Abstract: Exercising optimal control on the internal stochastic inventory systems is essential to elevating the coordination of supply chain.We develop a practical model of optimal control on stochastic inventory system by considering the time-limited free backorders,which is usually a common phenomenon in the practical inventory activities,and the impact on optimal inventory law of stochastic factors,e.g.,return of sold goods,spoilage of stocked items,etc.And then,we obtain the optimal control law explicitly with the aid of dynamic programming.In addition,we give the numerical examples and illustrations.The results of this paper would provide theoretical evidence for making decisions on the inventory management and would make special reference further to elevating the coordination of supply chain.

Key words: time-limited free backorders, stochastic inventory systems, optimal control, coordination of supply chain