Bin packing approximation with different bin sizes Is there any greedy solution with an approximation bound for the bin-packing problem when we have bins of different size?

More formally, there are $n$ bins of size $b_i$ for $i=1,\dotsc,n$, and $m$ objects, each of size $o_j$ for $j=1,\dotsc,m$.

Is there a solution that can pack all of these items into the bins?
I started a project under MIT license to try to solve this problem.  Currently it uses the 'best fit' approach.  Sorts 'items' from largest to smallest and sorts bins from smallest to largest.  Finds first bin that is large enough to use that has ALREADY been used (if possible).  Let's see if we can make it a good enough solution for all.

https://github.com/asharif/packit4.me