Two-part tariffs, inventory stockpiling, and the bullwhip effect

• We consider a supply chain for storable goods subject to demand uncertainty. • We show how suppliers may use two-part tariffs to dampen the bullwhip effect. • Two-part tariffs allow suppliers to control buyers’ inventory stockpiling. • Inventory reduces the variance of supplier production relative to buyer sales. • Supply chains should generally accept a certain degree of bullwhip. We study how upstream producers can use two-part tariffs (2PTs) to dampen the bullwhip effect in storable-good supply chains subject to strategic inventory stockpiling by downstream buyers. 2PTs are useful for this purpose because they give upstream producers some control over buyers’ inventory stockpiling. Inventory stockpiling makes upstream production less sensitive to demand shocks, which reduces the variance of upstream production relative to the variance of downstream sales and thus dampens the bullwhip effect. Since too much inventory stockpiling reduces expected supply chain profits, there is a limit to how much stockpiling there should be, and thus to how much the bullwhip effect should optimally be dampened. We demonstrate that, when demand shocks are not too persistent, 2PTs outperform linear wholesale prices by generating greater expected supply chain profit while also eliminating the bullwhip effect. 2PTs may still help to reduce the bullwhip effect even if demand shocks are very persistent, but supply chains should generally accept a certain degree of bullwhip in this case.