Linear Cutting Optimizer for Bars, Pipes and Profiles

What does the linear cutting optimizer do?

You have stock bars of given lengths (profiles, pipes, flat bar, rebar, timber) and a list of parts to cut. This tool distributes the parts over the bars so that the number of bars opened and the waste are as low as possible. You get a cutting plan for each bar, a scaled strip drawing, the remainder of each bar, the total bar count, the utilisation ratio and the waste percentage. Bars cut with the same pattern are grouped on one line with a repeat count.

How is saw kerf counted?

If a bar yields n parts, there are n − 1 cuts between them. The fit condition is:

Σ part length + (n − 1) × kerf ≤ stock length − head trim − tail trim

If material is left after the last part, one more cut is made and the remainder is shortened by one kerf. If the last part ends exactly at the end of the bar, that cut does not exist. Head and tail trims include the kerf of their own cuts.

An example

Three 2000 mm parts come out of one 6000 mm bar when the kerf is zero. With a 3 mm kerf the total is 3 × 2000 + 2 × 3 = 6006 mm, which does not fit, so two bars are needed. This is the most common reason why a plan that shows zero waste on paper fails in the workshop.

Lower bound and the word "optimal"

Next to the solution the tool shows a lower bound: the sum of part lengths and kerfs divided by the usable bar length, rounded up. No plan can use fewer bars than this. If the solution found equals the lower bound, or if every possibility was searched within the time limit for a small list, the result is marked as proven. Otherwise the tool only says "a good solution" and reports the gap to the lower bound.

Method

First Fit Decreasing, Best Fit Decreasing and a pattern filling heuristic run first. For lists of up to 60 parts a time limited branch and bound search follows. In the remaining time the parts are packed again in randomly perturbed orders and the best result is kept. With several stock lengths, each bar is downsized to the cheapest length that still holds its parts. If you enter prices the total price is minimised, otherwise the total stock length.

Limits

• Only square (90 degree) cuts are calculated. For mitre cuts enter the longest edge of the part as its length.
• All parts are assumed to share one cross section. Run the tool separately for each section.
• For large lists the plan found may not be the best one. The gap to the lower bound shows this openly.
• Workshop constraints such as cutting sequence, clamping allowance and bundle cutting are not considered.