Dynamic Modeling and Analysis for Supply Chain

Abstract

The objective of this study is to use system dynamics methodology to model the supply chain system and then present the optimal control to optimize the performance of supply chain by minimize the quadratic cost function while tracking and keeping the inventory close to target level. Under the system dynamics point of view, the supply chain was modeled as the continuous differential equation with lead time delay modeled as the first order delay model. In contrast to the frequency domain analysis of the classical control approach, the proposed control utilizes the time-domain state space representation with a set of input, output and state variables to build the dynamic system. On the other hand, by using the system dynamics it allows us to apply different control laws and analyze the dynamic behavior of system so that the decision policies can be found to improve the performance of supply chain. In this paper we employ the linear quadratic optimal control for such kind of supply chain dynamic system, the aim of controller is to find the control input as the order quantity to minimize the cost function and keep high customer satisfaction by tracking the target inventory level. Finally, the numerical simulation results are carried out in Matlab/Simulink environment and the performance of optimal controller will be compared with some classical control policies such as proportional and order-up-to level control policy. It is shown that our approach can obtain some good performances.