We first sort our items in non-increasing holder, then we consider one item after the other and we look for the first bin that can contain the current item. If there is a bin that can contain that item, then we put the item into that bin, otherwise we create a new bin and insert the new item into this new bin.
This is called the first fit decreasing algorithm because we first order in a non-increasing holder the item and then we put each item into the first bin that can contain this item. And it is possible to prove that this algorithm compute a solution whose measure is at most 3 or 2 time the optimal solution plus 1 bin. Actually it is possible to prove, with a very complicated analysis, that this algorithm computes a solution whose measure is major than 11 over 9 time the optimal solution plus 4. This is the best that you can do regarding this algorithm.
