基于截断需求的分布鲁棒报童问题

Distributionally robust newsvendor problem with censored demand

在实际库存决策中,通常我们只能观察到销售量而非真实需求量,这导致了库存决策的截断需求问题——部分需求信息被库存水平所截断.本文在报童问题设置下首次提出使用条件分布鲁棒优化技术来处理截断需求信息.具体而言,基于历史销售数据,我们考虑了包含需求条件分布矩信息的分布不确定集,进一步提出将库存状态信息引入该分布不确定集,并导出了两类模型的闭式解:1)在基于均值-支撑集的分布不确定集下,支撑集的上下界决定了分布鲁棒报童模型的闭式解;2)在基于均值-方差-支撑集的分布不确定集下,期望、方差以及订货价与零售价共同决定了分布鲁棒报童模型的闭式解;3)随着订货价与零售价之比增大,分布鲁棒报童问题的最优订货数量降低.实验结果表明:当订货价与零售价之比处于某一范围时,截断需求信息可以提高分布鲁棒报童模型的期望收益,并且随着截断水平增加,提升收益率增加.

We usually can only observe the sales instead of the true demand in practice,which results in the censored demand problem—Partial demand information is censored by the stocking level.Under a newsvendor setting,we first adopt the distributionally robust optimization technique to address this problem.To the best of our knowledge,our study is the first distributionally robust newsvendor problem paper that considers censored demand.Specifically,we construct different ambiguity sets which include the moments information of the demand distribution conditioning on stocking out information from historical data.We derive closed-form solution for the proposed models and compare them with the counterpart without the stocking out information:1) Under mean-support ambiguity set,the support determines the closed-form solution to the distributionally robust newsvendor model.2) Under mean-variance-support ambiguity set,the closed-form solution to the distributionally robust newsvendor model is determined by mean,variance,ordering cost and selling price.3) As the ratio of ordering cost to selling price increases,the optimal ordering quantities decrease.Numerical studies illustrate that the censored demand information can improve the expected revenue for the distributionally robust newsvendor model when the ratio is in some ranges.Furthermore,the revenue improves as censored level increases.