Small sample uncertainty aspects in relation to bullwhip effect measurement

The bullwhip effect as a concept has been known for almost half a century starting with the Forrester effect. The bullwhip effect is “allegedly” observed in many supply chains, and it is generally accepted as a potential malice. Despite this the bullwhip effect still seems to be first and foremost a conceptual phenomenon. Some even simply denies that the phenomenon exists at all in practice. This of course makes it important to perform measurements because only “what gets measured gets done” as the saying goes in analytics. Few measurements are reported in the literature, however, typically based on standard statistical assumptions. In the case of a standard measurement of the bullwhip effect independence amongst the participating variables are required amongst others, but this is definitely known not to be perfectly true if any systematic control at all have taken place in the supply chain. This paper analyses the bullwhip measurement implications in case the standard test assumptions are violated and illustrates how to improve on the testing setup. This is further done with a special emphasis on the unavoidable small-sample aspects relating to such measurement in practice, which typically renders all statistical asymptotic or robust arguments quite unusable. It is shown how H0-95%-confidence test intervals still easily can be obtained numerically in such cases.