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The stochastic generalized bin packing problem

机译:随机广义箱装箱问题

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摘要

The Generalized Bin Packing Problem (GBPP) is a recently introduced packing problem where, given a set of bins characterized by volume and cost and a set of items characterized by volume and profit (which also depends on bins), we want to select a subset of items to be loaded into a subset of bins which maximizes the total net profit, while satisfying the volume and bin availability constraints. The total net profit is given by the difference between the total profit of the loaded items and the total cost of the used bins. In this paper, we consider the stochastic version of the GBPP (S-GBPP), where the item profits are random variables to take into account the profit oscillations due to the handling operations for bin loading. The probability distribution of these random variables is assumed to be unknown. By using the asymptotic theory of extreme values a deterministic approximation for the S-GBPP is derived.
机译:通用装箱问题(GBPP)是最近引入的包装问题,在给定的情况下,给定一组以数量和成本为特征的垃圾箱,以及以数量和利润为特征的一组物品(这也取决于垃圾箱),我们希望选择一个子集将要装载到箱子集中的物品数量最大化,从而在满足数量和箱可用性限制的同时最大程度地提高总净利润。总净利润由已装载物品的总利润与已用垃圾箱的总成本之间的差得出。在本文中,我们考虑GBPP(S-GBPP)的随机版本,其中项目利润是随机变量,以考虑由于装箱操作而产生的利润波动。假定这些随机变量的概率分布是未知的。通过使用极值的渐近理论,可以得出S-GBPP的确定性近似。

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