We consider the NP Hard problems of online Bin Covering and Packing whilerequiring that larger (or longer, in the one dimensional case)items be placed at the bottom of the bins, below smaller (orshorter) items — we call such a version, the LIBversion of problems. Bin sizes can be uniform or variable. We lookat computational studies for both the Best Fit and Harmonic Fitalgorithms for uniform sized bin covering. The Best Fit heuristic forthis version of the problem is introduced here. The approximation ratios obtained were well within the theoretical upperbounds. For variable sized bin covering, a more thorough analysis revealeddefinite trends in the maximum and average approximation ratios. Finally, we prove that for online LIB bin packing with uniform sizebins, no heuristic can guarantee an approximation ratio better than1.76 under the online model considered.
