The first looks more like a bin packing problem to me:
http://sqlblog.com/blogs/hugo_kornelis/archive/2007/11/30/bin-packing-part-1-setting-a-baseline.aspx
There's a series of 5 articles by Hugo Kornelis at this link (to the first). Very complicated, but the fastest solutions typically involve a set-based loop of some sort.
You didn't mention if speed is an issue for you. The CURSOR will work OK as long as you don't have too many buckets to fill.
PM me if you would like more information.
My thought question: Have you ever been told that your query runs too fast?
My advice:
INDEXing a poor-performing query is like putting sugar on cat food. Yeah, it probably tastes better but are you sure you want to eat it?
The path of least resistance can be a slippery slope. Take care that fixing your fixes of fixes doesn't snowball and end up costing you more than fixing the root cause would have in the first place.
Need to UNPIVOT? Why not CROSS APPLY VALUES instead?[/url]
Since random numbers are too important to be left to chance, let's generate some![/url]
Learn to understand recursive CTEs by example.[/url]
[url url=http://www.sqlservercentral.com/articles/St