I should mention up front that I'm new to this forum and operations research in general. A problem has come up recently at work that I'm having a tough time solving.
Our machine shop acquires many long steel bars (typically 20 foot long, but could vary) that need to be cut to various sizes for further processing on a CNC lathe. I've been asked to minimize waste/trim from the process.
A couple special constraints are making it tough for me to formulate the problem. First, we can only feed ≤2 foot segments into the CNC at a time, so we cut the stock before cutting the final product. Additionally, each segment we cut must be fixed to the CNC (e.g. normally 2.5 inches of the segment are fixed and can't be cut), introducing a certain amount of inherent waste for each segment cut from the original bar. It is probably a naïve viewpoint, but this almost seems like two nested Cutting Stock Problems.
I will summarize briefly. We effectively have unlimited stock to cut from. In the usual case, we need to cut several hundred copies of two or more lengths from the stock. However, we can't feed the whole stock into the machine, so we must cut it into lengths of ≤2 feet. From each ≤2 foot segment, we can then cut the required lengths (i.e. the final product).
How would I go about formulating and solving this problem? As a mathematician, I always strive to find the most general solution. If it simplifies the solution, though, feel free to consider a more specific situation. Our normal use case (>50% of cases), we are using 20 foot stock and cutting 2 specific lengths.