How can I programmatically determine how to fit smaller boxes into a larger package? [closed]

Question

Does anyone know of existing software or algorithms to calculate a package size for shipping multiple items?

I have a bunch of items in our inventory database with length, width and height dimesions defined. Given these dimensions I need to calculate how many of the purchased items will fit into predefined box sizes.

Answer 1

This is a Bin Packing problem, and it's NP-hard. For small number of objects and packages, you might be able to simply use the brute force method of trying every possibility. Beyond that, you'll need to use a heuristic of some sort. The Wikipedia article has some details, along with references to papers you probably want to check out.

The alternative, of course, is to start with a really simple algorithm (such as simply 'stacking' items) and calculate a reasonable upper-bound on shipping using that, then if your human packers can do better, you make a slight profit. Or discount your calculated prices slightly on the assumption that your packing is not ideal.

Answer 2

The literature on "3D Bin packing" is far and wide. You can get a good overview by tracking the publications of Professor David Pisinger. He also published one of the few high quality implementations of bin packing with sourcecode: 3dbpp.c

My own logistics toolkit pyShipping comes with a 3D Bin Packing implementation for Warehousing applications. It is basically implementing 4D Bin Packing (3D size & weigth) and gets an acceptable solution for typical order sizes (a few dozens of packages) in under a second runtime. It is used in production (meaning a warehouse) for some months now to determine the upper bound of shipping crates to be used. The warehouse workers are often able to pack somewhat more efficiently but that's OK with me.

Answer 3

Pisinger is one of the few academics who posts working code. In one of his papers he mentions the "Minimum Depth" problem.

Here is a practical and efficient algorithm for 3D Rectangular Box Packing that adjusts the height of the enclosing box.

And here is an implementation in php.

Answer 4

Are you trying to see how many of a single type fits into a particular sized package, or are you trying to mix types as well?

Sounds like you're trying to solve the Knapsack Problem. You might be able to find some algorithms for that which could be adapted to your specific requirements. Just understand that it will be hard to find an efficient algorithm, as the problem is NP complete (though depending on your specific requirements you may be able to find an efficient approximation, or your inputs may be small enough that it doesn't matter).