Kernekoncepter
The core message of this paper is to characterize and compute the worst-case order fluctuation experienced by a supply chain vendor under bounded forecast errors and demand fluctuations, and to develop a forecast-driven affine control strategy that minimizes this transient Bullwhip measure.
Resumé
The paper focuses on mitigating the transient Bullwhip effect in supply chains, which refers to the amplification of demand fluctuations to upstream suppliers. The authors use tools from robust control theory to model forecast error and demand fluctuations as inputs to the inventory dynamics of a single-product supply chain vendor.
Key highlights:
- The authors define a transient Bullwhip measure that explicitly accounts for forecast errors, in contrast to the existing Bullwhip measure in the literature.
- They show that the transient Bullwhip measure is equivalent to the disturbance-to-control peak gain, and formulate an optimization problem with bilinear matrix inequalities to compute the controller that minimizes the worst-case peak gain.
- The authors demonstrate that the bilinear matrix inequality can be reduced to a quasi-convex function, enabling efficient computation of the optimal controller.
- Empirical results show that the backlog and perishing rates of the commodity do not significantly impact the region of the optimization parameter where the minimum peak gain occurs, but do affect the sensitivity of the peak gain to this parameter.
- The authors also evaluate the performance of the peak-gain minimizing controller under different forecast error scenarios, observing that the empirical order fluctuations are well within the predicted transient Bullwhip bound, while the inventory fluctuations are more sensitive to the forecast error.