Principles of operation
Bin packing is an NP-hard problem and there is no way to always achieve an optimum solution without running through every single permutation. But that’s OK because this implementation is designed to simulate a naive human approach to the problem rather than search for the “perfect” solution.
This is for 2 reasons:
It doesn’t require the person actually packing the box to be given a 3D diagram explaining just how the items are supposed to fit.
At a high level, the algorithm works like this:
Pack largest (by volume) items first
Pack vertically up the side of the box
Pack side-by-side where item under consideration fits alongside the previous item
If more than 1 box is needed to accommodate all of the items, then aim for boxes of roughly equal weight (e.g. 3 medium size/weight boxes are better than 1 small light box and 2 that are large and heavy)