风险偏好和需求不确定性对销售努力和补货决策库存系统的影响

Impact of Risk Preference and Demand Uncertainty on Inventory System with Sales Effort and Replenishment Decision

研究风险偏好和需求不确定性对库存和销售努力决策库存系统的影响。运用应用概率中的随机比较方法,分别在一阶和二阶随机占优的意义下给出比较需求分布不同两个系统的最优利润和努力水平的充分条件或充分必要条件。证明存在一类需求分布在一定条件下系统的最优利润和努力水平都随需求可变性的增加而增大。数值例子验证了获得的研究结果。

Marketing research shows that many policies,such as advertisement addition,salesman employment,and enhanced sales level of salesman,can increase market share and profit of enterprises.However,it is difficult to implement these policies because decision makers have different risk preference and need efforts to do so.This study analyzes the effect of risk preference and demand uncertainty on inventory system with replenishment and sales effort decisions.We consider demand model with additive-multiplicative form.First,we show that optimal profit and effort level can be represented by the generalized TTT transform.The monotonicities of optimal profit and effort level with respect to risk level can be obtained.Second,we prove that the inequality between generalized TTT transformation and second degree dominance function exist.We further introduce the first,second,and third degree dominance functions,and variable function defined on probability distributions with different supports.Third,we provide the sufficient conditions to compare the optimal profit and effort level with different demand distributions under first and second stochastic dominance by using those implication relations.We show that larger demand leads to higher profit and effort level for any risk level without regard to penalty cost.The optimal profit and effort level will decrease when demand variability increases for any penalty cost and risk level under the second degree stochastic dominance.Fourth,we prove the optimal profit and effort level will increase when demand variability increases for those penalty cost and risk level exceeds a certain key values.Finally,we provide three numerical examples to illustrate the obtained results.Therefore,inventory model considering decision maker＇s preference for risk,demand uncertainty and sales effort dependent demand have important theoretical and practical implications.The findings of this study provide insights for enterprises to enhance marketing efforts,promote product sales and optimize inventory decisions under demand uncertainty.