We study the Min-Weighted Sum Bin Packing problem, a variant of the classical Bin Packing problem in which items have a weight, and each item induces a cost equal to its weight multiplied by the index of the bin in which it is packed. This is in fact equivalent to a batch scheduling problem that arises in many fields of applications such as appointment scheduling or warehouse logistics. We give improved lower and upper bounds on the approximation ratio of two simple algorithms for this problem. In particular, we show that the knapsack-batching algorithm, which iteratively solves knapsack problems over the set of remaining items to pack the maximal weight in the current bin, has an approximation ratio of at most 17/10.

翻译：我们研究Min-Weighted Sum Bin Packing问题，这是经典装箱问题的一种变体，其中物品具有权重，每个物品产生的成本等于其权重乘以所在箱子的索引。这实际上等价于一种批处理调度问题，出现在预约调度或仓库物流等众多应用领域。我们改进了该问题两种简单算法的近似比上下界。特别地，我们证明了背包批处理算法（该算法通过迭代求解剩余物品集合上的背包问题，以在当前箱子中装载最大权重）的近似比不超过17/10。