I don't know which airlines are packing one-dimensional bins :). In dimensions 2 and above, bin packing has no PTAS unless P=NP, and in particular it's hard to derive anything with an approximation ratio appreciably better than sqrt(num_dimensions)).

And the famous Steiner tree result holds only in highly structured metrics like the Euclidean plane and some minor generalizations. For general metrics there's a lower bound of around 1.01 unless P=NP.