 m
- Reusable offcuts
- 5.99 m2 offcuts ≥ 300 mm
- Longest offcut
- 3997.0 mm
- Kerf loss
- 9.0 mm
- Parts
- 3
- Lengths are finished cut lengths: if a mitre cut or a machining allowance is needed, add it to the part length.
Step-by-step calculation
Parts to cut
N = Σ quantités ; ΣL = Σ (L × q)
N = 3 pieces; ΣL = 6000.0 mm
Usable length per bar
C = bar − end trim; each piece takes L + e (e = saw kerf)
C = 6000 − 0 = 6000 mm ; e = 3.0 mm
Lower bound
B = ⌈ Σ(L + e) / (C + e) ⌉ (without saw kerf: ⌈ ΣL / bar ⌉)
⌈ 6009.0 / 6003.0 ⌉ = 2 ; ⌈ 6000.0 / 6000 ⌉ = 1
Greedy packing (FFD / BFD)
pieces by decreasing length, first bar where it fits (FFD) or the fullest one (BFD)
FFD: 2 bar(s); BFD: 2 bar(s)
Total waste and rate
waste = N_bars × bar − ΣL; rate = waste / (N_bars × bar)
2 × 6000 − 6000.0 = 6000.0 mm ; 6000.0 / 12000 = 50.0 %
Cutting plan per bar
| Bar | Identical bars | Parts to cut | Parts (sum) (mm) | End offcut (mm) | Reusable offcut |
|---|---|---|---|---|---|
| 1 | 1 | 2 × 2000 | 4000.0 | 1994.0 | ✓ |
| 2 | 1 | 1 × 2000 | 2000.0 | 3997.0 | ✓ |
Parts requested
| Length (mm) | Quantity | Total (mm) |
|---|---|---|
| 2000.0 | 3 | 6000.0 |
How to use it
- Enter the bar length (6 m and 12 m are the usual delivery lengths).
- Enter the saw kerf measured on your saw, the end trim per bar and the minimum reusable offcut.
- Enter the parts: one line per length, with its quantity (up to 8 lines and 600 parts in total).
- Read the number of bars to cut.
Frequently asked questions
How does a bar cutting optimizer work?
It is a bin packing problem: the bars are the bins, the parts the items. Parts are sorted by decreasing length, then placed in the first bar where they fit (First Fit Decreasing) or in the fullest one (BFD); the calculation keeps the one that needs fewer bars, then looks for a packing with one bar less.
How does a linear cut list calculator count the saw kerf?
Example: 3 parts of 2000 mm in 6000 mm bars, 3.0 mm kerf. Each part takes L + e: ⌈ 6009.0 / 6003.0 ⌉ = 2 bars at least, whereas without kerf ⌈ 6000.0 / 6000 ⌉ = 1. The plan gives 2 bars: 2 × 2000 in the first (1994 mm offcut), 1 × 2000 in the second (3997 mm offcut).
How is the waste rate worked out?
Total waste = N_bars × bar − ΣL, rate = waste / (N_bars × bar). For the example: 2 × 6000 − 6000.0 = 6000.0 mm, so 6000.0 / 12000 = 50.0 %. Offcuts at least as long as the minimum reusable offcut (300 mm by default) count as reusable, shorter ones as lost.
Is the bar count optimal?
If the plan reaches the lower bound, or if the search for a packing with one bar less ends without a solution, the optimum is proven. Otherwise, the optimum lies between the bound and the count found; the FFD method uses at most 11/9 of the optimum + 6/9 bar (Johnson 1973, Dósa 2007).
Limits
Indicative results. Lengths are finished cut lengths: add a mitre cut or a machining allowance to the part if needed. The 3 mm kerf is only a starting value: measure your blade; 0 only applies to a lossless cut.
Sources
- Problème de rangement en boîtes (bin packing) : algorithme First Fit Decreasing : D. S. Johnson, « Near-optimal bin packing algorithms », thèse MIT, 1973 : FFD ≤ 11/9·OPT + 4 (link)
- Constante exacte de FFD : G. Dósa, « The tight bound of First Fit Decreasing bin-packing algorithm is FFD(I) ≤ 11/9 OPT(I) + 6/9 », ESCAPE 2007, LNCS 4614 (link)
- Longueurs de livraison courantes : 6 et 12 m (laminés marchands), 6 à 24 m (poutrelles) : Misetal, catalogue « Acier – produits longs » (consulté le 08/11/2026) (link)
- Géométrie : Capacité d’une barre : somme des pièces et des traits de scie ; borne inférieure par la longueur totale