不确定性对混合CVaR约束库存系统的影响

Effect of Uncertainty in Inventory Systems With Mixture CVaR Constrain

运用应用概率中的随机占优研究需求不确定性对混合CVaR约束库存系统最优订购量和最优利润的影响。引入刻画决策者风险态度的"风险偏好系数",得到系统最优订购量和最优利润关于风险偏好系数的单调性。研究表明随机大需求总会导致系统较高的最优订购量和最优利润;在割准则序意义下,最优订购量可能随需求可变性的增加而增加也可能随需求可变性的增加而减少;在二阶随机占优且风险偏好系数大于等于1的情况下系统最优利润具有随机单调性,然而当风险偏好系数小于1时最优利润在二阶随机占优意义下的结论不一定成立,我们通过一个数值例子来说明。

In this paper, we analyze the effect of demand uncertainty in inventory systems with mixture CVaR constrain by using stochastic dominance in applied probability. We introduce the concept of ＂ risk preference coefficient＂ and obtain monotonicities of optimal order quantity and optimal profit with respect to risk preference coefficient. We prove that stochastic larger demand leads to higher optimal order quantity and optimal profit; under the cut criterion ordering, more variable demand may lead to more or less optimal order quantity; optimal profit has stochastic monotonicity under second stochastic dominance when risk preference coefficient is larger than or equal to one, but, this state may not hold true as risk preference coefficient is smaller than one. We illustrate this by a numerical example.