Parcel Post - Packing Problem Brainteaser Wood Puzzle

Comprised of 18 pieces, mostly with varied dimensions (only three pairs of pieces share the same dimensions), Parcel Post has all the ingredients to make it a very hard packing problem puzzle to solve.
If you're not already intimidated by the puzzle, you should. This is one of those puzzles that's virtually impossible to solve without a careful mathematical analysis or without software. Randomly packing the pieces by trial and error won't get you anywhere.
The solution is anything but intuitive. There are some pieces that need to be packed vertically and, also having to pack them in three layers doesn't help either. Because the puzzle comes packaged in its solved state you get to have a peek at how the solution looks like, but if you really want a challenge, ask someone to take out the pieces for you.