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Two-level lot-sizing with inventory bounds

机译：与库存界限的两级批量尺寸

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We study a two-level uncapacitated lot-sizing problem with inventory bounds that occurs in a supply chain composed of a supplier and a retailer. The first level with the demands is the retailer level and the second one is the supplier level. The aim is to minimize the cost of the supply chain so as to satisfy the demands when the quantity of item that can be held in inventory at each period is limited. The inventory bounds can be imposed at the retailer level, at the supplier level or at both levels. We propose a polynomial dynamic programming algorithm to solve this problem when the inventory bounds are set on the retailer level. When the inventory bounds are set on the supplier level, we show that the problem is NP-hard. We give a pseudo-polynomial algorithm which solves this problem when there are inventory bounds on both levels. In the case where demand lot-splitting is not allowed, i.e. each demand has to be satisfied by a single order, we prove that the uncapacitated lot-sizing problem with inventory bounds is strongly NP-hard. This implies that the two-level lot-sizing problems with inventory bounds are also strongly NP-hard when demand lot-splitting is considered. (C) 2018 Elsevier B.V. All rights reserved.
机译：我们研究了一个两级未公布的批量尺寸问题，其中库存界限发生在由供应商和零售商组成的供应链中。需求的第一级是零售商水平，第二个是供应商级别。目的是最大限度地减少供应链的成本，以满足在每个时期库存中的物品数量有限的情况下满足需求。可以在供应商级别或两级施加库存范围。我们提出了一种多项式动态编程算法来解决零售商级别的库存界限时解决此问题。当库存界限设置在供应商级别上时，我们显示问题是NP-HARD。我们提供了一个伪多项式算法，当两个级别都有库存界限时解决了这个问题。在不允许需求批量分裂的情况下，即每次需求都必须满足单个订单，我们证明了库存界限的未列为批量尺寸问题强烈。这意味着当考虑需求批量分裂时，使用库存界限的两级批量问题也是强烈的NP - 硬。 （c）2018 Elsevier B.v.保留所有权利。

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