I needed 2 x 479mm and 2 x 1199mm bars.
The stock I had left over from the previous frame was 1 x 2000mm, 1 x 1385mm and 1 x 486mm.

I worked manually out that I needed to cut these as follows.

Given my stock and requirements this was fairly straight forward process but if I’d lots of bars to cut it would quickly become rather difficult. I checked with a work colleague who is a bit of a maths wiz and it turns out that the number of variations grows exponentially with increasing numbers of bars. Luckily there are techniques that you can use to work it out. The maths solution is called Linear programming and the particular problem is called the 1-dimensional Cutting Stock Problem. The technique for solving this is similar to those for cryptography problems and is in two steps, firstly to generate an approximate solution using “delayed column-generation” which provides a range of potential answers which is then passed to the second step which is called “the knapsack problem”.

Gary Darby has put together a little delphi application that allows you to work out what metal to order and how to cut the bars. Unfortunately Gary’s code can’t solve my original problem but he does provide the source code to allow you to calculate other options.

For those of you who prefer using Excel, there is the Microsoft Solver Foundation that can be used in .Net that can solve this kind of linear programing problem.