Decentralized and centralized model predictive control to reduce the bullwhip effect in supply chain management

• We model a benchmark supply chain in control engineering perspective.
• We develop a decentralized MPC scheme to make the ordering decisions.
• We derive an ordering policy based on centralized MPC scheme.
• Two control schemes can be chosen depending on different structure of supply chains.

Mitigating the bullwhip effect is one of crucial problems in supply chain management. In this research, centralized and decentralized model predictive control strategies are applied to control inventory positions and to reduce the bullwhip effect in a benchmark four-echelon supply chain. The supply chain under consideration is described by discrete dynamic models characterized by balance equations on product and information flows with an ordering policy serving as the control schemes. In the decentralized control strategy, a MPC-EPSAC (Extended Prediction Self-Adaptive Control) approach is used to predict the changes in the inventory position levels. A closed-form solution of an optimal ordering decision for each echelon is obtained by locally minimizing a cost function, which consists of the errors between predicted inventory position levels and their setpoints, and a weighting function that penalizes orders. The single model predictive controller used in centralized control strategy optimizes globally and finds an optimal ordering policy for each echelon. The controller relies on a linear discrete-time state-space model to predict system outputs. But the predictions are approached by either of two multi-step predictors depending on whether the states of the controller model are directly observed or not. The objective function takes a quadratic form and thus the resulting optimization problem can be solved via standard quadratic programming method. The comparisons on performances of the two MPC strategies are illustrated with a numerical example.