需求可变性降低对均值CVaR约束销售努力决策库存系统的影响

本文运用Levy提出的变换研究需求可变性降低对风险偏好零售商的库存决策、销售努力决策和期望效用的影响,用均值CVaR刻画零售商的风险偏好特性,它包括风险厌恶、风险追求,也具有损失规避的特性。首先,运用该变换定量刻画需求可变性的降低,证明该变换蕴含经典随机占优中的割准则序和二阶随机占优等。其次,给出系统的最优订货量、最优期望效用和最优销售努力水平,得到它们关于风险偏好系数的单调性,并给出降低需求可变性对期望效用的影响。第三,针对风险中性、风险厌恶(最大化CVaR)和风险追求(最小化CVaR)这三种特殊情况得到相应的结果,并给出企业在库存决策和促销决策的管理启示。最后,通过数值例子验证了得到的研究结果并给出相应的管理启示。

Impact of Reducing De mand Variability on Sales Effort Decision of Inventory Syste m u nder Mean-CVaR Constraint

In this paper, we use the transformation proposed by Levyto study the impact of reducing demand variability on inventory decision, sales effort decision and expected utility of risk appetite retailer. We also use the mean-CVaR criterion to characterize the retailer’s risk preference, including risk aversion and risk pursuit, and it has the property of loss-aversion as well. Firstly, we use LMPT to quantitatively describe the reduction of demand variability, and prove that LMPT contains the cut criterion ordering and the second order stochastic domination in the classical stochastic dominance. Secondly, we give the optimal order quantity, the optimal expected utility and the optimal sales effort of the system, and then we get the monotonicity about the risk preference coefficient, and give the influence of reducing the demand variability on the expected utility. Thirdly, corresponding results are obtained for the three special cases : risk neutrality, risk aversion(maximum CVaR) and risk pursuit(minimum CVaR) and we give the management insights of enterprise in inventory decision and sales promotion decision. Finally, the numerical examples are used to verify the research results and give corresponding management insights.