Abstract
In this paper we will consider a special relaxation of the well-known online bin packing problem. In a batched bin packing problem (BBPP)–defined by Gutin et al. (2005)–the elements come in batches and one batch is available for packing in a given time. If we have K≥2 batches then we denote the problem by K-BBPP. In Gutin et al. (2005) the authors gave a 1.3871… lower bound for the asymptotic competitive ratio (ACR) of any on-line 2-BBBP algorithm. In this paper we investigate the 3-BBPP, and we give 1.51211… lower bound for its ACR.
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