Bulk material is given by 30" x 80" rectangular sheets.
I have four (4) different strap lengths and quantities I need to optimize into the bulk material by using the minimal amount of bulk material sheets as possible.
Piece #1: 1" x 21" QTY 200
Piece #2: 1 1/8" x 22" QTY 200
Piece #3: 1 1/8" x 40" QTY 100
Piece #4: 1 5/8" x 38" QTY 200
Currently, I am doing this by hand for each different scenario. I have about 300 different styles that have different piece dimensions (but all resembling a "strip" as shown above). I am wondering if multi-variable calculus could come into play to create an optimization formula that I can populate across all styles.
This is a classic example of the cutting stock problem. This problem isn't solved with standard calculus tools, but rather through the use of linear programming.
Explaining the full technique here would be too difficult, but perhaps you should read up on the cutting stock problem as well as the technique called "column generation".
(Warning: if you're not familiar with linear programming, you're going to have some reading to do)