Quantifying and mitigating the bullwhip effect in a benchmark supply chain system by an extended prediction self-adaptive control ordering policy

• We model a benchmark supply chain system from control engineering perspective.
• We derive analytic expression of bullwhip effect based on control theoretic concept.
• We formulate customized MPC to obtain closed-form ordering policy transfer function.
• We use new bullwhip metric on conventional and MPC ordering policies for comparison.

An undesired observation known as the bullwhip effect in supply chain management leads to excessive oscillations of the inventory and order levels. This paper presents how to quantify and mitigate the bullwhip effect by introducing model predictive control (MPC) strategy into the ordering policy for a benchmark supply chain system. Instead of quantifying the bullwhip effect with commonly used statistical measure, we derive equivalently the expression of bullwhip metric via control-theoretic approach by applying discrete Fourier transform and (inverse) z-transform when the demand signal is stationary stochastic. A four-echelon supply chain is formulated and its dynamical features are analyzed to give the discrete model. An extended prediction self-adaptive control (EPSAC) approach to the multi-step predictor is implemented in the development of MPC formulation. The closed-form solution to MPC problem is derived by minimizing a specified objective function. The transfer function for MPC ordering policy is then obtained graphically from an equivalent representation of this closed-form solution. A numerical simulation shows that MPC ordering policy outperforms the traditional ordering policies on reducing bullwhip effect.