广义均值保持变换的随机单调性及其在库存系统中的应用

摘要

In this paper,we provide a generalized mean-preserving transformation which has non-linear and mean inequality conversions,to study the sufficient conditions or sufficient and necessary conditions which can achieve its stochastic comparison.We also characterize the effect of demand uncertainty in decision and profit in invento-ry system.First, we get the relationship between the distribution function and the random monotonicity before and after the conversion.We also get the connection between the generalized mean-preserving transformation and generalized TTT transformation.In addition,three special generalized mean-preserving transformations are used for validation.Finally,the transition is applied to the newsvendor model which has both minimize cost newsven-dor problem and maximize profit newsvendor problem, and the random monotonicity of the unified newspaper problem transformation is obtained.%本文提出一类非线性且均值可能不等的广义均值保持变换,研究实现其变换前后随机变量比较的充分条件或充分必要条件,并用此变换来定量刻画需求不确定性对库存系统决策和利润的影响.首先给出变换前后或不同参数下分布函数的关系及其满足一阶随机占优和割准则序的充分条件,特征刻画此变换与广义TTT变换之间的关系.进一步,用三类特殊的广义均值保持变换进行验证.最后,将此变换应用到报童模型中,得出该变换对包含最小化成本及最大化利润的一致化报童问题的随机单调性.