Mitigating the bullwhip effect by exploiting archetypes of complex production and inventory control systems

One of Forrester’s (1958) original intentions of presenting a production-distribution system model was to highlight that “feedback theory explains how decisions, delays, and predictions can produce either good control or dramatically unstable operation”. Using system simplification techniques on Laplace block diagrams, the model for a single echelon, consisting of 17 difference equations with five feedback loops is shown to actually contain no linear system state feedback in the ordering rule. Here we replicate the simplification study using the z-transform, allowing us to identify the resultant transfer function as directly mimicking Burns and Sivazlian’s (1978) model used to show the impact of the ‘false order’ wherein the order placed by an echelon is a combination of ‘real’ plus ‘safety’ orders to account for delays leading to inventory depletions. Hence Forrester’s original model, rather than showing the impact of feedback on decision making, is in fact a pre-existing case of the ‘false order’ effect. Therefore the so called ‘Forrester effect’, in which orders are amplified from sink to source, is not in this case due to linear feedback control but due to a first-order derivative term in the feedforward numerator path. In hardware control engineering terms this generates the well-known “phase advance”, or predictive, component. This paper indicates the value of the system simplification approach in system design. Without the simplification approach opportunities for drawing analogue with a system archetype with known solutions, such as the use of a ‘recovery’ filter, would have been missed. The approach is consistent with the “Power of Analogy” paradigm.