In the paper we deal with lower bounds constructed for the asymptotic competitive ratio of semi-online bin packing and batched bin packing algorithms. We determine the bounds as the solutions of a related nonlinear optimization problem using theoretical analysis and a reliable numerical global optimization method. Our results improve the lower bounds given in Gutin et al. (Discrete Optim 2:71-82, 2005) for some special cases of the batched bin packing problem. [PUBLICATION ABSTRACT]
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