3d bin packing algorithm
I have written an approximate algorithm for the case you describe i.e. 3D rectangular boxes, with orthogonal rotation, in C++. You can find the results and algorithm in the published paper: http://www.cs.ukzn.ac.za/publications/erick_dube_507-034.pdf
I converted wknechtel/3d-bin-pack C code to javascript. Can be easily port to C#.
https://github.com/keremdemirer/3dbinpackingjs
You can run example calculations from index.html
file and review the generated report. pack1.js
file contains the app and algorithm. I'm not sure how the algorithm works but the results are satisfying for packaging calculations.