So, I have an optimization/space management problem. This same question is posted on two SE sites simultaneously, Stack Overflow and Mathematics, since I think it is fitting for both.
Let's say I have containers of (X,Y) dimensions. Inside, I want to place as many smaller containers of (x_i, y_i) dimensions as possible. These smaller containers can vary in size. Inside these smaller containers, I have a given item wich is the smallest unit I have.
Basically: Items, inside variable small boxes, inside variable big boxes.
Provided I know all of the following:
- Larger containers' dimensions.
- Smaller containers' dimensions.
- Ammount of all containers available to me.
- Ammount of basic items that need to be packaged.
Is there currently a known alghorithm that can be applied to determine the following?
- The best selection of small boxes to be used (they can vary in size).
- The optimal ammount of large containers required for storage.
- The appropriate placement of the smaller packages inside the larger one.
IF this is a thing that already exists, can it be extended to three dimensions, rather than only two, as my example states? That is to say, calculate packaging configurations for dimensions (x,y,z).
EXAMPLE:
I have 25 items. I have small containers of the following dimensions: 3x3, 2x2, 1x2. I have large container of 5x5.
Through trial and error (or intuition?), I can see that a valid configuration is as follows:
1 small container of 3x3 3 small containers of 2x2 2 small containers of 1x2 All inside a 5x5 container.
Now, it's a matter of tetrising/tangraming my way into a solution. So, for example, the following two are valid placements/configurations:
While this one isn't since it would require a second large container:
