We study a periodic-review multi-supplier series inventory system in which the demand is restricted to partial sum uncertainty sets. We present and solve a robust rolling-horizon model for the system. We propose an induction framework to characterize the closed-form robust optimal solution of the problem. We show that the robust optimal policy combines the echelon base-stock policy and a gap-of-echelon-base-stock policy for the uppermost stage and a modified echelon base-stock policy for the other downstream stages. The policy structure is easy for the manager to understand and implement in practice. The policy parameters are directly determined by a sequence of nominal partial-sum demands, and its computation is very effective. In addition, the policy does not rely on complete information about the demand distribution; its solution can be more robust than that of stochastic optimization methods, especially when demand is highly uncertain, and forecasting is difficult. Based on the structure of the robust optimal policy, we design two heuristic policies for the system and evaluate the policies' performance through an extensive numerical study using both synthetic and real data.

中文翻译：

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与多个供应商的稳健的多级库存管理

我们研究了定期审查的多供应商系列库存系统，其中需求仅限于部分总和不确定性集。我们提出并解决了系统的鲁棒滚动范围模型。我们提出了一个归纳框架来描述问题的封闭式鲁棒最优解。我们证明，稳健的最优政策结合了最上层的梯队基础股政策和梯队缺口政策以及其他下游阶段的修正梯队基础股政策。该政策结构易于管理者理解并在实践中实施。策略参数直接由一系列名义部分和需求决定，其计算非常有效。此外，该政策不依赖于有关需求分布的完整信息；它的解决方案比随机优化方法更加稳健，尤其是在需求高度不确定且预测困难的情况下。基于鲁棒最优策略的结构，我们为系统设计了两种启发式策略，并使用合成数据和真实数据通过广泛的数值研究来评估策略的性能。