Regulating Bullwhip Effect in Supply Chains through Modern Control Theory

Abstract

Modeling and control of supply chain management (SCM) systems are still problematic today even though we have relatively powerful methods and IT tools available at our disposal. The complexity and the multi-disciplinary nature of the problem attracted the attention of many researchers from various different disciplines. It is possible to classify the available approaches to supply chain management as ad-hocacy, what-if-simulation, control theory, filter theory, and operations research theory. The studies that are based on control theoretic approach are limited to what is known as classical control theory; the modeling and control study presented in this work is based on the so called modern control theory. As far as the authors know, this is the first study of its kind. Through the use of modern control theory, the limitations that are imposed by its classical counterpart can be overcome, providing the opportunity to extend the modeling and control work to non-linear, time-varying, stochastic, adaptive, and large-scale systems, effectively. In the present study, a supply chain system is modeled through state-space techniques; the model is linear, discrete-time, and stochastic. The model is then analyzed to study the stability, controllability, and observability properties of the system, which are vitally important in control system design. Finally, a linear quadratic Gaussian (LQG) controller is designed with the aim of regulating the bullwhip effect in the system. The initial analyses suggest that the controller structure developed is well equipped to regulate the bullwhip effect in a supply chain system effectively.