# 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?

• “Is there a solution that can pack all of these items into the bins?” is a decision problem, and I do not know what you mean by approximation for it. I think that there are several natural optimization problems related to that decision problem. – Tsuyoshi Ito Aug 24 '12 at 1:14
• Thanks, can you refer me to any algorithm/paper that tries to solve this decision problem? – Masood_mj Aug 24 '12 at 1:29
• Um, brute force algorithm? I am not familiar with advances in exponential-time algorithms. – Tsuyoshi Ito Aug 24 '12 at 12:50