供应提前期和需求不确定下库存系统的随机比较

Stochastic Comparison of Inventory Systems Under Supply Leadtime and Demand Uncertainty

本文研究供应提前期和需求不确定下包含最小化成本和最大化利润的一致化报童问题中随机比较实现的充分条件,并通过随机比较定量刻画提前期和需求不确定性对库存系统决策和利润的影响。首先引入报童收益函数,给出其优化前后满足随机占优及拉普拉斯变换序的充分条件。进一步,在周期需求服从指数分布的情形下,定量刻画固定提前期与提前期服从几何分布两种情况的随机单调性。最后,将上述结论应用到报童模型中,得到提前期需求对一致化报童问题的随机单调性。

This paper studies sufficient conditions of stochastic comparison conformity on newsvendor problem which includes the minimization of cost and maximizing profit problem under lead time and demand uncertainty, and quantitative analysis characterizes the impact of lead time and demand uncertainty on order decision and inventory profit through stochastic comparison. We introduce newsvendor profit function to describe its sufficient condition of stochastic dominance and Laplace order before and after optimization, and then verify by exponential period demand with fixed and geometric leadtime. Finally, the above results are applied to the newsvendor model, and the random monotonicity of leadtime demand for the uniform newsvendor problem is obtained.