When the bullwhip effect is an increasing function of the lead time

International Federation of Automatic Control: Manufacturing, Modelling, Management and Control - 9th MIM, Berlin, Germany, 28th-30th August. Published in IFAC Papers Online, 52(13), 2297-2302.

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Abstract

We study the relationship between lead times and the bullwhip effect produced by the order-up-to policy The usual conclusion in the literature is that longer lead-time increase the bullwhip effect, we show that this is not always the case. Indeed, it seems to be rather rare. We achieve this by first showing that a positive demand impulse response leads to a bullwhip effect that is always increasing in the lead time when the order-up-to policy is used to make supply chain inventory replenishment decisions. By using the zeros and poles of the z-transform of the demand process, we reveal when this demand impulse is positive. To make concrete our approach in a nontrivial example we study the ARMA(2,2) demand process.