Order and inventory variance amplification: The equivalence of discrete and continuous time analyses

International Journal of Production Economics, 110, 128-137.

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Abstract

The well-known Bullwhip Effect concerns the increasing variance of orders as they proceed through the supply chain. In the continuous time representation we solve the delay-differential equation for the inventory balance, which is coupled to the ordering policy. The time domain evolution of the system emerges. We calculate the Bullwhip Effect and compare it to known results for the discrete time representation. The discrete and continuous Bullwhip Effect expressions have similar structures. We show that the two domains are managerially equivalent so that in practice either domain can be used to study a supply chain.