Delayed state feedback \(H_\infty\) control for periodic-review inventory systems

Abstract

We investigate delayed state feedback control of a periodic-review inventory management system with perishable goods. The stock under consideration is replenished from multiple supply sources. By using delayed states as well as current states of the inventory system, a delayed feedback \(H_\infty\) control strategy is developed to mitigate bullwhip effects of the system. Some conditions on the existence of the delayed feedback \(H_\infty\) controller are derived. It is found through simulation results that the proposed delayed \(H_\infty\) control scheme is capable of improving the performance of the inventory management significantly. In addition, the delayed controller is better than the traditional delay-free \(H_\infty\) controller. doi:10.1017/S1446181117000153