Mitigating Transient Bullwhip Effects Under Imperfect Demand Forecasts

Motivated by how forecast errors exacerbate order fluctuations in supply chains, we leverage robust feedback controller synthesis to characterize, compute, and minimize the worst-case order fluctuation experienced by an individual supply chain vendor. Assuming bounded forecast errors and demand fluctuations, we model forecast error and demand fluctuations as inputs to linear inventory dynamics, and use the $\ell_\infty$ gain to define a transient Bullwhip measure. In contrast to the existing Bullwhip measure, the transient Bullwhip measure explicitly depends on the forecast error. This enables us to separately quantify the transient Bullwhip measure's sensitivity to forecast error and demand fluctuations. To compute the controller that minimizes the worst-case peak gain, we formulate an optimization problem with bilinear matrix inequalities and show that it is equivalent to minimizing a quasi-convex function on a bounded domain. We simulate our model for vendors with non-zero perishable rates and order backlogging rates, and prove that the transient Bullwhip measure can be bounded by a monotonic quasi-convex function whose dependency on the product backlog rate and perishing rate is verified in simulation.