A robust optimization approach to inventory theory
A robust optimization approach to inventory theory
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DOI：
10.1287/opre.1050.0238
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发表时间：
2006-01-01
影响因子：
2.7
通讯作者：
Thiele, A
中科院分区：
文献类型：
--
作者：
Bertsimas, D;Thiele, A
我们提出了一个通用的方法，鲁棒优化的基础上解决问题的最优控制供应链的随机需求在离散时间。这个问题已经在过去使用动态规划进行了研究，动态规划受到维数问题的困扰，并假设对需求分布有充分的了解。所提出的方法考虑到供应链中的需求的不确定性，而不假设一个特定的分布，同时保持高度听话，并提供相应的最优策略的洞察力。它还允许调整解决方案的鲁棒性水平，以权衡性能和对不确定性的保护。所提出的方法的一个有吸引力的特点是它的数值易处理性，特别是当比较复杂的供应链中的多维动态规划问题，作为强大的问题是相同的难度作为标称问题，也就是说，线性规划问题时，没有固定成本，和混合整数规划问题时，固定成本。此外，我们表明，在强大的方法中获得的最优策略是相同的最优策略在名义上的情况下得到的修改和明确可计算的需求序列。在这种方式中，我们表明，最优鲁棒策略的结构是相同的基本库存字符的最优随机策略的范围广泛的库存问题，在单一的安装，串联系统，和一般的供应链。初步的计算结果是非常有希望的。
We propose a general methodology based on robust optimization to address the problem of optimally controlling a supply chain subject to stochastic demand in discrete time. This problem has been studied in the past using dynamic programming, which suffers from dimensionality problems and assumes full knowledge of the demand distribution. The proposed approach takes into account the uncertainty of the demand in the supply chain without assuming a specific distribution, while remaining highly tractable and providing insight into the corresponding optimal policy. It also allows adjustment of the level of robustness of the solution to trade off performance and protection against uncertainty. An attractive feature of the proposed approach is its numerical tractability, especially when compared to multidimensional dynamic programming problems in complex supply chains, as the robust problem is of the same difficulty as the nominal problem, that is, a linear programming problem when there are no fixed costs, and a mixed-integer programming problem when fixed costs are present. Furthermore, we show that the optimal policy obtained in the robust approach is identical to the optimal policy obtained in the nominal case for a modified and explicitly computable demand sequence. In this way, we show that the structure of the optimal robust policy is of the same base-stock character as the optimal stochastic policy for a wide range of inventory problems in single installations, series systems, and general supply chains. Preliminary computational results are very promising.