CAJ | 학술논문

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．
운용응용개솔중적수궤점우화가변서연구수구불학정성대량류보동문제적영향，일류시경전적최소화성본보동문제，령일류시대유이차정화책략적최대화리윤보동문제．득도대응우량류보동문제적최우성본（최우리윤）관우결화징벌비용（이차정화비용）적단조성，병종최우화화수궤비교량개방면분석량류모형적등개성．침대최대화리윤보동문제，급출재분산서의의하비교계통최우리윤적충분조건，병증명당이차정화비용소우혹등우령수개격시，수궤대수구도치교고적최우리윤，단당이차정화비용대우령수개격시차결론불일정성립．증명대임의이차정화비용，재이계수궤점우의의하계통최우리윤수수구가변성증가이감소．진일보，증명존재일류수구분포，당수구균치상등차이차정화비용대우모일고정치시，계통최우리윤수수구가변성적증가이증가．대최소화성본보동문제급출유사적결과．수치례자험증료득도적연구결과．
We study the effect of demand uncertainty on two classes of newsvendor problems by us-ing stochastic dominance and variability orderings in applied probability, one is the classical newsvendorproblem with minimization cost, the other is the newsvendor problem with maximization profit with twoordering policy. We get the monotonicities of the optimal cost （optimal profit） corresponding to the twoclasses of newsvendor problems with respect to the shortage penalty cost （two ordering cost）, and equiva-lence of the two classes of newsvendor problems from the optimization and stochastic comparison＇s pointof view. For the the newsvendor problem with maximization profit, we provide the sufficient conditionsto compare newsvendor＇s optimal profit under the dispersive ordering, and show that stochastic largerdemand leads to larger newsvendor＇s optimal profit when two ordering cost is smaller than or equal tosales price, however, this result may not be true when two ordering cost is larger than sales price. We showthat the optimal profit will decrease when demand variability increasing under the second degree stochasticdominance for any two ordering cost, and there exists a certain demand distribution, the optimal profitwill increase when demand variability increases for those two ordering cost that is larger fixed value.We obtain similar results for the newsvendor problem with minimization cost. Several numerical examplesare provided to show those obtained results.