Performance estimations of first fit algorithm for online bin packing with variable bin sizes and LIB constraints

We consider the NP Hard problem of online Bin Packing while requiring that larger (or longer) items be placed below smaller (or shorter) items --- we call such a version the {LIB} version of problems. Bin sizes can be uniform or variable. We provide analytical upper bounds as well as experimental results on the asymptotic approximation ratio for the first fit algorithm