This problem has some applications such as loading of boxes on pallets and, specifically, woodpulp stowage.
[3][4] When there is an additional restriction that the packing must be exact (with no wasted space), the small rectangles may be rotated only by multiples of 90°.
In this more general case, it is not clear if the problem is in NP, since it is much harder to verify a solution.
[4] In this variant, the small rectangles can have varying lengths and widths, and their orientation is fixed (they cannot be rotated).
The problem is NP-complete in general, but there are fast algorithms for solving small instances.