需求不确定性对最小化成本和最大化利润报童问题的影响

运用应用概率中的随机占优和可变序研究需求不确定性对两类报童问题的影响，一类是经典的最小化成本报童问题，另一类是带有二次订货策略的最大化利润报童问题. 得到对应于两类报童问题的最优成本（最优利润）关于缺货惩罚费用（二次订货费用）的单调性，并从最优化和随机比较两个方面分析两类模型的等价性. 针对最大化利润报童问题，给出在分散序意义下比较系统最优利润的充分条件，并证明当二次订货费用小于或等于零售价格时，随机大需求导致较高的最优利润，但当二次订货费用大于零售价格时此结论不一定成立. 证明对任意二次订货费用，在二阶随机占优意义下系统最优利润随需求可变性增加而减小. 进一步，证明存在一类需求分布，当需求均值相等且二次订货费用大于某一固定值时，系统最优利润随需求可变性的增加而增加. 对最小化成本报童问题给出类似的结果. 数值例子验证了得到的研究结果.

Effect of demand uncertainty on newsvendor problems with minimization cost and maximization profit

We study the effect of demand uncertainty on two classes of newsvendor problems by using stochastic dominance and variability orderings in applied probability, one is the classical newsvendor problem with minimization cost, the other is the newsvendor problem with maximization profit with two ordering policy. We get the monotonicities of the optimal cost (optimal profit) corresponding to the two classes of newsvendor problems with respect to the shortage penalty cost (two ordering cost), and equivalence of the two classes of newsvendor problems from the optimization and stochastic comparison's point of view. For the the newsvendor problem with maximization profit, we provide the sufficient conditions to compare newsvendor's optimal profit under the dispersive ordering, and show that stochastic larger demand leads to larger newsvendor's optimal profit when two ordering cost is smaller than or equal to sales price, however, this result may not be true when two ordering cost is larger than sales price. We show that the optimal profit will decrease when demand variability increasing under the second degree stochastic dominance for any two ordering cost, and there exists a certain demand distribution, the optimal profit will increase when demand variability increases for those two ordering cost that is larger than a fixed value. We obtain similar results for the newsvendor problem with minimization cost. Several numerical examples are provided to show those obtained results.