Stochastic comparison on an inventory system with yield uncertainty

In this paper we discuss the optimal problem on a discrete-time, single item, periodic review inventory system with yield and demand uncertainty, the main objective is to analyze how the uncertainty of yield rate and demand affect the optimal policy and cost in the system. For the single period case, by using the properties of stochastic ordering, the stochastic comparison results on the optimal inventory level and optimal expected cost are obtained. For the system with multi-period and with independent yield rates and demands in each period, by using the dynamic programming method, we show that the optimal inventory level is stochastic monotone in time period under a certain condition. The stochastic comparison results on the optimal cost for the inventory system with dependent yield rates and demands are also provided.