We propose a novel robust optimization approach to analyze and optimize the expected performance of supply chain networks. We model uncertainty in the demand at the sink nodes via polyhedral sets which are inspired from the limit laws of probability. We characterize the uncertainty sets by variability parameters which control the degree of conservatism of the model, and thus the level of probabilistic protection. At each level, and following the steps of the traditional robust optimization approach, we obtain worst case values which directly depend on the values of the variability parameters. We go beyond the traditional robust approach and treat the variability parameters as random variables. This allows us to devise a methodology to approximate and optimize the expected behavior via averaging the worst case values over the possible realizations of the variability parameters. Unlike stochastic analysis and optimization, our approach replaces the high-dimensional problem of evaluating expectations with a low-dimensional approximation that is inspired by probabilistic limit laws. We illustrate our approach by finding optimal base-stock and affine policies for fairly complex supply chain networks. Our computations suggest that our methodology (a) generates optimal base-stock levels that match the optimal solutions obtained via stochastic optimization within no more than 4 iterations, (b) yields optimal affine policies which often times exhibit better results compared to optimal base-stock policies, and (c) provides optimal policies that consistently outperform the solutions obtained via the traditional robust optimization approach.

中文翻译：

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供应链网络中的随机优化：平均可靠的解决方案

我们提出了一种新颖的鲁棒优化方法来分析和优化供应链网络的预期性能。我们通过多面体集对汇点节点的需求不确定性进行建模，该多面体集受概率极限定律的启发。我们通过可变性参数来表征不确定性集，该可变性参数控制模型的保守程度，从而控制概率保护的水平。在每个级别上，按照传统鲁棒优化方法的步骤，我们获得最坏情况值，该值直接取决于可变性参数的值。我们超越了传统的鲁棒方法，将可变性参数视为随机变量。这使我们能够设计一种方法，通过对可变性参数的可能实现上的最坏情况值求平均来近似和优化预期行为。与随机分析和优化不同，我们的方法用概率极限定律启发的低维近似代替了评估期望的高维问题。我们通过为相当复杂的供应链网络找到最佳的基本库存和仿射策略来说明我们的方法。我们的计算表明，我们的方法（a）在不超过4次迭代中生成与通过随机优化获得的最优解决方案相匹配的最优基础库存水平，（b）产生了最佳仿射策略，与最优基础库存相比，仿射策略通常表现出更好的结果政策，