Simple greedy algorithms like that have a lot of ways to fail:

Example 1: 5,3,3,3,2,2 with capacity 9

Greedy algorithm gets: [5+3] [3+3+2] [2]
Optimal is instead:    [3+3+3] [5+2+2]
[download]

The problem in general is not easy!

Additionally, the OP problem involves different requirements; having a small number of large items in the first few bins and a whole lot of small items in the last few bins is undesirable.