需求依赖销售努力库存系统的随机比较

研究需求依赖销售努力库存系统中需求不确定性对系统最优订货量、利润和销售努力的影响.对一般需求模型给出期望利润关于订货量和努力水平为联合凹的充分条件,证明期望利润函数的超模性质.对加乘需求模型证明系统最优利润和最优努力水平都可由一类与需求分布有关的广义TTT变换来表示.通过引入定义在不同支撑分布集合上一阶、二阶和三阶随机占优,得到广义TTT变换之差与二阶和三阶随机占优之间的关系式,建立了比较库存系统最优利润或努力水平的理论基础.在一阶和二阶随机占优意义下对加乘需求模型得到比较系统最优利润和努力水平的充分条件或充分必要条件.进一步,证明存在一类需求分布当系统关键比(或市场价格)足够大时系统最优利润和努力水平随需求可变性的增加而增加.最后给出几个数值例子验证了研究结果.

Stochastic Comparison in Inventory System with Effort Dependent Demand

In this article,we analyze the effect of demand uncertainty on the optimal order quantity,profit and sales effort in inventory system with effort dependent demand.For the general demand model,we give sufficient conditions under which the expected profit is jointly concave with respect to order quantity and effort level,and show supermodularity of the expected profit.For the additive-multiplicative demand model,we prove that the optimal profit and effort level may be expressed by a class of generalized TTT transform with respect to demand distribution.By introducing the first,second and third degree stochastic dominance defined on distributions with different supports,the relationship between the difference of generalized TTT transforms and the second and third degree stochastic dominance are obtained,this establishes the theory foundation to compare the optimal profit or effort level in inventory system.We get the sufficient conditions or necessary and sufficient to compare the optimal profit and effort level for the additive-multiplicative demand model under the first and second degree stochastic dominances.Furthermore,we show there exists a class of demand distributions such that the optimal profit and effort level will increase for larger critical ratio(or market price) when demand variability increases.Numerical examples illustrate the obtained results.