Ship Packaging Optimizer

You are given a list of items that need to be shipped. Each item has a unique id, weight, and volume. Additionally, you are provided with a list of boxes where each box has a maximum weight capacity and maximum volume capacity. Your task is to write a function that determines a packing strategy, aiming to minimize the total number of boxes used while ensuring that the sum of the weights and volumes of the items in each box does not exceed its respective limits.

Your function should return a list of boxes, where each box is represented as a list of item ids that are packed inside that box. You may assume that it is always possible to pack all items given the box constraints.

Example:

Items:

[
  {"id": "item1", "weight": 10, "volume": 5},
  {"id": "item2", "weight": 20, "volume": 10},
  {"id": "item3", "weight": 5, "volume": 3},
  {"id": "item4", "weight": 15, "volume": 7}
]

Boxes:

[
  {"max_weight": 30, "max_volume": 15},
  {"max_weight": 40, "max_volume": 20}
]

One possible valid solution:

[
  ["item1", "item3"],
  ["item2", "item4"]
]

Constraints:

• You may assume that the number of items is at most 10^4.
• The number of boxes is at most 10^3.
• Your solution does not need to guarantee a strictly optimal solution (i.e., the absolute minimum number of boxes) but should strive to use boxes efficiently.

Write your solution in the programming language of your choice.

Good luck!