I have the following problem:
Given $n$ items, where each item has weight $w_{i}$, $i=1,2\ldots n$, what is the number of ways to partition these items into boxes of fixed size $C$, such that the sum of weights of items in any box does not exceed the capacity of the box. There can be any number of these boxes, as long as the partition is valid.
Does this problem have some kind of a well known name or definition? My first thought led me to Stirling's numbers of the second kind, or Bell's number, or some modification of this that would include multiple knapsack problem, but the difference here is that the subsets(boxes) have fixed capacity and I actually don't know the number of boxes in advance. Thanks a bunch.