Lower bound for 3-batched bin packing

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≥2K≥2 batches then we denote the problem by KK-BBPP. In Gutin et al. (2005) the authors gave a 1.3871…1.3871… lower bound for the asymptotic competitive ratio (ACR) of any on-line 22-BBBP algorithm. In this paper we investigate the 3-BBPP, and we give 1.51211…1.51211… lower bound for its ACR.