3-d bin packing with additional constraints and subsets of items

Question

I'm dealing with a problem that is a slight twist on the 3-d bin packing problem.

I have a finite set of bins (on the order of 100's), and a finite set of items (one the order of 10's). Below is an simplified example.

bins = [
    Bin(10, 10, 10, 50),
    Bin(20, 20, 20, 100),
    Bin(30, 30, 30, 200),
]

items = [
    Item(5, 5, 5, 10),
    Item(8, 8, 8, 20),
    Item(12, 12, 12, 30),
    Item(15, 15, 15, 40),
    Item(18, 18, 18, 50),
]

Lets assume the bin and item objects are as follows

class Bin:
    def __init__(self, length, width, height, max_weight):
        self.length = length
        self.width = width
        self.height = height
        self.max_weight = max_weight
        self.volume = length * width * height

class Item:
    def __init__(self, length, width, height, weight):
        self.length = length
        self.width = width
        self.height = height
        self.weight = weight
        self.volume = length * width * height

I need the system, given a set of bins and items to assign every item to a box given the following constraints.

• If any of the dimensions of the item are more than the dimension of the box, the item cannot be boxed.
• The summed weight of the items cannot exceed the boxes max_weight.

The variable we are optimizing for is volumetric weight of the boxes.

• Volumetric weight = (length * width * height) * multiplier

• We want to minimize the summed volumetric weight of all the assigned boxes. (Same as minimizing the summed volume).

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The output should look like: (The following is not correct, just for demo)

Box A: [Item_A,Item_B]
Box B: [Item_C]
No Box: [Item_D]

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Ideally, I would prefer if there is a python package that does this. I'm aware the solution is NP-hard, I need some output though.