Distributionally robust multi-item newsvendor problems with multimodal demand distributions
Distributionally robust multi-item newsvendor problems with multimodal demand distributions
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DOI：
10.1007/s10107-014-0776-y
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发表时间：
2014-04
影响因子：
2.7
通讯作者：
G. A. Hanasusanto;D. Kuhn;S. Wallace;Steve Zymler
中科院分区：
文献类型：
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作者：
G. A. Hanasusanto;D. Kuhn;S. Wallace;Steve Zymler
我们针对一类产品提出了一种规避风险的多维报童模型，这些产品的需求密切相关，并且受到下订单时尚未完全了解的时尚趋势的影响。已知需求分布是多峰的，因为存在空间上分离的概率质量簇，但缺乏完整的描述。我们假设报童通过最小化与给定模态信息兼容的所有分布上的订单组合的最坏情况风险来对冲分布模糊性。我们证明了由此产生的分布鲁棒优化问题是困难的，但在二次决策规则中承认有效的数值解。这种近似是保守的并且计算上易于处理。此外，它在数值测试中达到了很高的精度。我们进一步证明，忽视歧义性或多模态可能会导致解决方案不稳定，在压力测试实验中表现不佳。
We present a risk-averse multi-dimensional newsvendor model for a class of products whose demands are strongly correlated and subject to fashion trends that are not fully understood at the time when orders are placed. The demand distribution is known to be multimodal in the sense that there are spatially separated clusters of probability mass but otherwise lacks a complete description. We assume that the newsvendor hedges against distributional ambiguity by minimizing the worst-case risk of the order portfolio over all distributions that are compatible with the given modality information. We demonstrate that the resulting distributionally robust optimization problem is-hard but admits an efficient numerical solution in quadratic decision rules. This approximation is conservative and computationally tractable. Moreover, it achieves a high level of accuracy in numerical tests. We further demonstrate that disregarding ambiguity or multimodality can lead to unstable solutions that perform poorly in stress test experiments.