Approximation algorithm for the partition problem
Consider what happens if you have 1000 items of size 1, and 1 of size 1000.  Optimally, you would have 2 sets of size 1000, but if you followed the heuristic with items in ascending order, you will have one set of 500, and one of 1500, for a 3/2 approximation, worse than 7/6.