In the set multicover problem we are given a set $N$ of $n$ elements and a set $S$ of $m$ subsets of $N$. Additionally, each element has a coverage requirement (the number of times it has to be covered) and each set has a weight. The question is to cover $N$ with the minimum weight subsets from $S$. I'm aware of the approximation algorithm for this problem using (Rajagopalan & Vazirani) .
But I am interested in finding an algorithm for this problem that uses the randomized rounding and study its approximation factor.
Thanks in advance!