We consider batched bin packing. Items are presented in a constant number of batches, and each batch should be packed before the next batch is presented. The cases of two, three, and four batches are studied. We prove improved lower bounds for the standard and parametric variants in some of the cases, and shorten the proofs for all other cases. To achieve this, we apply a new technique in our analysis, which differs from the ones previously used for proving such results.

中文翻译：

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分批装箱的下限

我们考虑分批装箱。物品以固定数量的批次展示，每批应在展示下一批之前进行包装。分别研究了二批、三批、四批的情况。我们在某些情况下证明了标准和参数变体的改进下界，并缩短了所有其他情况的证明。为了实现这一点，我们在分析中应用了一种新技术，该技术不同于之前用于证明此类结果的技术。