Technical Note—On the Optimality of Reflection Control

Abstract

The so-called reflection control is easy to implement and widely applied in many applications such as inventory management and financial systems. To apply reflection control in a production-inventory system, for example, production will stop when the finished-goods inventory reaches a certain level. What is the best level for this control? In what sense is it optimal? In their paper, “On the Optimality of Reflection Control,” Jiankui Yang, Heng-Qing Ye, and David D. Yao have established the optimality of reflection control under an exponential holding cost in three settings—namely, a Brownian motion model, a single-server system, and a birth–death queue model. The study provides a thorough understanding of the control and extends significantly its domain of applications.