An Analysis of the Effect of Response Speed on the Bullwhip Effect Using Control Theory

In this paper, we use linear control theory to analyze the performance of a firm generating material orders as a function of the difference between actual inventory and pipeline and their respective targets (APIOBPCS: Automatic Pipeline, Variable Inventory Order Based Production Systems). We explicitly model managerial behavior by allowing fractional –instead of full– adjustments to be performed in each period, thus introducing a proxy to the firms’ reactiveness to changes. We develop a new procedure for the determination of the exact stability region for such a system, and derive an asymptotic region of stability that gives a sufficient stability criteria independent of the lead time. We then quantify the performance of the system by analyzing the effect of different demand signals on order and inventory variations. We find that firms with low reactiveness perform well in the presence of stationary demands but perform poorly when encountering finite demand shocks. Furthermore, we find that the ratio of the reactiveness of inventories and pipeline affects both the performance, and robustness of the system. When the inventory is more reactive than the pipeline the system can achieve increased performance at the cost of being sensitive to the parameters. When the pipeline is more reactive than inventories, on the other hand, the system is robust, but at the cost of sub-optimal performance.