We consider the NP Hard problems of online Bin Covering and Packing while
requiring that larger (or longer, in the one dimensional case)
items be placed at the bottom of the bins, below smaller (or
shorter) items — we call such a version, the LIB
version of problems. Bin sizes can be uniform or variable. We look
at computational studies for both the Best Fit and Harmonic Fit
algorithms for uniform sized bin covering. The Best Fit heuristic for
this version of the problem is introduced here.
The approximation ratios obtained were well within the theoretical upper
bounds.
For variable sized bin covering, a more thorough analysis revealed
definite
trends in the maximum and average approximation ratios.
Finally, we prove that for online LIB bin packing with uniform size
bins, no heuristic can guarantee an approximation ratio better than
1.76 under the online model considered.