3d bin packing programing in C#

Question

I am developing a windows application in C#.

The goal is this. You have a number of "Containers" of varying sizes (these are boxes that we have on hand to ship orders in, usually we have thousands in about 5 different sizes). When someone makes an order they will have a number of products, the "boxes" need to be arranged in the least number of "containers" with the least amount of waisted space. I've looked at a couple existing implementations that use volume calculations but it isn't very practical.

I've found tons of academic articles which all have theoretical algorithms and math formulas, but none have any sample code or anything. 

If anyone has any ideas or any general direction it would be greatly appreciated.