I'm trying to classify the following problem:
I have $N$ empty boxes ($n_i$ is the volume of the $i$-th box, $1 \leq i \leq N$) and $M$ divisible items ($m_j$ is the volume of $j$-th item, $1 \leq j \leq M$). The total volume of all boxes is exactly equal to the total volume of all items. I need to find a distribution of items among boxes which minimizes the number of item divisions.
I suppose this problem is NP-complete, and is some kind of set coverage problem, but I can't find appropriate variation of it.