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Bullwhip effect is a problem of paramount importance that reduces competitiveness of supply chains around the world. A significant effort is being devoted by both practitioners and academics to understand its causes and to reduce its pernicious consequences. Nevertheless, limited research has been carried out to analyze potential metrics to measure it, that typically are summarized in the coefficient of variation ratio of different echelons demand.
This work proposes a new metric based on a time-varying extension of the aforementioned bullwhip effect metric by employing recursive estimation algorithms expressed in the State Space framework to provide at each single time period a real-time bullwhip effect estimate. In order to illustrate the results, a case study based on a serially-linked supply chain of two echelons from the chemical industry is analyzed. Particularly, this metric is employed to analyze the effect of promotional campaigns on the bullwhip effect on a real-time fashion. The results show that, effectively, the bullwhip effect is not constant along time, but interestingly, it is reduced during the promotional periods and it is bigger before and after the promotion takes place.

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