Approximate optimal inventory control of supply chain networks with lead time

This paper deals with the approximate optimal inventory control problem of the supply chain networks with lead time. By introducing a sensitivity parameter, the original optimal problem is transformed into a sequence of two-point boundary value (TPBV) problems without time-delay term. Then the uniqueness and the existence of the optimal control law is presented. Then by using a finite sum of the series, a suboptimal inventory replenishment strategy of supply chain networks system is proposed. Simulation examples show that the inventory replenishment strategy proposed in this paper is effective to reduce bullwhip and thereby improve the performance of supply chain networks system.